## IAM Catalogue

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## IAM CATALOGUE

#### BA5814 - Investment Management

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

The purpose of this course is to introduce the student to the area of investment with emphasis upon why individuals and institutions invest and how they invest. Topics include measures of risk and return; capital and money markets; process and techniques of investment valuation; principles of fundamental analysis; technical analysis; analysis and management of bonds; analysis of alternative investments; portfolio theory and application.

Course Objectives

Course Learning Outcomes

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#### IAM500 - M.S. Thesis

Credit: 0(0-0); ECTS: 50.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

The Program of research leading to M.S. degree arranged between the student and a faculty member. Students register to this course in all semesters while the research program or write up of thesis is in progress. Student must start registering to this course no later than the second semester of his/her M.S. study.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

The Program of research leading to M.S. degree arranged between the student and a faculty member. Students register to this course in all semesters while the research program or write up of thesis is in progress. Student must start registering to this course no later than the second semester of his/her M.S. study.

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#### IAM501 - Introduction to Cryptography

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Historical Introduction to Cryptography: General Principles, Monographic-Polygraphic Systems, Monoalphabetic-Polyalphabetic Systems, Substitution Ciphers, Transposition Ciphers, Frequency Analysis, Kasiski Analysis. Shannon's Theory: Perfect Secrecy, Entropy. Cryptographic Evaluation Criteria and Cryptanalysis. Public and Private Key Cryptography. Block Ciphers: Diffusion, Confusion, Feistel Structure. Stream Ciphers: Shift Registers, Synchronous and Self-synchronous Ciphers, Linear Complexity. Public Key Cryptography: Fundamental Concepts, NP-Hard Problems, Discrete Logarithm, Factorization, Subset Sum, RSA, Diffie Hellman Key Exchange Protocol, DSA, Cryptographic Protocols.

Course Objectives

The aim of this course is to give the fundamental concepts of cryptography and introduce to students the classical private-key and public key cryptographic systems. The course also serves as an introduction for students who are interested in persuing research in cryptography.

Course Learning Outcomes

This is one of the core courses of the Cryptography Program at IAM, which gives the fundamentals of cryptography and the classical private-key and public-key cryptographic systems. After taking the course, the students should have an overview of some of the classical cryptosystems, which are in use.

Tentative (Weekly) Outline

Historical Introduction to Cryptography: General Principles, Monographic-Polygraphic Systems, Monoalphabetic-Polyalphabetic Systems, Substitution Ciphers, Transposition Ciphers, Frequency Analysis, Kasiski Analysis. Shannon's Theory: Perfect Secrecy, Entropy. Cryptographic Evaluation Criteria and Cryptanalysis. Public and Private Key Cryptography. Block Ciphers: Diffusion, Confusion, Feistel Structure. Stream Ciphers: Shift Registers, Synchronous and Self-synchronous Ciphers, Linear Complexity. Public Key Cryptography: Fundamental Concepts, NP-Hard Problems, Discrete Logarithm, Factorization, Subset Sum, RSA, Diffie Hellman Key Exchange Protocol, DSA, Cryptographic Protocols.

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#### IAM502 - Stream Ciphers

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Linear Feedback Shift Registers: Generating Functions, Minimal Polynomial and Families of Recurring Sequences, Characterizations and Properties of Linear Recurring Sequences. Design and Analysis of Stream Ciphers: Stream Ciphers Using LFSRs, Additive Generators, Gifford, Algorithm M, PKZIP. Other Stream Ciphers and Real Random Sequence Generators: RC4, SEAL, WAKE, Feedback with Carry Shift Registers, Stream Ciphers using FCSRs, Non-Linear-Feedback Shift Registers. Cascading Multiple Stream Ciphers, Generating Multiple Streams from a Single Pseudo-Random-Sequence Generator.

Course Objectives

Course Learning Outcomes

This is one of the core courses of the Cryptography Program at IAM introducing Stream Ciphers. A stream cipher is a type of private key encryption algorithm. Stream ciphers can be designed to be very fast compared to block ciphers. Block ciphers operate on large blocks of data, whereas a stream cipher typically operates on single bits. With a stream cipher, the transformation of plaintext units varies, depending on when they are encountered during the encryption process. A stream cipher generates a sequence of bits used as a key and encryption is accomplished by combining these bits with the plaintext. This course will attempt to cover the various kinds of building blocks of stream ciphers, and a variety of mathematical tools that can be used to design such ciphers. After taking the course, the students should have an overview of stream ciphers. In industry, they should be able to carefully choose and design a security scheme for a given application.

Tentative (Weekly) Outline

Linear Feedback Shift Registers: Generating Functions, Minimal Polynomial and Families of Recurring Sequences, Characterizations and Properties of Linear Recurring Sequences. Design and Analysis of Stream Ciphers: Stream Ciphers Using LFSRs, Additive Generators, Gifford, Algorithm M, PKZIP. Other Stream Ciphers and Real Random Sequence Generators: RC4, SEAL, WAKE, Feedback with Carry Shift Registers, Stream Ciphers using FCSRs, Non-Linear-Feedback Shift Registers. Cascading Multiple Stream Ciphers, Generating Multiple Streams from a Single Pseudo-Random-Sequence Generator.

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#### IAM503 - Applications of Finite Fields

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Structure of Finite Fields, Polynomials over Finite Fields, Factorization of Polynomials, Construction of Irreducible Polynomials, Normal and Optimal Normal Basis.

Course Objectives

The primary focus of this course is to give structure theory of Finite Fields and the related mathematical tools that are needed in Cryptography Graduate Program of IAM.

Course Learning Outcomes

This is one of the core courses of the Cryptography Graduate Program which gives the mathematical background on Finite Fields and Their Applications to Cryptography. The contents discussed in this course will be needed throughout various courses including Stream ciphers and various Public Key cryptosystems. So one can understand through these courses whether the outcome of this course is achieved or not.

Tentative (Weekly) Outline

- Algebraic Foundations 1) Groups 2) Rings and Fields 3) Polynomials 4) Field Extensions - Structure of Finite Fields 1) Characterization of finite fields 2) Roots of irreducible polynomials 3) Traces, norms and bases 4) Roots of unity and cyclotomic polynomials 5) Representation of elements of finite fields 6) Wedderburn’s theorem (without proof) - Polynomials over finite fields 1) Order of polynomials and primitive polynomials 2) Irreducible polynomials 3) Construction of irreducible polynomials

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#### IAM504 - Public Key Cryptography

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Idea of Public Key Cryptography, Computational Complexity and Number-theoretical algorithms. The Merkle-Hellman Knapsack System, Attacks on Knapsack Cryptosystems, Attacks to RSA; Primality and Factoring, Algorithms.

Course Objectives

The aim of this course is to introduce the fundamental ideas of public key cryptography and discuss some of the the algorithms used. The emphasis will be in understanding Knapsack, RSA, and discuss the attacks to these systems.

Course Learning Outcomes

Idea of public key cryptography. Computational complexity and Number-theoretical algorithms. Knapsack, RSA, Primality and Factoring Algorithms.

Tentative (Weekly) Outline

Idea of Public Key Cryptography, Computational Complexity and Number-theoretical algorithms. The Merkle-Hellman Knapsack System, Attacks on Knapsack Cryptosystems, Attacks to RSA; Primality and Factoring, Algorithms.

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#### IAM505 - Elliptic Curves in Cryptography

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Elliptic curves over finite fields, group structure, Weil conjectures, Super singular curves, efficient implementation of elliptic curves, determining the group order, Schoof algorithm, the elliptic curve discrete logarithm problem, the Weil pairing, MOV attack.

Course Objectives

The aim of this course is to introduce the Elliptic Curves in Cryptography. After introducing the basic facts about the elliptic curves, we shall discuss the implementation of Elliptic Curves and Algorithms to compute group order. The emphasis will be given the elliptic curve cryptosystems and the related algorithms. The other applications of Elliptic Curves in Cryptography such as primality and factorization tests will also be discussed.

Course Learning Outcomes

At the end of the course the student is expected to learn: the basic facts about the elliptic curves, the implementation of Elliptic Curves and Algorithms to compute group order and MOV algorithm. the elliptic curve cryptosystems and the related algorithms.

Tentative (Weekly) Outline

Elliptic curves over finite fields, group structure, Weil conjectures, Super singular curves, efficient implementation of elliptic curves, determining the group order, Schoof algorithm, the elliptic curve discrete logarithm problem, the Weil pairing, MOV attack.

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#### IAM506 - Combinatorics

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Algebraic Enumeration Methods: Bijections, generating functions, free monoids. Lagrange inversion, multisets and partitions. Inclusion-Exclusion, Mobius inversion, symmetric functions. Asymptotic Enumeration: Estimation of sums, formal power series, elementary estimates for convergent generating functions, analytical generating functions, singularities, Darboux’s theorem, algorithmic and automated asymptotics. External set systems: Intersecting families, families with prescribed intersection sizes, s-wise t-intersection families, covering number. Computational complexity.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Algebraic Enumeration Methods: Bijections, generating functions, free monoids. Lagrange inversion, multisets and partitions. Inclusion-Exclusion, Mobius inversion, symmetric functions. Asymptotic Enumeration: Estimation of sums, formal power series, elementary estimates for convergent generating functions, analytical generating functions, singularities, Darboux’s theorem, algorithmic and automated asymptotics. External set systems: Intersecting families, families with prescribed intersection sizes, s-wise t-intersection families, covering number. Computational complexity.

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#### IAM507 - Algorithmic Graph Theory

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Basic concepts: Walks, connection, external graphs, search trees, hyper graphs, Hamilton paths. Fundamental Parameters: Connectivity, edge connectivity, stability number, matching number, chromatic number, toughness. Bipartite graphs, line graphs, Thowrason’s lemma, Pora’s lemma, Woodall’s hopping lemma. Lengths of circuits. Packing's and coverings. External graphs. Ramsey theory.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Basic concepts: Walks, connection, external graphs, search trees, hyper graphs, Hamilton paths. Fundamental Parameters: Connectivity, edge connectivity, stability number, matching number, chromatic number, toughness. Bipartite graphs, line graphs, Thowrason’s lemma, Pora’s lemma, Woodall’s hopping lemma. Lengths of circuits. Packing's and coverings. External graphs. Ramsey theory.

#### IAM508 - Computer Algebra

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Number systems and elementary arithmetic with (arbitrary large) integers, Polynomial arithmetic, Fast Fourier transforms, Resultants and Sub-resultants, Factorization of polynomials, Arithmetic with power series, Gröbner bases. Applications of Gröbner basis algorithms. Coursework and computer lab with MATLAB.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Number systems and elementary arithmetic with (arbitrary large) integers, Polynomial arithmetic, Fast Fourier transforms, Resultants and Sub-resultants, Factorization of polynomials, Arithmetic with power series, Gröbner bases. Applications of Gröbner basis algorithms. Coursework and computer lab with MATLAB.

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#### IAM509 - Algebraic Aspects of Cryptography

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Cryptography based on Groups, Discrete Logarithm Problem (DLP) in finite fields, The ElGamal Cryptosystem, Diffie-Hellman and Digital Signature Algorithm. Algorithms to attack DLP in finite fields: The Silver-Pohling-Hellman, The Index-Calculus, Basic facts on Elliptic Curves, Group structure, Elliptic Curve cryptosystems Elliptic curve primality test, Elliptic curve factorizaton. Lucas, GH and XTR cryptosystems.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Cryptography based on Groups, Discrete Logarithm Problem (DLP) in finite fields, The ElGamal Cryptosystem, Diffie-Hellman and Digital Signature Algorithm. Algorithms to attack DLP in finite fields: The Silver-Pohling-Hellman, The Index-Calculus, Basic facts on Elliptic Curves, Group structure, Elliptic Curve cryptosystems Elliptic curve primality test, Elliptic curve factorizaton. Lucas, GH and XTR cryptosystems.

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#### IAM510 - Quantum Cryptography

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Basic notions of quantum mechanics: Hilbert spaces, postulates of quantum mechanics, qubits, density operator, entanglement, EPR and Bell inequality. Quantum gates, quantum circuits. Quantum Fourier transform. Quantum algorithms: Deutsch's, Deutsch-Jozsa, Grover`s and Shor's algorithms. Quantum cryptography: quantum key distribution, BB84, B92, and EPR protocols.

Course Objectives

The aim of this course is to introduce the basics of quantum information theory with an emphasis on quantum cryptography and quantum algorithms.

Course Learning Outcomes

- Familiarity of students with basic concepts of quantum mechanics
- Knowledge of quantum information theory for further studies

Tentative (Weekly) Outline

- Review of Quantum Mechanics (Weeks 1 - 6)
- Quantum Gates, Quantum Circuits (Weeks 7 - 8)
- Quantum Algorithms (Weeks 9 -10)
- Quantum Cryptography (Weeks 11 -14)

Course Textbook(s)

- Nielsen and Chuang, Quantum Computation and Quantum Information, Cambridge 2000
- Benenti, Casati and Strini, Principles of Quantum Computation and Information, Vol 1. World Scientific 2004

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#### IAM511 - Algorithms and Complexity

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Formal techniques for design and analysis of algorithms, methods for specifying algorithms,proving an algorithm´s correctness, basics of algorithmic efficiency, asymptotic notations and basic efficiency classes, computational complexity, complexity classes P, NP,NP-completeness/hardness, mathematical analysis of algorithms, divide-and-conquer, space and time trade-offs, and number-theoretical algorithms.

Course Objectives

The aim of the course is to present the basic topics in algorithms and complexity needed in cryptography. The fundamental algorithms in cryptography will be introduced and their complexities will be studied .

Course Learning Outcomes

Students are going to be familiar with the design and analysis of algorithms used in cryptography. They will be able to compute the complexities of the algorithms and to design new algorithms with the improved complexities.

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#### IAM512 - Block Ciphers

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Block Cipher Systems: Building Blocks and Design Criteria. Modes of Operation: ECB, CBC, CFB, OFB, PCBC. Boolean Functions, Correlations and Walsh Transforms. Cryptographic Criteria: Propagation Characteristics, Nonlinearity, Resiliency and Generalization to S-Boxes. Differential and Linear Cryptanalysis, Algebraic Attacks. Descriptions of DES, SAFER, IDEA and AES Semi-Finalist Algorithms: Rijndael, Mars, Serpent, Twofish and RC6. Statistical Evaluation and Performance Comparison of AES Semi-Finalist Algorithms.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Block Cipher Systems: Building Blocks and Design Criteria. Modes of Operation: ECB, CBC, CFB, OFB, PCBC. Boolean Functions, Correlations and Walsh Transforms. Cryptographic Criteria: Propagation Characteristics, Nonlinearity, Resiliency and Generalization to S-Boxes. Differential and Linear Cryptanalysis, Algebraic Attacks. Descriptions of DES, SAFER, IDEA and AES Semi-Finalist Algorithms: Rijndael, Mars, Serpent, Twofish and RC6. Statistical Evaluation and Performance Comparison of AES Semi-Finalist Algorithms.

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#### IAM517 - Basic Mathematics for Cryptography I

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Basic properties of Integers, Divisibility, Primes, The fundamental theorem of arithmetic, Fermat numbers, Factorization methods, Diophantine equations, Congruences, Theorems of Fermat, Euler, Chinese Remainder and Wilson. Arithmetical functions, Primitive roots, Quadratic congruences.

Course Objectives

The main objective of this course is to prepare students for later studies in Cryptography Graduate Program of IAM, and also to explain some problems that are easy to ask but still unsolved and to give some ideas about why abstractions are to be made, by giving fundamental properties of integers and some algebraic preliminaries.

Course Learning Outcomes

This is one of the core courses of the Cryptography Program at IAM, which gives Familiarity of students basic arithmetical tools to solve cryptographical problems.

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#### IAM518 - Basic Mathematics for Cryptography II

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Algebraic Preliminaries: Group, Ring, Ideals, Prime and Maximal ideals, Homomorphisms, Isomorphism theorems, Field, Polynomials, Field extensions, Finite fields, Factorization of polynomials, Splitting field. Quadratic residues and quadratic reciprocity.

Course Objectives

The main objective of this course is to prepare students for later studies in Cryptography Graduate Program of IAM, and also to explain some problems that are easy to ask but still unsolved and to give some ideas about why abstractions are to be made, by giving fundamental properties of integers and some algebraic preliminaries.

Course Learning Outcomes

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#### IAM519 - Basic Mathematics for Cryptography

Credit: 4(4-0); ECTS: 10.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Groups, Rings, Polynomials, Prime and maximal ideals, Divisibility, Concurrences, Euler, Chinese Remainder and Wilson’s Theorems, PIDs, UFDs, Fields, Arithmetical functions, Quadratic residues and quadratic reciprocity.

Course Objectives

The main objective of this course is to prepare students for later studies in Cryptography Graduate Program of IAM, and also to explain some problems that are easy to ask but still unsolved and to give some ideas about why abstractions are to be made, by giving fundamental properties of integers and some algebraic preliminaries.

Course Learning Outcomes

Tentative (Weekly) Outline

Groups, Rings, Polynomials, Prime and maximal ideals, Divisibility, Concurrences, Euler, Chinese Remainder and Wilson’s Theorems, PIDs, UFDs, Fields, Arithmetical functions, Quadratic residues and quadratic reciprocity.

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#### IAM520 - Financial Derivatives

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Introduction to Derivative and Financial Markets. The Structure of Options Markets. Principles of Option Pricing. Option Pricing Models. Basic Option Strategies. Advanced Option Strategies. The Structure of Forward and Futures Markets. Principles of Spot Pricing. Principles of Forward and Futures Pricing. Futures Hedging Strategies. Advanced Futures Strategies. Options on Futures. Foreign Currency Derivatives. Swaps and Other Interest Rate Agreements.

Course Objectives

This course is designed to provide a solid foundation in the principles of financial derivatives and risk management. It attempts to strike a balance between institutional details, theoretical foundations, and practical applications. The course equally emphasizes pricing and investment strategies in order to motivate students to start thinking about risk management in financial markets. Parallel to the already increasing attempts to integrate derivative securities and markets into the Turkish financial system, it is believed that this course will fill a gap and students will be exposed to a rather comprehensive coverage of theory and application in the derivatives area. This course is expected to give the students a “competitive advantage” when they enter the job market since “derivatives” is a “hot topic” nowadays and BA4825/5825/IAM520 is one of the very few courses offered on this topic in Turkey!

Course Learning Outcomes

Tentative (Weekly) Outline

This course is designed to provide a solid foundation in the principles of derivatives. It attempts to strike a balance between institutional details, theoretical foundations, and practical applications. Parallel to the already increasing attempts to integrate derivative securities and markets into the Turkish financial system, it is believed that this course will fill a gap in that students will be exposed to a rather comprehensive coverage of theory and application in the derivatives area.

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#### IAM521 - Financial Management

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Examination of special issues in finance incorporating advanced theory and practice with emphasis on investment and financing decisions of the firm. Special references to applications in Turkey. Outline of Topics: An Overview of Financial Management. Financial Statements, Cash Flow, and Taxes. Analysis of Financial Statements. The Financial Environment: Markets, Institutions, and Interest Rates. Risk and Return. Time Value of Money. Bonds and Their Valuation. Stocks and Their Valuation. The Cost of Capital. The Basics of Capital Budgeting. Cash Flow Estimation and Other Topics in Capital Budgeting. Capital Structure Decisions. Distribution to Shareholders: Dividends and Repurchases. Issuing Securities, Refunding, and Other Topics. Lease Financing. Current Asset Management. Mergers, LBOs, Divestitures, and Holding Companies.

Course Objectives

The objective of this course is to familiarize the students with the world of finance, viewed especially from a corporation’s angle. The technical objectives include teaching about a wide array of concepts ranging from the basics of risk, return, time value of money and valuation to the more advanced discussions of capital budgeting and capital structure. The conceptual objectives include creating awareness about the variety and complexity of the financial decisions that are faced by the manager of a corporation on a daily basis. Finally, the philosophical objectives include demonstrating how the "world of finance" can be fascinatingly interesting and surprisingly challenging in a rather enjoyable way!

Course Learning Outcomes

- Understand how the various parts of a business and its environments interact with the financial decisions of the firm
- Develop skills in financial statement analysis, pro-forma preparation and performance evaluation by using financial statements
- Understand the fundamental risk/return tradeoff in finance
- Acquire the state-of-the-art know-how related to asset pricing by learning the chronological evolution of asset pricing models
- Understand the essentials of bond and stock valuation and learn how to apply the basic framework to valuation in general
- Learn the project evaluation process; acquire the technical skills for assessing project alternatives financially; understand the practical difficulties in capital budgeting; identify, analyze, and propose reasonable solutions to these problems
- Understand the strategic financial decisions of a firm by learning about the dividend policy and capital structure choices
- Understand the multinational setting in which companies operate and assess the effect of such a setting on corporate financial policies

Tentative (Weekly) Outline

Examination of special issues in finance incorporating advanced theory and practice with emphasis on investment and financing decisions of the firm. Special references to applications in Turkey. Outline of Topics: An Overview of Financial Management. Financial Statements, Cash Flow, and Taxes. Analysis of Financial Statements. The Financial Environment: Markets, Institutions, and Interest Rates. Risk and Return. Time Value of Money. Bonds and Their Valuation. Stocks and Their Valuation. The Cost of Capital. The Basics of Capital Budgeting. Cash Flow Estimation and Other Topics in Capital Budgeting. Capital Structure Decisions. Distribution to Shareholders: Dividends and Repurchases. Issuing Securities, Refunding, and Other Topics. Lease Financing. Current Asset Management. Mergers, LBOs, Divestitures, and Holding Companies.

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#### IAM522 - Stochastic Calculus for Finance

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

The objective of this course is an introduction to the probabilistic techniques required for understanding the most widely used financial models. In the last few decades, financial quantitative analysts have used sophisticated mathematical concepts in order to describe the behavior of markets and derive computing methods. The course presents the martingales, the Brownian motion, the rules of stochastic calculus and the stochastic differential equations with their applications to finance. Outline of Topics: Discrete time models, Martingales and arbitrage opportunities, complete markets, European options, option pricing, stopping times, the Snell envelope, American options. Continuous time models: Brownian motion, stochastic integral with respect to the Brownian motion, the Itô Calculus, stochastic differential equations, change of probability, representation of martingales; pricing and hedging in the Black-Scholes model, American options in the Black-Scholes model; option pricing and partial differential equations; interest rate models; asset models with jumps.

Course Objectives

The objective of this course is an introduction to the probabilistic techniques required for understanding the most widely used financial models. In the last decades financial quantitative analysts have used sophisticated mathematical concepts, such as martingales and stochastic integration, in order to describe the behaviour of markets or derive computing methods. The course presents the martingales, the Brownian motion, the rules of stochastic calculus and the stochastic differential equations oriented to applications to finance.

Course Learning Outcomes

This course contains the most basic tools of mathematical models for financial markets. Therefore the acquired ability will give the students the necessary skill in financial studies.

Tentative (Weekly) Outline

Discrete-time models: trading strategies, self-financing strategies, admissible strategies, arbitrage, martingales and viable markets, complete markets and option pricing. Optimal stopping problem and American options : Stopping time, Snell envelope, American options, European options. Brownian motion and stochastic differential equations: Brownian motion, martingales, stochastic integral and Itô calculus, Ornstein-Uhlenbeck process, stochastic differential equations. The Black-Scholes model: the behavior of prices, self-financing strategies, the Girsanov theorem, pricing and hedging of options, hedging of calls and puts, American options, perpetual puts. Option pricing and partial differential equations: European option pricing and diffusions, partial differential equations and computation of expectations, numerical solutions, application to American options. Interest rate models: modelling principles, some classical models. Asset models with jumps: Poisson process, dynamics of risky assets, pricing and hedging of options. Simulation and algorithms for financial models.

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#### IAM523 - Elements of Stochastic Calculus

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

The aim of this course is an initiation to the Itô Calculus (Stochastic Calculus by means of the Brownian motion) which constitutes one of the most important branches of stochastic processes because of their applications and extensions. Outline of Topics: Basic concepts of Probability Theory, stochastic processes, Brownian Motion, conditional expectation, martingales, stochastic integral, representation of martingales, Itô Lemma, change of probability, stochastic differential equations (existence and uniqueness of the solutions, approximations of the solutions), applications.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

The aim of this course is an initiation to the Itô Calculus (Stochastic Calculus by means of the Brownian motion) which constitutes one of the most important branches of stochastic processes because of their applications and extensions. Outline of Topics: Basic concepts of Probability Theory, stochastic processes, Brownian Motion, conditional expectation, martingales, stochastic integral, representation of martingales, Itô Lemma, change of probability, stochastic differential equations (existence and uniqueness of the solutions, approximations of the solutions), applications.

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#### IAM524 - Financial Economics

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

The focus of this course is on asset pricing. The topics that will be discussed can be summarized as follows: Individual investment decisions under uncertainty are analyzed and the optimal portfolio theory is discussed using both static and dynamic approach. Then the theory of capital market equilibrium and asset valuation is introduced. In this context several equilibrium models of asset markets are presented. These include the Arrow-Debreu model of complete markets, the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT). Besides mutual fund separation and aggregation theorems are analyzed. Finally, the financial decisions of firms are considered and the Modigliani-Miller theorems are analyzed.

Course Objectives

This course focuses on:

- the different criteria that can be used by financial decision makers under uncertainty and the following optimal choices
- the analyses of the optimal portfolio formation processes
- the core asset pricing models: the Capital Asset Pricing Model and the Arbitrage Asset Pricing Model
- the interactions of economic agents under uncertainty with the general equilibrium approach

Course Learning Outcomes

The succesful student will be able to:

- analyze different financial decision making criteria and the associated optimal choices
- solve optimal portfolio management problems
- use the core asset pricing theories to understand financial pheomena in financial markets
- identify financial interactions of the economic agents in examining financial markets and in solving financial problems

Tentative (Weekly) Outline

The focus of this course is on asset pricing. The topics that will be discussed can be summarized as follows: Individual investment decisions under uncertainty are analyzed and the optimal portfolio theory is discussed using both static and dynamic approach. Then the theory of capital market equilibrium and asset valuation is introduced. In this context several equilibrium models of asset markets are presented. These include the Arrow-Debreu model of complete markets, the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT). Besides mutual fund separation and aggregation theorems are analyzed. Finally, the financial decisions of firms are considered and the Modigliani-Miller theorems are analyzed.

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#### IAM525 - Game Theory

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Strategic games, Nash equilibrium, Bayesian Games, Mixed, Correlated, Evolutionary equilibrium, Extensive games with perfect information, Bargaining games, Repeated games, Extensive games with imperfect information, Sequential equilibrium, Coalition games, Core, Stable sets, Bargaining sets, Shapley value, Market games, Cooperation under uncertainty.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Strategic games, Nash equilibrium, Bayesian Games, Mixed, Correlated, Evolutionary equilibrium, Extensive games with perfect information, Bargaining games, Repeated games, Extensive games with imperfect information, Sequential equilibrium, Coalition games, Core, Stable sets, Bargaining sets, Shapley value, Market games, Cooperation under uncertainty.

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#### IAM526 - Time Series Applied To Finance

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

This course introduces time series methodology emphasizing the data analytic aspects related to financial applications. Topics that will be discussed are as follows: Univariate linear stochastic models: ARMA and ARIMA models building and forecasting using these models. Univariate non-linear stochastic models: Stochastic variance models, ARCH processes and other non-linear univariate models. Topics in the multivariate modeling of financial time series. Applications of these techniques to finance such as time series modeling of equity returns, trading day effects and volatility estimations will be discussed.

Course Objectives

The course intends to meet two goals. It provides tools for empirical work with time series data and is an introduction into the theoretical foundation of time series models. Much of statistical methodology is concerned with models in which the observations are assumed to be independent. However, many data sets occur in the form of time series where observations are dependent. In this course, we will concentrate on univariate time series analysis, with a balance between theory and applications. After completing this course, a student will be able to analyze univariate time series data using available software as well as pursue research in this area. In order to emphasize application of theory to real (or simulated) data, we will use R or SAS.

Course Learning Outcomes

Student who completes this course successfully

- will have solved a reasonable number of exercises on classical time series models
- find research texts (books / articles) using time series models more accessible
- may get involved in applied research making use of basic time series models
- will have a reasonable background to study more advanced texts and models

Tentative (Weekly) Outline

- Fundamental Concepts
- Properties of autocovariance and autocorrelation of time series
- Stationary and nonstationary time series models
- Time series modeling (identification, parameter estimation, and model selection)
- Seasonal time series models
- Time series forecasting
- Testing for a unit root
- Diagnostic Checking
- VAR models, Granger Causality
- Cointegration

Course Textbook(s)

- D. C. Cryer and K. Chan, Time Series Analysis with Application in R, 2nd Edition, Springer, 2008.

Supplementary Materials and Resources

- J. D. Cryer, Time Series Analysis, PWS-Kent Publishing Company, Boston, 1986.
- William W.S Wei, Time Series Analysis, Univariate and Multivariate Methods, Second Edition, Addison-Wesley, 2006.
- G. E. P. Box, G. M. Jenkins, and G. C. Reinsel, Time Series Analysis, Forecasting and Control 3rd ed., Prentice-Hall, 1994.
- C. Chatfield, The Analysis of Time Series, Sixth Edition Chapman & Hall/CRC, 2004.
- D. Pena, G. C. Tiao, and R. S. Tsay, A Course in Time Series Analysis, Wiley Interscience, 2001.
- Robert A. Yaffee, Introduction to Time Series Analysis and Forecasting with Applications of SAS and SPSS, San Diego, Academic Press, 2000.
- R. S. Tsay, Analysis of Financial Time Series, Wiley Interscience, 2002.

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#### IAM527 - Advanced Calculus and Integration

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Review of linear algebra and multivariate calculus, sequences of series and functions, Riemann-Stieltjes and Lebesgue integration.

Course Objectives

Real analysis, multivariable calculus and linear algebra (along with probability theory) constitute the mathematical foundations of mathematical finance. The objective of the course is to help the student gain an understanding of these subjects so that s/he can participate in research and learning activities (such as taking courses, reading literature, solving research/ applied problems) in mathematical finance and related fields.

Course Learning Outcomes

Student who passed this course will

- Have an easier time in understanding the mathematical concepts when taking courses on or related to math finance (such as IAM 541 Probability Theory and IAM 526 Stochastic Calculus for Finance course in our program),
- Find research material on math finance more mathematically accessible (such as current research papers on math finance or textbooks on the subject). It takes an enormous effort to get used to the technical language that is prevalent today in the field of mathematical finance. After taking this course, the student will find it easier and quicker to master this technical language.
- Find it easier to work on research problems in mathematical finance and related fields which use the language of real analysis, linear algebra and multivariable calculus.

Tentative (Weekly) Outline

Review of linear algebra and multivariate calculus, sequences of series and functions, Riemann-Stieltjes and Lebesgue integration.

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#### IAM528 - Markov Decision Processes

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

The course containing a strong emphasis on applications purports to give students the skills needed in dealing with the control of Markov Chains. The outline of Topics: Discrete-time Markov chains : Ordinary and strong Markov properties, classification of states, stationary probabilities, limit theorems. Continuous-time Markov chains (a survey). Discrete-time Markovian Decision Processes: Various policies, policy-iteration algorithm, linear programming formulation, value-iteration algorithm. Semi-Markov Decision Processes. Applications to inventory problems, to portfolio optimization and to communication systems.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

The course containing a strong emphasis on applications purports to give students the skills needed in dealing with the control of Markov Chains. The outline of Topics: Discrete-time Markov chains : Ordinary and strong Markov properties, classification of states, stationary probabilities, limit theorems. Continuous-time Markov chains (a survey). Discrete-time Markovian Decision Processes: Various policies, policy-iteration algorithm, linear programming formulation, value-iteration algorithm. Semi-Markov Decision Processes. Applications to inventory problems, to portfolio optimization and to communication systems.

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#### IAM529 - Applied Nonlinear Dynamics

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

The course consists of a detailed description of continuous and discrete dynamical systems. We shall combine the introduction to the general theory with the consideration of bifurcations and chaos, the most important subtopics. The analysis of appropriate mechanical, physical, economic and biological models is an essential part of almost every lecture of the course. To support the course numerical and computational toolbox will be used.

Course Objectives

- The aim of this course is to study mathematical basis of dynamical systems to prepare students for further investigations in related fields.

Course Learning Outcomes

Student, who passed the course satisfactorily will:

- learn the basic concepts of dynamical systems
- have the ability to do research in related fields

Tentative (Weekly) Outline

- Linear Dynamical Systems
- Fundamental Theorem of Continuous Systems
- A Review of Eigenvectors, Eigenvalues
- A Qualitative Investigation of Planar Systems
- Stability of Linear Systems
- Nonlinear Dynamical Systems
- A Short review of Manifold Approach
- Fixed Points and Phase Flow
- Local Nonlinear Systems, Linearization
- Stability of Nonlinear Systems, Hyperbolic, Non-hyperbolic Cases
- Limit Cycles, the Poincaré Map
- Liapunov Function
- The Hartman-Grobman Theorems
- Bifurcations and Hamiltonian Systems
- One Dimensional Bifurcations, Saddle Node, Pitchfork, Transcritical Bufircations
- The Hopf Bifurcations
- Hamiltonian Flows
- Classification of Flows
- Examples
- Chaos and Fractals
- The Lorenz Equations, and Chaos on a Strange Attractor
- Lorenz Map
- The Cantor Set, Dimension of Fractals

Course Textbook(s)

- Stephen Lynch, Dynamical Systems with Applications using MATLAB, Birkhäuser Basel, 2014
- James D. Meiss, Differential Dynamical Systems, SIAM, 2007

Supplementary Materials and Resources

- Books:
- J. Jost, Dynamical Systems:Examples of Complex Behaviour, Springer, 2005
- S. H. Strogatz, Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry, and Engineering, 2nd edition, Westview Press, 2015
- Resources:
- Lecture Notes: Furthermore, lecture notes and recent research articles will be provided during the course.
- MATLAB Student Version is available to download on MathWorks website, http://www.mathworks.com, or METU FTP Severs (Licenced)

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#### IAM530 - Elements of Probability and Statistics

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Part I: Probability spaces, random variables, probability distributions and probability densities, conditional probability, Bayes formula, mathematical expectation, moments. Part II: Sampling distributions, decision theory, estimation (theory and applications), hypothesis testing (theory and applications), regression and correlation, analysis of variance, non-parametric tests.

Course Objectives

The objective of this course is to introduce students to the basic probability theory and mathematical statistics and help them in establishing a good theoretical background for their future professions. This course provides a comprehensive introduction to probability, statistical theory and methodology. Lectures will explain the theoretical origins and practical implications of statistical formulae. This course initiate students to Probability Calculus and statistical methods used in current application problems.

Course Learning Outcomes

Student, who passed the course satisfactorily will be able to:

- apply the conditional probability concepts and Bayes' theorem to the problems in finance and actuarial mathematics
- do mathematical modelling using the distributions of continuous and discrete random variables
- apply the concepts learn in the second part of the course to do statistical inference

Tentative (Weekly) Outline

- Probability
- Random Variables and Their Distributions
- Special Probability Distributions
- Joint Distributions
- Properties of Random Variables
- Functions of Random Variables
- Limiting Distributions
- Statistics and Sampling Distributions
- Point Estimation
- Sufficiency and Completeness
- Interval Estimation
- Tests of Hypotheses
- Contingency Tables and Goodness-of-Fit
- Nonparametric Methods
- Regression and Linear Models

Course Textbook(s)

- Introduction to Probability and Mathematical Statistics, L. J. Bain and M. Engelhardt, 2nd edition, 1992.
- Statistical Inference, Second Edition, Casella, G. and Berger, R.L., Thomson Learning, 2002.

Supplementary Materials and Resources

- Books:
- Introduction to Probability and Statistics Using R, G. Jay Kerns, First Edition, 2010.
- Probability and Statistical Inference, Robert V. Hogg, Elliot A. Tanis, Dale Zimmerman, 9th edition, 2015.
- All of Statistics - A Concise Course in Statistical Inference, Larry Wasserman, 2004.
- An Introduction to R - Notes on R: A Programming Environment for Data Analysis and Graphics, W. N. Venables, D. M. Smith, and the R Core Team, Version 3.4.2 (2017-09-28).
- Resources:
- Those who do not have R on their PCs can download it from the site http://www.r-project.org.
- A very nice Quick-R website is located on http://www.statmethods.net.
- Related to the textbook, check the site http://www.stat.pitt.edu/stoffer/tsa3/R_toot.htm.

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#### IAM532 - Statistical Methods

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Random variables and transformation of random variables. Common families of distributions. Multiple random variables. Properties of random sample and sampling methods. Principles of data reduction. Estimation and hypotheses testing. Asymptotic evaluations. Decision theory. Analysis of Variance. Linear and nonlinear regression.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Random variables and transformation of random variables. Common families of distributions. Multiple random variables. Properties of random sample and sampling methods. Principles of data reduction. Estimation and hypotheses testing. Asymptotic evaluations. Decision theory. Analysis of Variance. Linear and nonlinear regression.

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#### IAM541 - Probability Theory

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Probability spaces. Independence. Conditional probability. Product probability spaces. Random variables and their distributions. Distribution functions. Mathematical expectation (Integration with respect to a probability measure.) Lp-spaces. Moments and generating functions. Conditional expectation. Linear estimation. Gaussian vectors. Various convergence concepts. Central Limit Theorem. Laws of large numbers.

Course Objectives

The objective of this course is to initiate students to Probability Theory and its applications.

Course Learning Outcomes

Student who passed this course will

- Be able to take courses which build on probability theory (such as the 526 Stochastic Calculus for Finance course in our program)
- Find research material on math finance more mathematically accessible (such as current research papers on math finance or textbooks on the subject). It takes an enormous effort to get used to the technical language that is prevalent today in the field of mathematical finance. After taking this course, the student will find it easier and quicker to master this technical language
- Find it easier to work on research problems in mathematical finance and related fields which use the language of probability theory

Tentative (Weekly) Outline

Probability spaces. Independence. Conditional probability. Product probability spaces. Random variables and their distributions. Distribution functions. Mathematical expectation (Integration with respect to a probability measure.) Lp-spaces. Moments and generating functions. Conditional expectation. Linear estimation. Gaussian vectors. Various convergence concepts. Central Limit Theorem. Laws of large numbers.

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#### IAM542 - Stochastic Processes

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

This course is a nonmeasure theoretic introduction to stochastic processes, and as such assumes a knowledge of calculus and elementary probability. Some of the theory of stochastic processes is presented and diverse range of its applications is indicated. Outline of Topics: Poisson process, Renewal Theory, discrete-time Markov chains, continuous-time Markov chains, martingales, random walks, Brownian Motion. Applications to queueing and to ruin problems.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

This course is a nonmeasure theoretic introduction to stochastic processes, and as such assumes a knowledge of calculus and elementary probability. Some of the theory of stochastic processes is presented and diverse range of its applications is indicated. Outline of Topics: Poisson process, Renewal Theory, discrete-time Markov chains, continuous-time Markov chains, martingales, random walks, Brownian Motion. Applications to queueing and to ruin problems.

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#### IAM543 - Regulation and Supervision of Financial Risks

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Rationale for Regulating/Supervising Financial Risks. International Regulatory & Supervisory Framework. Quantitative Techniques and Application (based on Excel/VBA/Cyristall Ball). Financial Scandals. Hedge Funds. Project works.

Course Objectives

This course is concerned with recent developments in the regulation and supervision of banking risks with special reference to Basel II within a regulatory and supervisory context. The course also aims to provide a rigorous account of issues on financial scandals with a special reference to banking. Finally the course aims to equip students with a rigorus understanding and application of financial risks within an Excel-based calculation environment.

Course Learning Outcomes

Course attendants will be able to understand the rationale for the regulation and supervision of financial risks and will grasp the recent methodologies for calculating financail risks such as market and credit risk.

Tentative (Weekly) Outline

Rationale for Regulating/Supervising Financial Risks. International Regulatory & Supervisory Framework. Quantitative Techniques and Application (based on Excel/VBA/Cyristall Ball). Financial Scandals. Hedge Funds. Project works.

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#### IAM544 - Financial Risk Assessment

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Introduction to programming in Matlab. Matlab toolboxes related to financial computations. Computations of Probability Distributions in Matlab. Distribution fit. Mixed distributions. Computation of Unconditional and conditional probabilities. Introduction to econometrics. OLS, MLE, properties of the estimators. Autocorrelation-heteroscedasticity-nonlinearity in time series. Time series modeling in Matlab. Commands for AR-MA-ARMA-ARIMA-ARCH-GARCG-Multivariate GARCH modeling. Measuring the risk of foreign exchange, equities, derivatives, bonds. Computation of Zero Coupon Bond-Duration-Convexity-Forward Rate-Yield Curve (Interpolation and function based approaches i.e. Nelson-Siegel). Computation of Portfolio Value at Risk, Covariance VaR, Delta-Normal VaR, Historical Simulation-Filtered Historical Simulation-Bootstrap, Monte Carlo Simulation of Geometric Brownian Motion, CRR, CIR, Vasicek, HJM models.

Course Objectives

To provide students with an extensive knowledge of portfolio risk assessment. Students will be asked to solve the everyday problems being faced by professionals. This course will be a project-driven course in which the daily events of the financial markets will be modeled, simulated and programmed in matlab environment.

Course Learning Outcomes

Tentative (Weekly) Outline

Introduction to programming in Matlab. Matlab toolboxes related to financial computations. Computations of Probability Distributions in Matlab. Distribution fit. Mixed distributions. Computation of Unconditional and conditional probabilities. Introduction to econometrics. OLS, MLE, properties of the estimators. Autocorrelation-heteroscedasticity-nonlinearity in time series. Time series modeling in Matlab. Commands for AR-MA-ARMA-ARIMA-ARCH-GARCG-Multivariate GARCH modeling. Measuring the risk of foreign exchange, equities, derivatives, bonds. Computation of Zero Coupon Bond-Duration-Convexity-Forward Rate-Yield Curve (Interpolation and function based approaches i.e. Nelson-Siegel). Computation of Portfolio Value at Risk, Covariance VaR, Delta-Normal VaR, Historical Simulation-Filtered Historical Simulation-Bootstrap, Monte Carlo Simulation of Geometric Brownian Motion, CRR, CIR, Vasicek, HJM models.

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#### IAM545 - Fundamentals of Insurance

Credit: 2(0-2); ECTS: 3.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Basic concepts, Insurance related institutions, their relations with insurance companies, connection to market and investment tools, the role of laws, regulations, terms and conditions, parties and partners in insurance sector, types of insurance, pricing, product development, managerial and financial operations in an insurance company, investment strategies, financial management in insurance companies.

Course Objectives

Basic concepts and terminology in insurance, major players in insurance sector, role of insurance within financial markets, the regulatory framework, insurance regulations, types of insurance, reinsurance, pricing, product development, basic financial analysis, key operations of an insurance company, visit to an insurance company.

Course Learning Outcomes

This course aims to give a general perspective of insurance and insurance related areas without entering the mathematical and statistical models. It enables students to get accustomed to the concepts, terminology and issues in insurance. The composition of insurance sector, working of insurance companies, role of various key players, insurance regulations, types of insurance and financial operations in an insurance company will be presented both in a national and international perspective during the semester.

Tentative (Weekly) Outline

Basic concepts, Insurance related institutions, their relations with insurance companies, connection to market and investment tools, the role of laws, regulations, terms and conditions, parties and partners in insurance sector, types of insurance, pricing, product development, managerial and financial operations in an insurance company, investment strategies, financial management in insurance companies.

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#### IAM546 - Actuarial Risk Theory

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Basic concepts of probability in sense of risk theory, Introduction to risk processes (claim number process, claim amount process, total claim number process, total claim amount process, inter-occurrence process), Convolution and mixed type distributions, Risk models ( individual and collective risk models), Numerical methods ( simple methods for discrete distributions, Edgeworth approximation, Esscher approximation, normal power approximation), Premium calculation principles, Credibility Theory, Retentions and reinsurance, Ruin theory, Ordering of risks.

Course Objectives

Establishing knowledge and skills in actuarial risk analysis, developing insurance risk management capacities.

Course Learning Outcomes

Tentative (Weekly) Outline

Basic concepts of probability in sense of risk theory, Introduction to risk processes (claim number process, claim amount process, total claim number process, total claim amount process, inter-occurrence process), Convolution and mixed type distributions, Risk models ( individual and collective risk models), Numerical methods ( simple methods for discrete distributions, Edgeworth approximation, Esscher approximation, normal power approximation), Premium calculation principles, Credibility Theory, Retentions and reinsurance, Ruin theory, Ordering of risks.

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#### IAM547 - Risk Management and Insurance

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Definition of risk, insurance and surety. Risk management techniques and some applications in real life problems. Economic and social significance of insurance. Laws of agency, contract, and negligence and their applications to insurance. Types, scope and organization of insurance companies. Construction of policies including limitations on recovery. Underwriting, marketing, rating and regulation of insurance. Covers the principles of risk management, property-liability insurance and life health insurance. Insurance regulations, laws, and insurance practice in Turkey.

Course Objectives

Financial objectives of corporate risk management process, empirical evidence of how and why firms manage risk, institutional environment and regulations of risk management. This course surveys risk fundamentals, the risk management process, and insurance as a systematic approach to transfer and finance risk. It examines how to determine, analysis and evaluate risk for different types of insurance and how insurance offers financial protection against major risks individuals face, how the insurance market is structured, and how and why the industry is regulated. This course also provides the theories and practical applications from the industry as well as issues related to the furtherance of insurance as a viable risk management solution.

Course Learning Outcomes

Understanding the risk structure and the methods to handle the risk in insurance, how to determine risk for different types of insurance, insurance operations and products.

Tentative (Weekly) Outline

- Basic concepts in insurance: hazard, risk, insurable risk, coverage, insurance terms and conditions, loss assessment
- Risk management
- Risk measures
- The need for and development of insurance, Insurance policy: contents, types, special features; Types of insurance: Property and casualty, liability, life
- Types of Insurance companies: Insurance, reinsurance, mutual, composite Insurance market and key players, Key insurance professionals: actuary, agency, broker, loss adjuster, Reinsurance
- Pricing in insurance
- Accounting and financial analysis in insurance: Technical reserves
- Insurance Law in Turkey- Guest Speaker
- Risk measures, VaR, Coherent risk measures
- Dependent risk measures
- Term Project presentations and discussions

Course Textbook(s)

- Principles of Risk Management and Insurance, Rejda, Adison Wesley
- Risk Yönetimi ve Sigorta, M.Çipil, Nobel Yayın Dağıtım
- Hossack, Pollard, Zehnwirth, Indroductory statistics with applications in general insurance, Cambridge, 1995

Supplementary Materials and Resources

- Trieschmann, Hoyt, Sommer, Risk Management and Insurance, 12th Ed., 2005
- Vaughan, E., Vaughan, T., Essentials of Insurance: A Risk Management Perspective
- Temel Sigortacılık Bilgileri ve Uygulamalı Hasar Yönetimi, T. Alpay, Yüce Yayımları
- Uygulamalı Sigorta Hukuku: Mal ve Sorumluluk Sigortaları 5684 Sayılı Sigortacılık Kanununa Göre, Turhan Kitabevi

#### IAM548 - Stochastic Processes for Insurance and Finance

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Essentials of stochastic integrals and stochastic differential equations. Probability distributions and heavy tails. Concepts from insurance and finance. Ordering of risks. Aggregate claim amount distributions. Risk processes. Renewal processes and random walks. Markov chains. Continuous Markov models. Martingale techniques and Brownian motion. Point processes. Diffusion models. Applications to insurance and finance processes.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

- Essentials of stochastic integrals and stochastic differential equations. Probability distributions and heavy tails. Concepts from insurance and finance. Ordering of risks. Aggregate claim amount distributions. Risk processes. Renewal processes and random walks. Markov chains. Continuous Markov models. Martingale techniques and Brownian motion. Point processes. Diffusion models. Applications to insurance and finance processes.

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#### IAM549 - Fundamentals of Insurance

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Basic concepts, Insurance related Institutions, their relations with insurance companies, connection to market and investment tools, the role of laws, regulations, terms and conditions, parties and partners in insurance sector, types of insurance, pricing, product development, managerial and financial operations in an insurance company, investment strategies, financial management in insurance companies, field trip to insurance companies.

Course Objectives

Basic concepts and terminology in insurance, major players in insurance sector, role of insurance within financial markets, the regulatory framework, insurance regulations, types of insurance, reinsurance, pricing, product development, basic financial analysis, key operations of an insurance company, visit to an insurance company.

Course Learning Outcomes

This course aims to give a general perspective of insurance and insurance related areas without entering the mathematical and statistical models. It enables students to get accustomed to the concepts, terminology and issues in insurance. The composition of insurance sector, working of insurance companies, role of various key players, insurance regulations, types of insurance and financial operations in an insurance company will be presented both in a national and international perspective during the semester.

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#### IAM550 - Portfolio Optimization

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Mean-Variance (Markowitz) analysis; continuous-time market model in finance; options and exotic options, pricing (valuation) of options; self-financing, optimal strategies, optimal portfolios (problems); martingale method; stochastic control and portfolio optimization.

Course Objectives

The objective of the course is to introduce central elements of the theory, methods (algorithms) and applications on how optimization theory is used to decide on optimal portfolios.

Course Learning Outcomes

At the end of this course, students should be able to approximately model, analyze and tackle optimization problems of the financial sector related with portfolios. This includes a macro-economical understanding, a representation of individual interests, and a familiarity with modern mathematical methods. Both lectures and exercises serve for this aim of learning, deepening, applying and preparing.

Tentative (Weekly) Outline

Mean-Variance (Markowitz) analysis; continuous-time market model in finance; options and exotic options, pricing (valuation) of options; self-financing, optimal strategies, optimal portfolios (problems); martingale method; stochastic control and portfolio optimization.

#### IAM552 - Credibility Theory

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Risk rating, Bayes premiums, credibility estimators, large claims and credibility, Buhlman-Straub and other relevant models, hierarchical and multidimensional credibility, linear models, linear trend models, evolutionary models.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Risk rating, Bayes premiums, credibility estimators, large claims and credibility, Buhlman-Straub and other relevant models, hierarchical and multidimensional credibility, linear models, linear trend models, evolutionary models.

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#### IAM554 - Interest Rate Models

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Interest Rate Derivatives: Futures, Options on Bonds, and Options on Interest Rates such as Caps and Floors. Models of Arbitrage-Free pricing of Interest-Rate Derivatives: Arbitrage Pricing Theory for Derivative Securities. Basics for The Modeling of Interest-Rate movements. Dynamics of Interest-Rate movements. Short-Rate Models and the Heath-Jarrow-Morton Model of Forward Rates. Change of Numéraire Technique. Derivation of Formulae for the Pricing and Hedging of Certain Derivatives. Numerical Methods for the Actual Implementation of the Valuation of Term Structure Models.

Course Objectives

The uncertainty attached to future movements of interest rates is an essential part of the Financial Decision Theory and requires an awareness of the stochastic movement of these rates. The aim of the course is to give an insight to the notion of interest rate, the construction of various models and their applications to computation of interest rate products. Particular emphasis will be placed on the adaptation of the models to the observed market data.

Course Learning Outcomes

Tentative (Weekly) Outline

Interest Rate Derivatives: Futures, Options on Bonds, and Options on Interest Rates such as Caps and Floors. Models of Arbitrage-Free pricing of Interest-Rate Derivatives: Arbitrage Pricing Theory for Derivative Securities. Basics for The Modeling of Interest-Rate movements. Dynamics of Interest-Rate movements. Short-Rate Models and the Heath-Jarrow-Morton Model of Forward Rates. Change of Numéraire Technique. Derivation of Formulae for the Pricing and Hedging of Certain Derivatives. Numerical Methods for the Actual Implementation of the Valuation of Term Structure Models.

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#### IAM555 - Statistical Decision Theory

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Introduction to decision making, expected loss, decision rules and risk, decision principles, utility and loss, prior information and subjective probability, Bayesian analysis, posterior distribution, Bayesian inference, Bayesian Decision theory, minimax analysis, value of information, sequential decision procedures, multi decision problems.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Introduction to decision making, expected loss, decision rules and risk, decision principles, utility and loss, prior information and subjective probability, Bayesian analysis, posterior distribution, Bayesian inference, Bayesian Decision theory, minimax analysis, value of information, sequential decision procedures, multi decision problems.

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#### IAM556 - Simulation

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Basic introduction to simulation concepts, generation of random variants from distributions, test for randomness, Monte Carlo Simulation, selecting input distribution, discrete event simulation, variance reduction techniques, statistical analysis of output.

Course Objectives

The objective of this course is to introduce students an experimental problem solving methodology, which is extensively utilized when the problem to be solved is too complex or does not have any analytical solution.

Course Learning Outcomes

Students taking this course will be equipped with the use of the tools and techniques of statistical simulation to be able to solve especially complex real-world problems.

Tentative (Weekly) Outline

Basic introduction to simulation concepts, generation of random variants from distributions, test for randomness, Monte Carlo Simulation, selecting input distribution, discrete event simulation, variance reduction techniques, statistical analysis of output.

#### IAM557 - Statistical Learning and Simulation

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Brief introduction to Statistical Learning: Regression versus Classification; Linear Regression: simple and multiple Linear Regression; Classification: Logistic Regression, Discriminant Analysis; Resampling Methods: Cross-Validation, the Bootstrap; Regularization: Subset Selection, Ridge Regression, the Lasso, Principle Components and Partial Least Squares Regression; Nonlinear Models: Polynomial; Splines; Generalized Additive Models; Tree-Based Models: Decision Trees, Random Forest, Boosting; Support Vector Machines; Unsupervised Learning: Principle Component Analysis, Clustering Methods.

Course Objectives

At the end of the course, the student will learn:

- the fundamentals of Statistical Learning, regression and classification
- linear and nonlinear regressions including splines
- Generalised Additive Models for both regression and classification problems
- regularisation techniques including Ridge regression and the Lasso
- the tree-based methods for regression and classification
- Support Vector Machine which is highly appreciated among Data Science and Machine Learning Community
- the difference between supervised and unsupervised learning methods

Course Learning Outcomes

Student, who passed the course satisfactorily will be able to:

- present the data and its descriptive analysis
- distinguish between regression and classification problems
- apply regression or classification algorithms to solve related problems
- code their own algorithms for specific applications in Statistical and Machine Learning
- understand the fundamentals of Support Vector Machine and be able to apply to specific problems
- distinguish between supervised and unsupervised learning methods in related applications

Tentative (Weekly) Outline

- Brief introduction to Statistical Learning: a) Regression versus Classification
- Linear Regression: a) simple and multiple Linear Regression
- Classification: a) Logistic Regression b) Discriminant Analysis (Linear and Quadratic)
- Resampling Methods: a) Cross-Validation b) the Bootstrap
- Regularisation: a) Subset Selection b) Ridge Regression c) the Lasso d) Principle Components Regression e) Partial Least Squares Regression
- Nonlinear Models: a) Polynomial and Splines b) Generalised Additive Models
- Tree-Based Models: a) Decision Trees b) Random Forest c) Boosting
- Support Vector Machines
- Unsupervised Learning: a) Principle Component Analysis b) Clustering Methods

Course Textbook(s)

- Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani, An Introduction to Statistical Learning - with Applications in R, 8th ed., Springer, 2013 (Corrected at 8th printing 2017)

Supplementary Materials and Resources

- Books:
- Trevor Hastie, Robert Tibshirani, Jerome Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd ed., Springer, 2009 (Corrected at 12th printing 2017)
- Kevin P. Murphy, Machine Learning: A Probabilistic Perspective, The MIT Press, 2012
- Peter Harrington, Machine Learning in Action, Manning Publications Co., 2012
- Charu C. Aggarwal, Neural Networks and Deep Learning: A Textbook, Springer, 2018
- G. Jay Kerns, Introduction to Probability and Statistics Using R, 1st ed., 2015
- Robert V. Hogg, Elliot A. Tanis, Dale Zimmerman, Probability and Statistical Inference, 9th ed., 2015
- Larry Wasserman, All of Statistics - A Concise Course in Statistical Inference, 2004
- W. N. Venables, D. M. Smith, and the R Core Team, An Introduction to R - Notes on R: A Programming Environment for Data Analysis and Graphics, Version 3.4.2 (2017-09-28)
- Resources:
- The R Project for Statistical Computing: https://www.r-project.org/
- python: https://www.python.org/
- RStudio: https://www.rstudio.com/
- Anaconda: https://www.anaconda.com/

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#### IAM558 - Reinsurance Theory

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Fundamentals of reinsurance including historical development, terminology and distribution systems. Treaty forms, facultative reinsurance, underwriting, rating, accounting and contract issues, analysis of annual statement, testing methods, advanced rating methods in property and casualty excess contracts, analysis accumulations, retention, contract wording and programming.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Fundamentals of reinsurance including historical development, terminology and distribution systems. Treaty forms, facultative reinsurance, underwriting, rating, accounting and contract issues, analysis of annual statement, testing methods, advanced rating methods in property and casualty excess contracts, analysis accumulations, retention, contract wording and programming.

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#### IAM560 - Stochastic Aspects of Dynamics

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Mathematical modelling of stochastic reaction systems. Deterministic approach: ODE models, Reaction Rate Equations. Stochastic Models: Chemical Master Equation, Chapman-Kolmogorov Equations, Gillespie Algorithms, Explicit Solution Formulas, Hybrid Methods, Tau-Leaping method. Lotka-Volterra Models, Michaelis-Menten Models.

Course Objectives

This course covers mathematical methods used for modelling biochemical reaction systems. It explains the general properties of these models and gives the theoretical background of these models which are based on Ordinary Differential Equations and Markov Chains. Objectivess of this course are:

- to understand the basics of modelling reaction systems
- to construct the traditional deterministic equations to model any biochemical reaction systems and solve these equations
- to understand the stochastic modelling approach
- to construct Chemical Master Equation for any given reaction systems
- to understand the relation between deterministic and stochastic modelling approach
- to learn how to simulate reaction systems via MATLAB

Course Learning Outcomes

Upon successful completion of this course, the student will be able to:

- understand deterministic and stochastic modelling approaches
- construct ODE systems and CME systems to model any given biochemical process
- simulate biochemical reaction systems
- understand the main differences between different modelling approaches and simulation strategies

Tentative (Weekly) Outline

- Representation of biochemical reactions
- Classical continuous deterministic models
- Basics of probability
- Probability distributions
- Stochastic Processes
- Molecular approach to kinetics, Mass Action Kinetics, Markov Processes
- Discrete Time Markov Chains, Continuous Time Markov Chains
- Chapman-Kolmogorov (forward) Equation, Rate Constant Conservation, Chemical Master Equation
- Gillespie Algorithm (Direct Method)
- Gillespie Algorithm (First Reaction Method)
- Case Studies- Michaelis Menten Kinetics, Lotka-Volterra Systems
- Explicit Solution Formulas
- Exact-Approximate Solution Strategies
- Hybrid Methods

Course Textbook(s)

- D. J. Wilkinson, Stochastic modelling for systems biology. Boca Raton, FL: Taylor & Francis. 2006.
- EJ. R. Norris, Markov Chains, Cambridge University Press, 1997

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#### IAM561 - Introduction to Scientific Computing I

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Computer Arithmetic; Linear Equations: Gauss elimination, LU decomposition; Linear Least Squares: data fitting, normal equations, orthogonal transformations; Eigenvalue Problems; Singular Value Decomposition; Nonlinear Equations: bisection, fixed-point iteration, Newton’s method, optimization; Interpolation: polynomials, piecewise polynomials; Numerical Differentiation and Integration.

Course Objectives

This course is intended for relatively new graduate students who require knowledge of and background in numerical methods. At the end of this course, the student will:

- understand the errors, source of error and its effect on any numerical computations, and also analyse the efficiency of any numerical algorithms
- learn how to obtain numerical solution of nonlinear equations
- learn how to approximate the functions using interpolating polynomials
- learn how to numerically differentiate and integrate functions
- learn to implement the numerical methods using MATLAB

Course Learning Outcomes

Upon successful completion of this course, the student will be able to:

- determine the effect of round off error and loss of significance
- design and analyze algorithms for solutions of linear equations
- derive appropriate numerical methods to solve algebraic and transcendental equations
- derive appropriate numerical methods to calculate a definite integral
- code various numerical methods using MATLAB

Tentative (Weekly) Outline

- Computer Arithmetic
- Linear Equations: Gauss elimination
- Linear Equations: LU decomposition
- Linear Least Squares: data fitting, normal equations
- Linear Least Squares: orthogonal transformations
- Eigenvalue Problems
- Singular Value Decomposition
- Nonlinear Equations: bisection, fixed-point iteration
- Nonlinear Equations: Newton’s method, optimization
- Interpolation: polynomials
- Interpolation: piecewise polynomials
- Numerical Differentiation
- Numerical Integration: basic quadrature algorithms
- Numerical Integration: Gaussian quadrature

Course Textbook(s)

- U. Ascher and C. Greif, A First Course in Numerical Methods, SIAM, 2011.

Supplementary Materials and Resources

- Books:
- M. T. Heat, Scientific Computing, McGraw Hill, 1997
- A. Quarterioni, R. Sacco, and F. Salari, Numerical Mathematics, Springer, 2000.
- Resources:
- MATLAB Student Version is available to download on MathWorks website, http://www.mathworks.com, or METU FTP Severs (Licenced)

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#### IAM562 - Introduction to Scientific Computing II

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Ordinary Differential Equations: Euler’s method, multistep methods, Runge-Kutta methods, stiff equations, adaptivity; Boundary Value Problems: shooting, collocation, Galerkin; Partial Differential Equations: parabolic, hyperbolic, and elliptic equations; Iterative Methods for Sparse Linear Systems: splitting methods.

Course Objectives

This is a course on scientific computing for ordinary differential equations (ODEs) and partial differential equations (PDEs). It includes the construction, analysis and application of numerical methods for ODEs/PDEs. Objects of this course are:

- to motivate the need for efficient numerical methods for solving differential equations
- to understand basic finite difference methods for partial differential equations
- to analyze consistency, stability, and convergence of the finite difference methods
- to solve system of linear equations numerically using direct and iterative methods
- to implement numerical methods on the computer to solve partial differential equations arising from the sciences and engineering.

Course Learning Outcomes

Upon successful completion of this course, the student will be able to:

- understand mathematics-numeric interaction, and how to match numerical method to mathematical properties
- make a good choice of methods for a particular ODE problem
- construct appropriate finite-difference approximations to PDEs
- analyze consistency, stability, and accuracy of a finite difference method
- write programs to solve ODEs/PDEs by finite difference methods
- solve challenging problems that are either purely mathematical or practical from various disciplines.

Tentative (Weekly) Outline

- Introduction to ODEs
- Euler’s Method
- Multistep Methods for ODEs
- Runge-Kutta Methods for ODEs
- Linear Stability Domain
- Stiff Equations and Adaptivity in Time
- Boundary Value Problems: shooting, collocation, Galerkin
- Introduction to PDEs
- Parabolic Equations
- Parabolic Equations: stability
- Hyperbolic Equations
- Elliptic Equations
- PDEs in Cylindrical and Spherical Coordinates
- Iterative Solvers: splitting methods

Course Textbook(s)

- A. Iserles, A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, 2009.
- R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady- State and Time-Dependent Problems, SIAM, 2007.

Supplementary Materials and Resources

- Books:
- M. T. Heat, Scientific Computing, McGraw Hill, 1997.
- A. Quarterioni, R. Sacco, and F. Salari, Numerical Mathematics, Springer, 2000.
- A. Quarterioni and F. Salari, Scientific Computing with MATLAB and Octave, Springer-Verlag, 2006.
- David F. Griffiths, John W. Dold, David J. Silvester, Essential Partial Differential Equations: Analytical and Computational Aspects, Springer, 2015.
- Resources:
- MATLAB
- htps://odtuclass.metu.edu.tr

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#### IAM563 - Methods of Applied Mathematics

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Development of exact, numerical and approximate solution methods towards a qualitative strategy for understanding the behavior of ordinary differential equations. Methods for derivation, solution and computation of partial differential equations models based on several examples taken from classical sciences. Linear PDEs, investigated through the development of various solution techniques: first-order quasilinear equations, elliptic, parabolic and hyperbolic equations, free boundary value problems, quasi-linear equations, eigenfunction expansions, Green's functions and integral transformations, linear and nonlinear wave phenomena.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Development of exact, numerical and approximate solution methods towards a qualitative strategy for understanding the behavior of ordinary differential equations. Methods for derivation, solution and computation of partial differential equations models based on several examples taken from classical sciences. Linear PDEs, investigated through the development of various solution techniques: first-order quasilinear equations, elliptic, parabolic and hyperbolic equations, free boundary value problems, quasi-linear equations, eigenfunction expansions, Green's functions and integral transformations, linear and nonlinear wave phenomena.

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#### IAM564 - Basic Algorithms and Programming

Credit: 0(0-4); ECTS: 4.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Basics of programming, introducing MATLAB, programming with MATLAB, basic algorithms and problem solving in Linear Algebra, Differential Equations, Optimization, and so an. Reporting and presenting problems and their solutions, introducing LATEX and/or Scientific Workplace, Typesetting text and mathematical formulae,graphing, making bibliography and index, packages and defining your own styles.

Course Objectives

The aim of this course is to help students acquire basic programming techniques and various fundamental algorithms in applied sciences. Also in this course, students are hoped to learn both programming using MATLAB and reporting their work using LATEX/ ScientificWorkplace.

Course Learning Outcomes

At the end of the course students should have a basic knowledge on programming their own algorithms and documenting them. Also, they are expected to be qualified in typesetting using Latex packages.

Tentative (Weekly) Outline

Basics of programming, introducing MATLAB, programming with MATLAB, basic algorithms and problem solving in Linear Algebra, Differential Equations, Optimization, and so an. Reporting and presenting problems and their solutions, introducing LATEX and/or Scientific Workplace, Typesetting text and mathematical formulae,graphing, making bibliography and index, packages and defining your own styles.

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#### IAM565 - Introduction to Algorithms and Complexity

Credit: 3(2-2); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

This course is intended to all students at the Institute. After a short introduction to Matlab various algorithms, their complexity will be introduced and symbolic, numerical and stochastic algorithms will be followed. Students will be encouraged to carry out several projects in groups. Moreover, students in groups will complete a term project at the end of the semester.

Course Objectives

The aim of this course is to give on overview of mathematical background of various fundamental algorithms used frequently in applications and scientific programming. They will, hopefully, be couraged to work in groups on some projects.

Course Learning Outcomes

At the end of the course students should have a good overview of algorithms and their complexities. They will have a knowledge of basic algorithms and they will gain the skills of applying algorithmic approaches to scientific problems. Studying in groups will provide them with the experiences and responsibilities of working in groups.

Tentative (Weekly) Outline

This course is intended to all students at the Institute. After a short introduction to Matlab various algorithms, their complexity will be introduced and symbolic, numerical and stochastic algorithms will be followed. Students will be encouraged to carry out several projects in groups. Moreover, students in groups will complete a term project at the end of the semester.

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#### IAM566 - Numerical Optimization

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Unconstrained Optimization: steepest descent, line search methods, trust-region methods, conjugate gradient methods, Newton and quasi-Newton methods, large-scale unconstrained optimization, least-square problems; Theory of Constrained Optimization; Linear Programming: simplex method, interior point method; Quadratic Programming; Active Set Methods; Interior Point Methods; Penalty, Barrier and Augmented Lagrangian Methods; Sequential Quadratic Programming.

Course Objectives

Computational science, engineering and applied mathematics face a growing need to develop algorithms, methods, and simulation codes that solve difficult and large scale problems. Solutions are desired that can provide designs, controls, and inversion results for the best choice of input parameters. Numerical optimization algorithms can provide computer scientist, engineers and mathematicians an avenue to the most desirable solution, automate the execution, and achieve efficient convergence rates.

This course is designed for graduate students majoring in mathematics as well as mathematically inclined graduate engineering students. At the end of this course, the student will:

- learn the central ideas behind algorithms for the numerical solution of differentiable optimization problems by presenting key methods for both unconstrained and constrained optimization, as well as providing theoretical justification as to why they succeed;
- learn the computational tools available to solving optimization problems on computers once a mathematical formulation has been found.

Course Learning Outcomes

Upon successful completion of this course, the student will be able to

- recognize the character of an optimization problem (constrained, unconstrained, smooth, nonsmooth) and choose appropriate algorithms for their solutions;
- understand the basic convergence analysis for the learned optimization methods;
- solve optimization problems using Matlab, Phyton, Julia or other commercial software;
- how to use and design efficient numerical optimization algorithms for their own research problems.

Tentative (Weekly) Outline

- Fundamentals of unconstrained optimization
- Line search methods
- Trust-region methods
- Conjugate gradient methods
- Newton and quasi-Newton methods
- Large-scale unconstrained optimization, least-square problems
- Theory of Constrained Optimization
- Linear Programming: simplex method
- Linear Programming: interior point method
- Quadratic programming
- Active set methods
- Interior point methods
- Penalty, barrier and augmented Lagrangian methods
- Sequential quadratic programming

Course Textbook(s)

- I. Griva, S. G. Nash and A. Sofer, Linear and nonlinear programming, 2nd edition, SIAM, Philadelphia, 2009
- J. Nocedal and S. J. Wright, Numerical Optimization, Springer, 1999

Supplementary Materials and Resources

- Books:
- J. F. Bannans, J. C. Gilbert, C. Lemaréchel and C. A. Sagastizábal, Numerical Optimization: Theoretical and Practical Aspects, Springer, 2006
- W. Forst and D. Hoffmann, Optimization -Theory and Practice, Springer, 2010
- R. Flechter, Practical Methods of Optimization, Wiley, 1987
- Lecture Notes:
- B. Karasözen and G.-W. Weber, Numerical Optimization: Constrained optimization, available at IAM Website (download)
- Resources:
- MATLAB Student Version is available to download on MathWorks website, http://www.mathworks.com, or METU FTP Severs (Licenced)

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#### IAM567 - Mathematical Modelling

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Models and cases studies from biology, engineering and mechanics, in form of ordinary and partial differential equations. Geometric and discrete models. Elements of inverse problems (image and data processing). Stochastic models in finance. Coursework and computer lab with MATLAB.

Course Objectives

This course gives an introduction to mathematical modelling of several systems and phenomena in science, enginerring and finance. In addition to the modelling techniques, numerical methods for solving these models are presented.

Course Learning Outcomes

Students will learn about the nature of mathematical modelling, starting with a physical or biological model, representing it mathematically, simplifying and solving the resulting model and interpreting the results. They will be suggested to work in teams, to communicate appropriately and to present their results.

Tentative (Weekly) Outline

Models and cases studies from biology, engineering and mechanics, in form of ordinary and partial differential equations. Geometric and discrete models. Elements of inverse problems (image and data processing). Stochastic models in finance. Coursework and computer lab with MATLAB.

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#### IAM568 - Mathematical Modelling of Transport Phenomena

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Introduction to transport phenomena, heat transfer, mass transfer and momentum transfer. Conservation laws, macroscopic balances with and without generation.

Course Objectives

The main aim of this course is to show students how to translate a real or engineering problem into a mathematical problem at both macroscopic and microscopic levels. The emphasis is on obtaining the equation representing a physical phenomenon and its interpretation. The pathway from the real problem to the mathematical problem has two stages: perception and formulation. The difficulties encountered in both of these stages can be easily solved by applying basic principles and laws, i.e., conservation of chemical species, conservation of mass, conservation of momentum, and conservation of energy.

Course Learning Outcomes

Most of students from basic sciences have difficulty in formulating real or engineering problems and in converting them to a mathematical problem. At the end of the course, the students will be able to mathematically formulate some engineering problems using basic conservation laws and principles.

Tentative (Weekly) Outline

Introduction to transport phenomena, heat transfer, mass transfer and momentum transfer. Conservation laws, macroscopic balances with and without generation.

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#### IAM569 - Wavelets,Transform Domain and Multiresolution Tech.

Credit: 3(2-2); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Wavelets, multiresolution analysis, applications of wavelets and multiresolution techniques. General constructions. Some important wavelets. Compactly supported wavelets. Multivariable wavelets. Estimators and Laplacian Pyramid decomposition. Adaptive de-noising and lossy compression. Parameter estimation. Uses in inverse problems. Uses in modelling and attractor reconstruction.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Wavelets, multiresolution analysis, applications of wavelets and multiresolution techniques. General constructions. Some important wavelets. Compactly supported wavelets. Multivariable wavelets. Estimators and Laplacian Pyramid decomposition. Adaptive de-noising and lossy compression. Parameter estimation. Uses in inverse problems. Uses in modelling and attractor reconstruction.

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Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Classification of dynamical systems according to resolution, basic qualitative features of dynamical systems, introduction of hybrid systems and their examples, hybrid systems according to different concerns, linear and piecewise linear systems, qualitative features of hybrid dynamical systems , hybrid models of complex non-linear dynamic systems Hybrid models of dynamical systems with delay, inference problem, intervention problem, hybrid control systems.

Course Objectives

Even thought hybrid systems are among the oldest technologies, their first formalization started with the process control applications. Today, use of hybrid systems are still increasing due to increasing extent of the automation and they posses several advances for emerging needs like modelling of several complex systems in biology, ecology, climatics, seismology, etc. This interdisciplinary course is aimed at providing a background and understanding of hybrid systems considering various approaches developed in dynamical systems theory, control theory and computer science.

Course Learning Outcomes

At the end of the course students are expected to attain an understanding of hybrid systems and the skills to solve real life modelling and control problems by using hybrid system models.

Tentative (Weekly) Outline

Classification of dynamical systems according to resolution, basic qualitative features of dynamical systems, introduction of hybrid systems and their examples, hybrid systems according to different concerns, linear and piecewise linear systems, qualitative features of hybrid dynamical systems , hybrid models of complex non-linear dynamic systems Hybrid models of dynamical systems with delay, inference problem, intervention problem, hybrid control systems.

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#### IAM571 - Applications of Differential Quadrature Method in Engineering

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Mathematical Fundamentals of Differential Quadrature method based on Polynomials and Fourier expansion, solution techniques for resulting equations, computation of weighting coefficients. Applications to Burger’s, Helmholtz, wave and Navier-Stokes equations. Applications to beams, thin plates, heat transfer, chemical reactor and Lubrication problems. Computer implementations.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Mathematical Fundamentals of Differential Quadrature method based on Polynomials and Fourier expansion, solution techniques for resulting equations, computation of weighting coefficients. Applications to Burger’s, Helmholtz, wave and Navier-Stokes equations. Applications to beams, thin plates, heat transfer, chemical reactor and Lubrication problems. Computer implementations.

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#### IAM572 - Finite Element Methods for Partial Differential Equations: Theory and Applications

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor (Elementary knowledge of PDEs, basics of linear algebra, basic MATLAB coding skills)

Course Catalogue Description

Abstract Finite Element Analysis: weak derivatives, Sobolev spaces, Lax-Milgram lemma; Piecewise Polynomials Approximations 1D and 2D: interpolation, projection; Finite Element Method 1D and 2D: weak formulation, derivation of linear system of equations, a priori estimates; Time Dependent Problems: finite differences for systems of ODE, stability estimates; Semi-elliptic equations; a posteriori Error Analysis: estimator, mesh Refinement

Course Objectives

This course is designed for graduate students majoring in mathematics as well as mathematically inclined graduate engineering students. At the end of this course, the student will:

- learn the fundamental concepts of the theory of the finite element method
- learn how to formulate and solve second order partial differential equations in one and two spatial dimensions using finite element method
- learn how to solve time dependent non(linear) problems using finite differences in time and finite element method in space
- develop proficiency in the applications of the finite element method (modelling, analysis, and interpretation of results) to realistic engineering problems through the use of major commercial general purpose finite element code
- learn to implement finite element method using MATLAB.

Course Learning Outcomes

Upon successful completion of this course, the student will be able to:

- formulate and solve (with a computer) second order partial differential equations in one and two spatial dimensions using finite element method
- derive a priori error bounds for elliptic equations in one and two spatial dimensions
- solve time dependent partial differential equations using finite element method in space and finite differences in time, and to compare different time stepping algorithms and choose appropriate algorithms
- apply the finite element methods in their thesis and understand the current research in this area
- evaluate different techniques for solving problems and be able to motivate when to use existing software and when to write new code
- use MATLAB in their own project work.

Tentative (Weekly) Outline

- Abstract Finite Element Analysis: weak derivatives, Sobolev spaces
- Abstract Finite Element Analysis: Lax-Milgram lemma
- Piecewise Polynomials Approximations 1D: interpolation, projection
- Finite Element Method 1D: weak Formulation, derivation of linear system of equations
- Finite Element Method 1D: computer Implementation
- Finite Element Method 1D: a priori error estimates
- Piecewise Polynomials Approximations 2D: meshes, interpolation, projection
- Finite Element Method 2D: weak formulation, derivation of linear system of equations
- Finite Element Method 2D: computer Implementation
- Finite Element Method 2D: a priori error estimates
- Time Dependent Problems: finite differences for systems of ODE
- Time Dependent Problems: stability Estimates, computer Implementation
- Semi-elliptic equations: discrete formulation
- A Posteriori Error Analysis: estimator, mesh refinement

Course Textbook(s)

- M. G. Larson and F. Bengzon, The Finite Element Method: Theory, Implementation, and Applications, Springer-Verlag Berlin Heidelberg, 2013.

Supplementary Materials and Resources

- Books:
- M. S. Gockenbach, Understanding and Implementing the Finite Element Method, SIAM, 2006.
- Resources:
- MATLAB

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#### IAM573 - System Parameter Estimation and its Applications

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Estimation theory, various estimation problems, modeling of deterministic systems, modeling of stochastic processes, linear estimators, nonlinear estimation, system identification, maximum likelihood and least squares estimation, denoising, impulse analysis of systems, density estimation.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Estimation theory, various estimation problems, modeling of deterministic systems, modeling of stochastic processes, linear estimators, nonlinear estimation, system identification, maximum likelihood and least squares estimation, denoising, impulse analysis of systems, density estimation.

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#### IAM581 - Special Topics in Financial Mathematics

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Contents vary from year to year according to interest of students and instructor in charge.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Contents vary from year to year according to interest of students and instructor in charge.

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#### IAM582 - Life Insurance Mathematics

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

The theory of compound interest: Effective and nominal interest rates, present values, annuities. Survival distributions and life tables. Life Insurance: Level benefit insurance, endowments, varying level benefit insurance. Life annuities. Benefit premiums. Benefit reserves.

Course Objectives

The theory of compound interest: effective and nominal interest rates, present values, annuities, survival distributions and life tables, life insurance: benefits, endowments, life annuities, benefit premiums and benefit reserves.

Course Learning Outcomes

Introduce the mathematical models used in life insurance with emphasis on the probabilistic approach.

Tentative (Weekly) Outline

The theory of compound interest: Effective and nominal interest rates, present values, annuities. Survival distributions and life tables. Life Insurance: Level benefit insurance, endowments, varying level benefit insurance. Life annuities. Benefit premiums. Benefit reserves.

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#### IAM583 - Pension Fund Mathematics

Credit: 3(3-0); ECTS: 8.0

Prerequisites: IAM582 - Life Insurance Mathematics

Course Catalogue Description

Risk theory for pension funds. Pension schemes for active and retired lives. Valuation of pension plans. Funding Methods: Unit Credit, Attained Age, Entry Age Normal and other Methods. Contributory and Benefit Plans.

Course Objectives

Introduce the actuarial cost and contributory plan concepts, theory and methods for pension funds.

Course Learning Outcomes

Introduce the actuarial cost and contributory plan concepts, theory and methods for pension funds.

Tentative (Weekly) Outline

- Introduction, Pension Benefits
- Increasing Cost Individual Cost methods
- Level Cost Individual Cost methods
- Aggregate Cost Methods
- Experience Gains and Losses
- Changes and Ancillary Benefits
- Options and Assets
- Comparisons of Methods and retirement systems
- Individual Retirement Systems (BES)
- Social Security Systems
- Term Project Presentations

Course Textbook(s)

- W.H. Aitken, "A Problem Solving Approach to Pension Funding and valuation", ACTEX Publications, 1996 (second edition)
- A.W. Anderson, "Pension Mathematics for Actuaries", ACTEX Publications, 1992
- Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A., Nesbitt, C.J., "Actuarial Mathematics", The Society of Actuaries, 1997

Supplementary Materials and Resources

- Beard, R.E., Pentikainen, T., Pesonen, E., "Risk Theory, The Stochastic Basis of Insurance", Chapman and Hall, 1994
- R.Booth, R.Chadburn, D.Cooper, S. Haberman, D.James, "Modern Actuarial Theory and Practice", Chapman and Hall, 1999
- C.D. Daykin, T. Pentikainen, M. Pesonen, "Practical Risk Theory for Actuaries", Chapman and Hall, 1994
- H.U. Gerber, "Life Insurance Mathematics", Springer, 1997
- W-R. Heilmann, "Fundamentals of Risk Theory", WW Karlsruhe, 1988
- L.Workman, "Mathematical Foundations of Life Insurance" LOMA-Life Office Management Association, 1992

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#### IAM584 - Advanced Actuarial Mathematics

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Insurance models including expenses. Special annuities and insurance. Advanced multiple life theory. Population theory. Interest as a random Variable.

Course Objectives

Developing knowledge and skills in actuarial analyses. Using probability and statistics, stochastic processes and advanced mathematical methods in actuarial model building and applications. Insurance models. Multiple life and multiple decrements theory.Actuarial risk. Population theory. Interest as a random variable.

Course Learning Outcomes

Tentative (Weekly) Outline

Insurance models including expenses. Special annuities and insurance. Advanced multiple life theory. Population theory. Interest as a random Variable.

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#### IAM585 - Decision-Making Under Uncertainty

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Basic methods based on probability. Distorted probabilities. Decision and utility theories, state dependent utilities, risk taking agent types. Techniques for bounding the effects of missing information or the effects of incorrect information. Trading time and space resources with certainty. Fusing uncertain information of different kinds. Real-time inference algorithms.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Basic methods based on probability. Distorted probabilities. Decision and utility theories, state dependent utilities, risk taking agent types. Techniques for bounding the effects of missing information or the effects of incorrect information. Trading time and space resources with certainty. Fusing uncertain information of different kinds. Real-time inference algorithms.

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#### IAM589 - Term Project

Credit: 0(0-2); ECTS: 20.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

M.S. students working on a common area choose a research topic to study and present to a group under the guidance of a faculty member.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

M.S. students working on a common area choose a research topic to study and present to a group under the guidance of a faculty member.

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#### IAM590 - Graduate Seminar

Credit: 0(0-2); ECTS: 10.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

This course is designed to provide students with a chance to prepare and present a professional seminar on subjects of their own choice.

Course Objectives

Preparing the students to give short (20 min) talks.

Course Learning Outcomes

At the end of the course students should be to give good presentations.

Tentative (Weekly) Outline

This course is designed to provide students with a chance to prepare and present a professional seminar on subjects of their own choice.

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#### IAM591 - Programming Techniques in Applied Mathematics

Credit: 2(2-0); ECTS: 6.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

LaTeX and Matlab; Basic Commands and Syntax of LaTeX and Matlab; Working within a Research Group via Subversion; Arrays and Matrices; Scripts and Function in Matlab; Commands and Environments in LaTeX; More on Matlab Functions; Toolboxes of Matlab; Packages in LaTeX; Graphics in Matlab; Handling Graphics and Plotting in LaTeX; Advanced Techniques in Matlab: memory allocation, vectoristaion, object orientation, scoping, structures, strings, file streams.

Course Objectives

At the end of this course, the student will learn:

- basic programming techniques
- writing their own procedures and functions
- handling with graphics and functions
- cooperating and working with others using subversion
- debugging and optimising their programs
- reporting their work in scientific typesetting using LaTeX

Course Learning Outcomes

Student, who passed the course satisfactorily will be able to:

- collaborate with members of their groups while improving their codings
- prepare their reports and presentations in scientific typesetting LaTeX
- learn and improve their Matlab knowledge in programming

Tentative (Weekly) Outline

- Introduction: installation and basics
- Basic Commands and Syntax: LaTeX and Matlab
- Subversion: getting ready to collaborate
- Basic Programming Structures and Datatypes
- Arrays and Matrices
- Defining Commands and Environments in LaTeX
- Scripts and Functions in Matlab
- Working with Function Handles in Matlab
- Toolboxes and Environments
- Graphics: handling and plotting
- Optimising and Debugging the Codes
- Object Orientation Programming (OOP): basics
- Projects
- Project Presentations: the beamer class

Course Textbook(s)

- Tobin A. Driscoll, Learning MATLAB, SIAM, 2009
- Tobias Oetiker, Hubert Partl, Irene Hyna and Elisabeth Schlegl, The Not So Short Introduction to LaTeX 2e, 2016 (https://tobi.oetiker.ch/lshort/lshort.pdf)

Supplementary Materials and Resources

- Readings:
- http://www.mathworks.com/support/learn-with-matlab-tutorials.html
- https://en.wikibooks.org/wiki/LaTeX
- Resources:
- MATLAB Student Version is available to download on MathWorks website, http://www.mathworks.com, or METU FTP Servers (Licenced)
- MikTeX for LaTeX can be downloaded from http://miktex.org

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#### IAM592 - Programming Techniques in Applied Mathematics II

Credit: 2(2-0); ECTS: 6.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Review of Programming and Toolboxes, Packages, Modules; Iterative Linear Algebra Problems; Root Finding Programs; Recursive Functions and Algorithms; Optimisation Algorithms; Data Fitting and Interpolation; Extrapolation; Numerical Integration; Numerical Solutions of Differential Equations: IVPs and BVPs; Selected Topics (algorithms and coding in different fields).

Course Objectives

At the end of this course, the student will learn:

- how to solve linear algebra equations
- how to solve root finding problems in different fields
- recursive algorithms
- how to solve optimisation problems
- data analysis tools and data description
- numerical integration methods to calculate integrals involved in applied mathematics
- how to numerically solve initial as well as boundary value problems in differential equations

Course Learning Outcomes

Student, who passed the course satisfactorily will be able to:

- understand basic problems in applied mathematics
- be aware of possible ways to solve problems from different fields
- analise and interpret data from measurements or observations
- numerically solve basic optimisation problems
- numerically solve basic differential equations

Tentative (Weekly) Outline

- Review of Programming and Toolboxes, Packages, Modules
- Iterative Linear Algebra Problems
- Root Finding Problems
- Recursive Functions and Algorithms
- Optimisation Algorithms
- Data Fitting and Interpolation (and Extrapolation)
- Numerical Integration
- Numerical Solutions of Differential Equations: IVPs and BVPs
- Selected Topics: algorithms and coding distinctively from
- Actuarial Sciences
- Cryptography
- Financial Mathematics
- Scientific Computing

Course Textbook(s)

- Tobin A. Driscoll, Learning MATLAB, SIAM, 2009
- Tobias Oetiker, Hubert Partl, Irene Hyna and Elisabeth Schlegl, The Not So Short Introduction to LaTeX 2e, 2016 (https://tobi.oetiker.ch/lshort/lshort.pdf)

Supplementary Materials and Resources

- Readings:
- http://www.mathworks.com/support/learn-with-matlab-tutorials.html
- https://en.wikibooks.org/wiki/LaTeX
- Resources:
- MikTeX for LaTeX can be downloaded from http://miktex.org

More Info on METU Catalogue

#### IAM600 - Ph.D. Thesis

Credit: 0(0-0); ECTS: 130.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Program of research leading to Ph.D. degree arranged between the student and a faculty member. Students register to this course in all semesters starting from the beginning of their second semester while the research program or write up of thesis is in progress.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Program of research leading to Ph.D. degree arranged between the student and a faculty member. Students register to this course in all semesters starting from the beginning of their second semester while the research program or write up of thesis is in progress.

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#### IAM601 - Elliptic Curves

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

The Geometry of Elliptic Curves: Weirstrass equations, The group law, j-invariants, Isogenies, The dual isogeny, The Tate module, The Weil pairing. The Formal Group of an Elliptic Curve: Expansion around 0, Formal groups, Groups associated to formal groups, The invariant differential, The formal logarithm, Formal Groups over discrete valuation rings. Elliptic Curves over Finite Fields: Number of rational points, The Weil conjectures, The Endomorphism rings, Calculating Hasse invariant.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

The Geometry of Elliptic Curves: Weirstrass equations, The group law, j-invariants, Isogenies, The dual isogeny, The Tate module, The Weil pairing. The Formal Group of an Elliptic Curve: Expansion around 0, Formal groups, Groups associated to formal groups, The invariant differential, The formal logarithm, Formal Groups over discrete valuation rings. Elliptic Curves over Finite Fields: Number of rational points, The Weil conjectures, The Endomorphism rings, Calculating Hasse invariant.

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#### IAM602 - Algebraic Geometric Codes

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

AG-Codes: Constructions and properties, Duality and spectra, Codes of small genera, Elliptic codes, Other families of AG-Codes, Decoding: Basic algorithm, modified algorithm, Asymptotic results: Basic AG-bounds, Expurgation bound. Constructive bounds, Other bounds.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

AG-Codes: Constructions and properties, Duality and spectra, Codes of small genera, Elliptic codes, Other families of AG-Codes, Decoding: Basic algorithm, modified algorithm, Asymptotic results: Basic AG-bounds, Expurgation bound. Constructive bounds, Other bounds.

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#### IAM603 - Computational Number Theory

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

The aim of computational number theory is the design, implementation and analysis of algorithms for solving problems in number theory. This includes efficient algorithms for computing fundamental invariants in algebraic number fields and algebraic function fields, as well as deterministic and probabilistic algorithms for solving the discrete logarithm problem in any structure. Computational methods in quadratic fields.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

The aim of computational number theory is the design, implementation and analysis of algorithms for solving problems in number theory. This includes efficient algorithms for computing fundamental invariants in algebraic number fields and algebraic function fields, as well as deterministic and probabilistic algorithms for solving the discrete logarithm problem in any structure. Computational methods in quadratic fields.

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#### IAM611 - Numerical Methods for Financial Models

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Numerical methods for discrete time models: Algorithms for option prices, algorithms for discrete time optimal control problems. Reminders on continuous models: Stochastic Calculus, option pricing and partial differential equations, dynamic portfolio optimization. Monte-Carlo methods for options: Convergence results, variance reduction, simulation of stochastic processes, computing the hedge, Monte-Carlo methods for pricing American options. Finite difference methods for option prices: numerical analysis of elliptic and parabolic Kolmogrov equations, computation of European and American option prices in the lognormal model. Finite difference methods for stochastic control problems: Markov Chain approximation method, elliptic Hamilton-Jacobi-Bellman equations, computational methods.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Numerical methods for discrete time models: Algorithms for option prices, algorithms for discrete time optimal control problems. Reminders on continuous models: Stochastic Calculus, option pricing and partial differential equations, dynamic portfolio optimization. Monte-Carlo methods for options: Convergence results, variance reduction, simulation of stochastic processes, computing the hedge, Monte-Carlo methods for pricing American options. Finite difference methods for option prices: numerical analysis of elliptic and parabolic Kolmogrov equations, computation of European and American option prices in the lognormal model. Finite difference methods for stochastic control problems: Markov Chain approximation method, elliptic Hamilton-Jacobi-Bellman equations, computational methods.

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#### IAM612 - Financial Modeling With Jump Processes

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Lévy processes. Building Lévy processes. Multidimensional models with jumps. Simulation of Lévy processes. Option pricing with jumps: Stochastic calculus for jump processes, measure transformations for Lévy processes, pricing and hedging in complete markets, risk-neutral modeling with exponential Lévy processes. Integro-differential equations and numerical methods. Inverse problems and model calibration.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Levy processes. Building Levy processes. Multidimensional models with jumps. Simulation of Levy processes. Option pricing with jumps: Stochastic calculus for jump processes, measure transformations for Lévy processes, pricing and hedging in complete markets, risk-neutral modeling with exponential Levy processes. Integro-differential equations and numerical methods. Inverse problems and model calibration.

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#### IAM613 - Finance and Stochastics In Insurance

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Risk in insurance systems. Short, medium and long term financial structures of insurance funds. Modelling and valuation of insurance plans. Contribution and benefit schemes for insurance and reinsurance. Economic dynamics, financial markets and assets management for insurance systems. Multiple decrements, actuarial balance and fair premiums.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Risk in insurance systems. Short, medium and long term financial structures of insurance funds. Modelling and valuation of insurance plans. Contribution and benefit schemes for insurance and reinsurance. Economic dynamics, financial markets and assets management for insurance systems. Multiple decrements, actuarial balance and fair premiums.

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#### IAM614 - Methods of Computational Finance

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Numerical Methods for Discrete Time Models: binomial method for options; discrete time optimal control problems. Reminders on Continuous Models: Ito process and its applications in stock market, Black-Scholes equation and its solution; Hedging, Volatility smile. Monte Carlo Method for Options: generating random numbers, transformation of random variables and generating normal variates; Monte Carlo integration; pricing by Monte Carlo integration; variance reduction techniques, quasi-random numbers and quasi-Monte Carlo method. Finite Difference Methods for Options: explicit and implicit finite difference schemes, Crank-Nicolson method; Free-Boundary Problems for American options. Finite Difference Methods for Control Problems: Markov Chain approximation method, elliptic Hamiltion-Jacobi-Bellman equations, computational methods.

Course Objectives

At the end of this course, the student will learn:

- the basics of fixed income securities and portfolio optimisation under discrete time models
- European and American type option pricing via Binomial (Lattice or Tree) method
- how to derive and solve the famous Black-Scholes differential equation for options
- Monte Carlo methods and variance reduction techniques in option pricing
- to generate pseudo-random numbers from a given distribution, in particular, normal distribution
- the basics of numerical solutions of stochastic differential equations, Euler-Maruyama scheme
- finite-difference methods to solve partial differential equations (PDEs) and apply the techniques in valuation of options
- the basic principles of pricing American options using PDEs and hence free boundary problems
- basic principles of control problems

Course Learning Outcomes

Student, who passed the course satisfactorily will be able to:

- apply basic optimisation algorithms to portfolio management and optimisation problems
- approximately price simple as well as complex (exotic) options by Binomial method
- use the famous Black-Scholes pricing formulae for vanilla options that are European type
- simulate stochastic differential equations using Euler-Maruyama scheme
- price options by Monte Carlo approach with variance reduction techniques
- price European and American options using finite difference approximation for the underlying PDE
- understand basic principles of control problems

Tentative (Weekly) Outline

- Fixed Income Securities
- Portfolio Optimisation
- Option Pricing by Binomial Method
- Stochastic Differential Equations
- Black-Scholes PDE
- Black-Scholes Formulae
- Generating Random Samples (Numbers)
- Monte Carlo Methods for Options
- Variance Reduction Techniques
- Finite-Difference Methods for Diffusion Equations
- Option Pricing by Partial Differential Equations
- Finite Difference Methods for American Options
- Finite Difference Methods for Control Problems
- Hamilton-Jacobi-Bellman Equations

Course Textbook(s)

- Uğur, Ö., An Introduction to Computational Finance, Imperial College Press, 2009
- Seydel, R., Tools for Computational Finance, 5th edition, Springer-Verlag, 2012

Supplementary Materials and Resources

- Books:
- Paolo Brandimarte, Numerical Methods in Finance and Economics (2nd ed.), 2006
- Readings:
- Resources:
- MATLAB Student Version is available to download on MathWorks website, http://www.mathworks.com, or METU FTP Servers (Licenced)

More Info on METU Catalogue

#### IAM615 - Advanced Stochastic Calculus for Finance

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Financial modelling beyond Black-Scholes Model. Stochastic processes. Building Lévy processes. Option pricing with stochastic processes: Stochastic calculus for semimartingales, change of measure, exponential Lévy processes, stochastic volatility models, pricing with stochastic volatility models. Hedging in incomplete markets, risk-neutral modeling. Integro-partial differential equations. Further topics in numerical solutions, simulation and calibration of stochastic processes.

Course Objectives

The current market models using Brownian Motion have difficulty in accounting for the abrupt changes of financial markets, whereas models based on Lévy processes, themselves practically a combination of Brownian motions and Poisson processes, are more incline to respond to this need. This course reconsiders almost all the models used in Financial Mathematics beyond Black-Scholes model and completes the knowledge of students who have already been initiated to models in terms of the Brownian Motion.

Course Learning Outcomes

Tentative (Weekly) Outline

Financial modelling beyond Black-Scholes Model. Stochastic processes. Building Lévy processes. Option pricing with stochastic processes: Stochastic calculus for semimartingales, change of measure, exponential Lévy processes, stochastic volatility models, pricing with stochastic volatility models. Hedging in incomplete markets, risk-neutral modeling. Integro-partial differential equations. Further topics in numerical solutions, simulation and calibration of stochastic processes.

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#### IAM664 - Inverse Problems

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of instructor (Basic knowledge in numerical and statistical methods and, if possible, in probability theory)

Course Catalogue Description

Classification of inverse problems, linear regression, discretizing continuous inverse problems, rank-deficiency, Tikhonov regularization, iterative methods, other regularization techniques, Fourier techniques, nonlinear inverse problems, Bayesian methods. Computer applications and MATLAB exercises are important elements of the course.

Course Objectives

- The objective of this course is to promote fundamental understanding of parameter estimation and inverse problems methodology, specifically regarding such issues like uncertainty, ill-posedness, regularization, bias and resolution using examples from various fields of applications, e.g., engineering, financial mathematics, economics, the environmental sector, Operational Research, computational biology and social sciences.

Course Learning Outcomes

- At the end of the course, students should have a good overview of modern scientific methods in inverse problems. They should also be able to choose and work them out appropriately in contexts of project applications and of their theses.

Tentative (Weekly) Outline

- Introduction
- Linear Regression
- Least Squares Theory
- Discretizing Continuous Inverse Problems
- Rank Deficiency and Ill-Conditioning
- Tikhonov Regularization
- Iterative Methods
- Fourier Techniques
- Other Regularization Techniques
- Nonlinear Inverse Problems
- Nonlinear Regression
- Nonlinear Least Squares
- Bayesian Methods
- Application to Tomography
- Discrete Tomography

Course Textbook(s)

- A. Aster, B. Borchers, C. Thurber, Parameter Estimation and Inverse Problems, Academic Press, 2nd edition, 2012

Supplementary Materials and Resources

- Books:
- J. Baumeister, Stable Solutions of Inverse Problems, Vieweg, 1987
- H.W. Engl, M. Hanke, A. Neubauer, Regularization of Inverse Problems, Kluwer, 1996
- P.C. Hansen, Rank-Deficient and Ill-Posed Problems, SIAM, 1996
- G.T. Herman, A. Kuba, Discrete Tomography: Foundations, Algorithms and Applications, Birkhaeuser, 1999
- A.N. Tikhonov, V.Y. Arsenin, Solution of Ill-Posed Problems, Wiley, 1977
- Resources:
- Lecture Notes: Furthermore, lecture notes and recent research articles will be provided during the course

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#### IAM665 - Advanced Continuous Optimization

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Globalization techniques, semidefinite and conic optimization, derivative free optimization, semi-infinite optimization methods, Newton Krylov methods, nonlinear parameter estimation and advanced spline regression, multi-objective optimization, nonsmooth optimization, optimization in support vector machines.

Course Objectives

The advances in computer technology have promoted the field of nonlinear optimization, which has become today an essential tool to solve intelligently complex scientific and engineering problems. The course will provide an introduction to modern continuous optimization algorithms which are used in most of the optimization software.

Course Learning Outcomes

Students will be able to understand how different optimization work and able to compare them. The emphasis of the course will be on the analysis of methods and their application to concrete problems based on an very well understanding of the foundations. Finally, short lectures prepared by the students and additionally embedded into the class hours will serve for a better learning, a support of existing thesis projects and for a growing maturity in presenting and teaching by those young colleagues.

Tentative (Weekly) Outline

Globalization techniques, semidefinite and conic optimization, derivative free optimization, semi-infinite optimization methods, Newton Krylov methods, nonlinear parameter estimation and advanced spline regression, multi-objective optimization, nonsmooth optimization, optimization in support vector machines.

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#### IAM690 - Graduate Seminar for Ph.D. Students

Credit: 0(0-2); ECTS: 10.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

This course is designed to provide students with a chance to prepare and present a professional seminar on subjects of their own choice. Students can work independently in issues that require expertise; they can share and make presentations of their research both verbally and in written form.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

This course is designed to provide students with a chance to prepare and present a professional seminar on subjects of their own choice. Students can work independently in issues that require expertise; they can share and make presentations of their research both verbally and in written form.

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#### IAM698 - Research Methods and Ethics

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

This course is a fundamental course for any kind of graduate program since its focus is on the scientific research methods. It provides an introduction to the research design as well as ethical issues in scientific research. More specifically, the course provides students with an integrated framework for doing research. Students will gain methodological skills which will assist them in applying to the research process, such as defining the research questions, design and define the research methods, survey design, data inquiries. In this way, the students learn to manage their thesis writing process independently, writing their own research paper. The role of ethics in research, ethical issues in conducting research will be emphasized to assure ethical aspects in scientific research.

Course Objectives

At the end of this course, participants will be able to:

- To identify the major approaches to educational research and related models for planning, analyzing, implementing and critiquing research;
- To understand the essential characteristics of basic research methods and their applications to research questions;
- To provide the knowledge and skills necessary to conduct research and to apply these skills in the development of a search proposal that investigates a question of personal interest;
- To be cautious and respectful to the other studies done in the literature.

Course Learning Outcomes

Tentative (Weekly) Outline

- Week 1: Introduction and nature of research
- Week 2: Principles of scientific inquiry
- Week 3: Conducting research: Research questions
- Week 4: Conducting research: Research design and methodology
- Week 5: Literature survey in research process
- Week 6-8: Research methods: Quantitative and qualitative, Survey research, Data collection and processing
- Week 9: Data use policy and ethics
- Week 10: Writing a research article: Strategizing, Structure and contents
- Week 11-13: Ethical Issues: Research, science, scientific evaluation, collaboration
- Week 14: Paper Submission, handling reviews and revisions
- Week 15: Term Project presentations

Course Textbook(s)

- Recker, J., Scientific Research in Information Systems: A Beginner’s Guide, Springer, 2013.
- Fraenkel, J.R. & Wallen, N.E., Hyun, H.H. (2012). How to design and evaluate research in education.(8th Ed.) McGraw-Hill Publishing Company. (International Edition).
- Creswell, J. W. (2012). Educational Research. Planning, Conducting, and Evaluating Quantitative & Qualitative Research. (4th Ed.). Pearson International Education
- Yüksek Öğrenim Kurumları Etik Davranış İlkeleri, http://kurul.odu.edu.tr/files/akademik-etik-ilkeler.pdf
- American Mathematical Society, http://www.ams.org/about-us/governance/policy-statements/sec-ethics

Supplementary Materials and Resources

- Christensen, L. B. (2001). Experimental Methodology. Needham Heights, MA: Allyn & Bacon.
- Strauss, A. & Corbin, J. (1990). Basics of qualitative research: grounded theory, procedures and techniques. Newbury Park, CA: Sage.

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#### IAM701 - Special Topics: Security Tests in Cryptography

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Courses not listed in catalogue. Contents vary from year to year according to the interest of students and instructor in charge.

Course Objectives

Course Learning Outcomes

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#### IAM702 - Special Topics: Quantum Information Theory

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Courses not listed in catalogue. Contents vary from year to year according to the interest of students and instructor in charge.

Course Objectives

The aim of this course is to introduce students with previous exposure to basic quantum information theory to more advanced topics.

Course Learning Outcomes

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#### IAM703 - Special Topics in Cryptography

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Courses not listed in catalogue. Contents vary from year to year according to the interest of students and instructor in charge.

Course Objectives

Course Learning Outcomes

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#### IAM704 - Special Topics On Hash Functions, Authentication Codes and Nonlinearity

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Course Objectives

The aim of this course is to introduce the students to some recent results on hash functions, authentication codes, connections with coding theory, function fields and cryptography. The emphasis will be on new constructions of hash functions and authentication schemes, and their relations with nonlinearity and function fields.

Course Learning Outcomes

Tentative (Weekly) Outline

Algebra-Geometric construction of hash functions and authentication codes, highly nonlinear mappings and their relations with exponential sums and algebraic function fields.

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#### IAM705 - Stream Cipher Cryptanalysis

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Course Objectives

The most significant issue in cryptographic system design may be developing tools and building blocks to make the system satisfactory resistant to known or expected attacks. This common criteria requires understanding analysis methods, especially for original designs. After taking the course, students can both enhance their skills in stream cipher design and gain an active research capacity on stream cipher cryptanalysis.

Course Learning Outcomes

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#### IAM706 - Special Topics on Cryptanalysis of Symm. Cipher Syst.

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Course Objectives

Course Learning Outcomes

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#### IAM707 - Special Topics: Block Ciphers

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Course Objectives

The primary focus of this course will be on definitions and constructions of Block Ciphers. Course will mainly cover what security properties are desirable in such ciphers, how to properly obtain these properties, and how to design systems satisfying given properties.

Course Learning Outcomes

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#### IAM708 - Special Topics: Cryptoanalysis of Recent Steram Ciphers

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Course Objectives

Course Learning Outcomes

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#### IAM709 - Special Topics: Nonlinear Feedback Shift Registers

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Nonlinear Feedback Shift Registers: Generating Functions, and Families of Recurring Sequences, Characterizations and Properties of Nonlinear Recurring Sequences. Boolean Functions, Linear Complexity and Nonlinear Complexity (span). Combining NFSR’s. Steam Ciphers Using NFSRs. GRAIN.

Course Objectives

The aim of this course is to introduce the students to some recent research areas in cryptography related with stream ciphers. The emphasis will be on nonlinear feedback shift register and their properties. Also design criteria for stream ciphers using NFSR’s and their cryptanalysis will be discussed.

Course Learning Outcomes

Tentative (Weekly) Outline

Nonlinear Feedback Shift Registers: Generating Functions, and Families of Recurring Sequences, Characterizations and Properties of Nonlinear Recurring Sequences. Boolean Functions, Linear Complexity and Nonlinear Complexity (span). Combining NFSR’s. Steam Ciphers Using NFSRs. GRAIN.

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#### IAM710 - Special Topics: Implement. Issues in Public Key Syst.

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Course Objectives

Course Learning Outcomes

How to design and implement a cryptosystem and the difficulties encountered during the implementation processes.

#### IAM711 - Elliptic Curve Cryptography

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Algorithms to compute the number of points of an Elliptic Curve, Divisors, Pairings, The crypto system based on pairings, isomorphism attacks to elliptic curve discrete logarithm problem (ECDLP) and the other attacks.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Algorithms to compute the number of points of an Elliptic Curve, Divisors, Pairings, The crypto system based on pairings, isomorphism attacks to elliptic curve discrete logarithm problem (ECDLP) and the other attacks.

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#### IAM712 - Applications of Finite Fields to Cryptography

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

The primary focus of this course is to give structure theory of Finite Fields and the related mathematical tools that are needed in Cryptography: Polynomials over finite fields, factorization of Polynomials over finite fields, Exponential Sums, Gröbner Basis Algorithms and Their Applications to Cryptography will be discussed.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

The primary focus of this course is to give structure theory of Finite Fields and the related mathematical tools that are needed in Cryptography: Polynomials over finite fields, factorization of Polynomials over finite fields, Exponential Sums, Gröbner Basis Algorithms and Their Applications to Cryptography will be discussed.

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#### IAM713 - Pairing-Based Cryptography

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Course Objectives

Course Learning Outcomes

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Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

The aim of this course is to study the various constructions of elliptic curves having large prime-order subgroups with small embedding degrees. We will study complex multiplication and other methods for this constructions and study the recommended pairing –friendly elliptic curves so far discussed in the litarature. We will also give efficient implementations of Tate Pairing and Pairing Based-Protocols.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

The aim of this course is to study the various constructions of elliptic curves having large prime-order subgroups with small embedding degrees. We will study complex multiplication and other methods for this constructions and study the recommended pairing –friendly elliptic curves so far discussed in the litarature. We will also give efficient implementations of Tate Pairing and Pairing Based-Protocols.

#### IAM715 - Cryptography and Coding Theory

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Additive and non-additive quantum codes, Boolean functions, operator quantum error correction, projection operators in Hilbert space, quantum error correction, Quadratic functions, t-Design, linear codes and self-dual codes, MDS codes, Reed Solomon Codes.

Course Objectives

At the end of the course, the student will learn:

- fundamental properties of Boolean Functions together with its connections to cryptography and related areas;
- incidence structures and combinatorial t-designs and their applications in coding theory, cryptography and communications;
- types of linear and self-dual code;
- MDS codes and constructions of self-dual MDS codes;
- Reed Solomon codes and relationship between Reed Solomon codes and algebraic geometry codes.

Course Learning Outcomes

Student, who passed the course satisfactorily will be able to:

- understand cryptographic properties of Boolean functions;
- understand t-designs and its connection to coding theory;
- give types of linear and self-dual codes;
- define MDS codes and construct of self-dual MDS codes;
- define Reed Solomon codes and giving relationship between Reed Solomon codes and algebraic geometry codes.

Course Textbook(s)

- D. W. Cohen ,"An Introduction to Hilbert Space and Quantum Logic", Springer-Verlag New York, 1989, doi: 10.1007/978-1-4613-8841-8.

Supplementary Materials and Resources

- C. Xiang, X. Ling, Q. Wang, "Combinatorial t-designs from quadratic functions", arXiv: 1903.07375, 2019.
- L. Sok, "Explicit Constructions of MDS Self-Dual Codes", IEEE Transactions on Information Theory (Volume:66, Issue:6, June 2020 ) pages: 3603-3615.
- L. Sok, "New families of self-dual codes", arXiv: 2005.00726 v1, 2020.
- V. Aggarwal and A. R. Calderbank, "Boolean Functions, Projection Operators, and Quantum Error Correcting Codes," in IEEE Transactions on Information Theory, vol. 54, no. 4, pp. 1700-1707, April 2008.

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#### IAM716 - Special Topics: Sequence Design and Rings

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Finite fields and finite rings, Sequnces, power series, Linear feedback shift registers and linear recurrences, Algebraic feedback shift register sequences, Pseudo-random sequences, Correlation, Special types of good sequences, Sequence synthesis, Some codes over rings.

Course Objectives

At the end of this course, the student will learn:

- to provide basic background on finite commutative rings
- their applications in cryptography and related areas

Course Learning Outcomes

Student, who passed the course satisfactorily will be able to:

- learn basic techniques in finite rings
- learn properties of sequences in application to cryptography and related area
- learn some design techniques

Tentative (Weekly) Outline

Finite fields and finite rings, Sequnces, power series, Linear feedback shift registers and linear recurrences, Algebraic feedback shift register sequences, Pseudo-random sequences, Correlation, Special types of good sequences, Sequence synthesis, Some codes over rings.

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#### IAM717 - Cryptological Characteristics of Boolean Function and S-Boxes

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Course Objectives

Course Learning Outcomes

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#### IAM718 - Special Topics: Block Cipher Cryptanalysis

Credit: 3(3-3); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Design principles of block ciphers. Differential cryptanalysis and linear cryptanalysis. Differential cryptanalysis of FEAL, LOKI, MacGuffin. Linear cryptanalysis of FEAL, DES. Combined attacks: differential-linear cryptanalysis, impossible differentials, boomerang attack, rectangle attack. Key schedule analysis: related key attacks, slide attack, reflection attack. Other attacks: interpolation attack, integral cryptanalysis.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Design principles of block ciphers. Differential cryptanalysis and linear cryptanalysis. Differential cryptanalysis of FEAL, LOKI, MacGuffin. Linear cryptanalysis of FEAL, DES. Combined attacks: differential-linear cryptanalysis, impossible differentials, boomerang attack, rectangle attack. Key schedule analysis: related key attacks, slide attack, reflection attack. Other attacks: interpolation attack, integral cryptanalysis.

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#### IAM719 - Special Topics: Algorithmic Number Theory

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

The aim of this course is to introduce advanced topics in algorithmic number theory for cryptographic purposes such as number field sieve algorithm for integer factorization and cryptography based on ideal class groups of quadratic number fields.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

The aim of this course is to introduce advanced topics in algorithmic number theory for cryptographic purposes such as number field sieve algorithm for integer factorization and cryptography based on ideal class groups of quadratic number fields.

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#### IAM720 - Special Topics: Hyperelliptic Curve

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Course Objectives

Course Learning Outcomes

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#### IAM721 - Special Topics: Sequence Synthesis Algorithmin Cryptography

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

The students are expected to know the theory of Finite Fields. The aim of this course is to teach how to construct algebraic sequences over finite rings for cryptographic purposes. We will generalize certain algebraic sequences over Finite Fields to finite commutative rings and in particular Galois Rings. There has been an increasing interest on this topic in the last decade.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

The students are expected to know the theory of Finite Fields. The aim of this course is to teach how to construct algebraic sequences over finite rings for cryptographic purposes. We will generalize certain algebraic sequences over Finite Fields to finite commutative rings and in particular Galois Rings. There has been an increasing interest on this topic in the last decade.

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#### IAM722 - Special Topics: Algebraic Aspects of Nonlinear Functions

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

This course introduces various aspects of nonlinearity in cryptography together with its connections to geometry, number theory, design theory, coding theory and related areas.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

This course introduces various aspects of nonlinearity in cryptography together with its connections to geometry, number theory, design theory, coding theory and related areas.

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#### IAM724 - Special Topics: Introduction to Cryptographic Hardware Design

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Combinational and sequential logic design, digital systems; hardware description languages (HDLs), reconfigurable logic devices; basic building blocks for cryptography; hardware design block ciphers, stream ciphers, asymmetrical cipher; design examples.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Combinational and sequential logic design, digital systems; hardware description languages (HDLs), reconfigurable logic devices; basic building blocks for cryptography; hardware design block ciphers, stream ciphers, asymmetrical cipher; design examples.

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#### IAM725 - Cryptography Processor Design

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Course Objectives

Course Learning Outcomes

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#### IAM726 - Special Topics: Introduction to Arithmetic Complexity of Computation

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

This course gives an introduction in the complexity theory of basic arithmetic operations. We will study the inherent difficulties of solving them. By this way, we will give arithmetic complexity bounds of some operations used in cryptographic implementations.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

This course gives an introduction in the complexity theory of basic arithmetic operations. We will study the inherent difficulties of solving them. By this way, we will give arithmetic complexity bounds of some operations used in cryptographic implementations.

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#### IAM727 - Special Topics: Combinatorics

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

The aim of this course is to introduce basic and advanced topics of combinatorics.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

The aim of this course is to introduce basic and advanced topics of combinatorics.

#### IAM728 - Special Topics: Design Theory And Cryptography

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Course Objectives

Course Learning Outcomes

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#### IAM729 - Special Topics: Normal Bases in Finite Fields

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

This course introduces some fundamental results in normal bases of low complexity together with its connections to cryptography and related areas.

Course Objectives

The aim of this course is to study some recent developments in representation of elements of finite fields. The main topics are construction of normal bases, optimal normal bases, normal bases of low complexity and the existence and nature of completely free elements in finite fields. The emphasis will be given on the

- some properties of characterization of normal elements,
- composition of normal bases and constructions of optimal bases.
- We will also study how to obtain good complexity normal elements in finite fields.

Course Learning Outcomes

This course will be beneficial for students interested in finite fields and their applications in cryptography and coding theory. At the end of this course, it is expected that students should have a good overview of recent approaches in normal bases over finite fields.

Tentative (Weekly) Outline

This course introduces some fundamental results in normal bases of low complexity together with its connections to cryptography and related areas.

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#### IAM730 - Special Topics: Quantum Information Theory

Credit: 3(0-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Quantum Information Theory: density matrix, composite systems, Shannon entropy; Quantum Data Compression; Decoherence: decoherence models for a single qubit, quantum black box; Quantum Error Correction: general properties of quantum error correction; Experimental Implementations: NMR quantum computation, cavity quantum electro dynamics.

Course Objectives

At the end of the course, the student will learn:

- The aim of this course is to study some selected topics in quantum information theory to prepare students for more advanced investigations in the field.

Course Learning Outcomes

Student, who passed the course satisfactorily will be able to:

- familiarity to some advanced concepts in the field;
- to gain some skills for advanced research.

Tentative (Weekly) Outline

- Weeks 1-5 Ouantum information theory
- Weeks 6-9: Decohernce
- Weeks 10-11: Quantum Error correction
- Weeks 12-14: Experimental implementations

Course Textbook(s)

- Nielsen and Chuang, Quantum Computation and Quantum Information,Cambridge 2000

Supplementary Materials and Resources

- Books
- Benenti, Casati and Strini, Principles of Quantum Computation and Information, Vols. 1,2. World Scientific

#### IAM731 - Special Topics: Lightweight Block Cipher Design

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Hardware implementation and optimization of block ciphers, lightweight cryptosystems: Attacks and design strategies for lightweight block ciphers.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Hardware implementation and optimization of block ciphers, lightweight cryptosystems: Attacks and design strategies for lightweight block ciphers.

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#### IAM732 - Special Topics: Applied Cryptography for Cyber Security

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Course Objectives

This course will help students understand the cryptographic issues and techniques to achieve cyber security.

Course Learning Outcomes

We learn how to analyze the many and various responsibilities involved with cyber security in view of the cryptographic techniques. We also evaluate the required issues to protect information and communication in hardware and software. We have an overview of security requirements of cryptographic modules.

Tentative (Weekly) Outline

In this course, we focus on applied cryptography for cyber security and defense. We systematically examine the roles of cryptography in cyber security, cryptography being the practice and study of techniques for secure communication in the presence of (probably malicious) third parties. To achieve cyber security, new cryptographic techniques such as efficient communication protocols are needed. Since changing the IT landscape from web applications to cloud computing, there are technical challenges in obtaining secure communication, especially in mobile networks. In those systems, the main problem is identity management.

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#### IAM733 - Special Topics: Cryptographic Protocols

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

The primary focus of this course is to focus on the advanced cryptographic primitives,their use in cryptographic applications; security and privacy weaknesses of the current protocols.Topics include homomorphic encryption,threshold cryptography, commitments, oblivious transfer,zero-knowledge protocols,secure multi-party computation and Yao`s garbled circuit approach.

Course Objectives

The focus of this course will be on the existing cryptographic protocols, formal analysis of cryptographic protocols, constructions of various modern cryptographic primitives, oblivious transfer, commitments, threshold cryptosystems, homomorphic encryption, zero-knowledge protocols and ID based cryptosystems. The course will cover also secure multi-party computation and solutions based on Yao’s garbled circuit approach. Solutions (underlying aforementioned primitives) will be proposed for particular cryptographic applications like privacy-preserving ID management for cloud computing, electronic voting, private (or pattern) search and RFID.

Course Learning Outcomes

Idea of modern cryptographic primitives such as oblivious transfer, threshold homomorphic cryptosystems, commitments, conventional cryptographic protocols for (Biometric/Anonymous/Attribute-based) Authentication, Formal Protocol Analysis, ID Based cryptosystems, and advanced protocols for secure multi-party computation.

Tentative (Weekly) Outline

The primary focus of this course is to focus on the advanced cryptographic primitives, their use in cryptographic applications; security and privacy weaknesses of the current protocols. Topics include homomorphic encryption, threshold cryptography, commitments, oblivious transfer, zero-knowledge protocols, secure multi-party computation and Yao’s garbled circuit approach.

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#### IAM734 - Special Topics: Network Coding and Cryptography

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Course Objectives

The aim of this course is to introduce the recent advances in theory of network coding and cryptography and also to give cryptography problems in network coding.

Course Learning Outcomes

Tentative (Weekly) Outline

Network codes and Grassmannian codes, Bounds on the size of network codes, Encoding and decoding schemes, Cryptographic aspects, Foundational aspects.

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#### IAM736 - Special Topics: Introduction to Cryptographic Engineering

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Prime field arithmetic. Extension field arithmetic. Efficient algorithms and implementation techniques for RSA, DSA, elliptic curve cryptography, DES, AES, selected random number generators and hash algorithms.

Course Objectives

The aim of this course is to present techniques for implementation of efficient algorithms in cryptography. Hardware and software realizations of basic cryptographic algorithms are studied.

Course Learning Outcomes

At the end of the course, students will become familiar with concepts and ideas related to design and implementation of efficient algorithms for hardware and software systems in cryptography.

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#### IAM737 - Special Topics: Post-Quantum Cryptography

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Public Key Cryptosystems, multivariate public key cryptosystems, Matsumato-Imai system, oil-vinegar signature scheme, lattice-based cryptography, hashed-based cryptography, isogeny-based cryptograph.

Course Objectives

Course Learning Outcomes

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#### IAM738 - Special Topics: Blockchain and Cryptocurrencies: Security & Privacy

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Public Key Cryptosystems; Pairing-based Cryptography; Hashed-based Cryptography; Zero Knowledge Proofs; Bitcoin; Cryptocurrencies; Blockchain; Distributed Ledger Technologies; Security; Privacy.

Course Objectives

The aim of this course is to present cryptocurrencies and blockchain technologies along with the underlying cryptographic primitives. Starting with Bitcoin, this course will cover fundamental concepts, types of proof of works, consensus mechanisms, how cryptographic primitives are used for integrity, authentication and preserving of privacy.

Course Learning Outcomes

At the end of the course, students will become familiar with concepts and ideas related to bitcoin, blockchain, cryptocurrencies.

Tentative (Weekly) Outline

- Week 1: Hash functions, ECDSA, Merkle Hash Trees, Byznatine Generals Problem, Fiat Currencies.
- Week 2-4: Bitcoin, Transactions, Blockchain.
- Week 5-6: Attacks on Bitcoin: scalability, security and privacy.
- Week 7: Proof of Work, Proof of Stake.
- Week 8: Etherium, IOTA.
- Week 9-10: Pairing-based Cryptography, zero knowledge proofs, ZK-snarks.
- Week 11-12: privacy preserving coins, Zerocash, Monero etc.
- Week: 13-14: Consensus algorithms.

Course Textbook(s)

Bitcoin and Cryptocurrency Technologies (Princeton textbook) by Arvind Narayanan, Joseph Bonneau, Edward Felten, Andrew Miller, and Steven Goldfeder.

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#### IAM742 - Special Topics in Asset Pricing

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Courses not listed in catalogue. Contents vary from year to year according to interest of students and instructor in charge.

Course Objectives

Course Learning Outcomes

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#### IAM743 - Special Topics: Malliavin Calculus and its Applications

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Important markets such as commodities or credit derivatives are essentially incomplete. The recent financial crisis has increased even more the importance of pricing and hedging in incomplete markets. Therefore these lectures concentrate on advanced methods of stochastic finance required in the context of incomplete markets. We will consider both, process in discrete and continuous time.

The content of the course covers in particular the following topics: market efficiency, market incompleteness; perfect hedges; equivalent martingale measures; attainable payoffs; asset management; contingent claims; replicating portfolio; dynamical arbitrage theory; arbitrage-free pricing; geometric characterization of arbitrage; von Neumann representation; robust Savage representation; expected utility; fair value; certainty equivalent; risk premium; risk aversion; equilibrium pricing; relative entropy; convex risk measures; robust representation; coherent risk measures; VAR; average VAR; upper/lower hedging prices; superhedging duality; risk indifference pricing; HJB equations; dynamical programming.

Course Objectives

The aim of this course is to introduce the fundamental ideas of Malliavin calculus and discuss some of the applications used in financial mathematics. The emphasis will be on understanding derivative and divergence operator, duality formula and Clark-Ocone formula. It is a high level calculus course which will help students to enhance their way of thinking in analysis and financial mathematics.

Course Learning Outcomes

Student, who passed the course satisfactorily will be able to:

- use Clark-Ocone formula in the integral representation of stochastic calculus
- identify Malliavin derivative operator, Skorohod integral operations in solving financial/mathematical problems
- formulate integral theorems in solving financial/mathematical problems

Tentative (Weekly) Outline

Important markets such as commodities or credit derivatives are essentially incomplete. The recent financial crisis has increased even more the importance of pricing and hedging in incomplete markets. Therefore these lectures concentrate on advanced methods of stochastic finance required in the context of incomplete markets. We will consider both, process in discrete and continuous time. The content of the course covers in particular the following topics: market efficiency, market incompleteness; perfect hedges; equivalent martingale measures; attainable payoffs; asset management; contingent claims; replicating portfolio; dynamical arbitrage theory; arbitrage-free pricing; geometric characterization of arbitrage; von Neumann representation; robust Savage representation; expected utility; fair value; certainty equivalent; risk premium; risk aversion; equilibrium pricing; relative entropy; convex risk measures; robust representation; coherent risk measures; VAR; average VAR; upper/lower hedging prices; superhedging duality; risk indifference pricing; HJB equations; dynamical programming.

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#### IAM745 - Special Topics: Stochastic and Deterministic Optimal Control With Applications to Finance

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Courses not listed in catalogue. Contents vary from year to year according to interest of students and instructor in charge.

Course Objectives

Course Learning Outcomes

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#### IAM746 - Actuarial Risk Theory

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Basic concepts of probability in connection with Risk Theory; introduction to risk processes (claim number process, claim amount process, total claim number process, total claim amount process, inter-occurance process); convolution and mixed type distributions; risk models (individual and collective risk models); numerical methods (simple methods for discrete distributions, Edgeworth approximation, Esscher approximation, normal power approximation); premium calculation principles; Credibility Theory; retentions and reinsurance; Ruin Theory; ordering of risks.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Basic concepts of probability in connection with Risk Theory; introduction to risk processes (claim number process, claim amount process, total claim number process, total claim amount process, inter-occurance process); convolution and mixed type distributions; risk models (individual and collective risk models); numerical methods (simple methods for discrete distributions, Edgeworth approximation, Esscher approximation, normal power approximation); premium calculation principles; Credibility Theory; retentions and reinsurance; Ruin Theory; ordering of risks.

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#### IAM747 - Quantitative Finance I

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Pricing financial instruments, algorithms and programming. Econometric estimation of the stochastic processes.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Pricing financial instruments, algorithms and programming. Econometric estimation of the stochastic processes.

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#### IAM749 - Numerical Algorithms with Financial Applications

Credit: 3(2-2); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Courses not listed in catalogue. Contents vary from year to year according to interest of students and instructor in charge.

Course Objectives

The main objective of the course is to introduce some numerical algorithms that are commonly used in financial applications. Moreover, to introduce basic options and their valuations both theoretically and numerically.

Course Learning Outcomes

Students are expected to gain, beside the theoretical concepts, programming skills that are related to option pricing as well as optimization.

Tentative (Weekly) Outline

Fixed-income securities, basic portfolio optimization, binomial method for options; Ito process and its applications in stock market, Black-Scholes equation and its solution; random numbers, transformation of random numbers and generating normal variates, Monte Carlo integration, pricing options by Monte Carlo simulation, variance reduction techniques, quasi-random numbers and quasi-Monte Carlo simulation; introduction to finite difference methods, explicit and implicit finite difference schemes, Crank-Nicolson method, free-boundary value problems for American options.

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#### IAM750 - Special Topics: Energy Trade and Risk Management

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

The course will follow two main textbooks and selected articles from scientific journals. Course will be supported by the presentation and speeches of guest speakers. This course discusses financial risk management from the perspective of energy. Course focuses mostly on the energy market, energy trading and energy risk management through various instruments. The topics also cover the interest of hedge funds. A special attention is also given to behavior of energy-dominant sovereign wealth funds.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

The course will follow two main textbooks and selected articles from scientific journals. Course will be supported by the presentation and speeches of guest speakers. This course discusses financial risk management from the perspective of energy. Course focuses mostly on the energy market, energy trading and energy risk management through various instruments. The topics also cover the interest of hedge funds. A special attention is also given to behavior of energy-dominant sovereign wealth funds.

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#### IAM751 - Special Topics: Financial Mathematics of Market Liquidity

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of the instructor.

Course Catalogue Description

This course is an introduction to the mathematical formulation and treatment of problems arising from trade execution in financial markets. When there are costs and constraints imposed on the execution of trades, how to best execute them? The course studies mathematical formulations and solutions of these types of problems.

Course Objectives

Having a working knowledge of the topics listed in the course outline.

Course Learning Outcomes

This course is a first step towards

- an in-depth study of the mathematics of market liquidity and
- working on research problems in this field

Tentative (Weekly) Outline

- Organization of markets
- Optimal liquidation: the Almgren-Chriss framework in continuous and discrete times
- Extensions of the Almgren-Chriss framework
- BSDE formulations of the liquidation problem
- Beyond Almgren-Chriss market impact models

Course Textbook(s)

The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making, Olivier Gueant

Supplementary Materials and Resources

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#### IAM753 - Special Topics Stochastic Energy Pricing Models

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Course Objectives

Course Learning Outcomes

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#### IAM754 - Special Topics: Financial Econometrics

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

The goal of this course is to establish a well background in this field. The important subjects in this course are stationarity, autocorrelation, partial autocorrelation, ARIMA models, VAR models, cointegration, difference equation and unit roots. Thus, using these concepts, a student can study and analyze the matters in the area of Financial Econometrics.

Course Objectives

The course is organized for the students to build up on solid background on Financial Econometrics

Course Learning Outcomes

The course is organized for the students to build up on solid background on Financial Econometrics

Tentative (Weekly) Outline

The goal of this course is to establish a well background in this field. The important subjects in this course are stationarity, autocorrelation, partial autocorrelation, ARIMA models, VAR models, cointegration, difference equation and unit roots. Thus, using these concepts, a student can study and analyze the matters in the area of Financial Econometrics.

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#### IAM755 - Special Topics: Risk Management For Corporations

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Within the context of value maximization, this course focuses at length on a corporations financial risk management needs and techniques. While we pay particular attention to financial institutions, our coverage is general enough for extending its lessons to other corporate entities, including multinationals.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Within the context of value maximization, this course focuses at length on a corporations financial risk management needs and techniques. While we pay particular attention to financial institutions, our coverage is general enough for extending its lessons to other corporate entities, including multinationals.

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#### IAM757 - Special Topics: Monte Carlo Methods in Finance and Insurance

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Generating Random Numbers; Basic Principles of Monte Carlo; Numerical Schemes for Stochastic Differential Equations; Simulating Financial Models; Jump-Diffusion and Levy Type Models; Simulating Actuarial Models; Markov Chain Monte Carlo Methods.

Course Objectives

At the end of this course, the student will learn:

- the generation of pseudorandom numbers from a given distribution
- basics of Monte Carlo methods and variance reduction techniques
- the algorithms for numerical solutions of stochastic differential equations, such as Euler-Maruyama and Milstein schemes, and convergence of numerical methods
- the simulation of Levy processes, in particular, jump-diffusion processes by Euler-Maruyama method for jump-diffusions
- possible fields of applications of continuous-time stochastic processes with continuous and discontinuous paths
- basic principles of Markov chain Monte Carlo methods and Bayesian estimation

Course Learning Outcomes

Student, who passed the course satisfactorily will be able to:

- generate pseudorandom numbers from a given distribution that is commonly used in finance and/or insurance
- apply Monte Carlo methods and variance reduction techniques to approximately integrate, or take, the underlying expectation and moments of random variables
- simulate continuous-time stochastic processes with continuous and discontinuous paths; characterise the convergence and rate of convergence of the numerical schemes used
- apply the methods to models in finance and/or insurance, such as pricing models under Black-Scholes or Heston model settings, interest rate models as well as derivatives, risk measures, pricing longevity products
- learn basics of Markov chain Monte Carlo methods and Bayesian estimation in actuarial mathematics

Tentative (Weekly) Outline

- Generating Random Numbers
- Generating Random Samples (Numbers) from a Specified Distribution
- Monte Carlo Method and Integration
- Variance Reduction Techniques: Antithetic and Control Variates
- Variance Reduction Techniques: Stratified, Conditional, and Importance Sampling
- Some Applications from Finance and Insurance
- Numerical Schemes for Stochastic Differential Equations: Euler-Maruyama
- Numerical Schemes for Stochastic Differential Equations: Milstein scheme and Lamperti transform
- Convergence Analysis of Numerical Schemes and Extrapolation Methods
- Basics of Multilevel Monte Carlo Method
- Numerical Solutions of Jump-Diffusion Processes
- Simulation of Lévy Processes
- Some Applications from Finance and Insurance
- Basics of Markov Chain Monte Carlo and its Applications

Course Textbook(s)

- R. Korn, E. Korn, G. Kroisandt, Monte Carlo Methods and Models in Finance and Insurance, Chapman & Hall/CRC, 2010

Supplementary Materials and Resources

Books

- P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, 2003
- G. S. Fishman, Monte Carlo: Concepts, Algorithms, and Applications, Springer, 1996

Readings

- Some of the papers or resources on the wikipage (https://en.wikipedia.org/wiki/Monte_Carlo_method) and the references therein might be useful and interesting to read and work on.

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#### IAM760 - Special Topics: Model Order Reduction

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Reduced Order Modeling: proper orthogonal decomposition (POD), evolution problems; Active Subspaces: parametrized models in physics and engineering, discover the active subspaces, exploit the active subspaces, active subspaces in action; Dynamic Mode Decomposition: introduction, Koopman analysis; PDE-constrained optimization: elliptic and parabolic linear optimal control problems; equality and inequality constraints; numerical algorithms for PDE-constrained optimization; reduced order modeling.

Course Objectives

The aim of the course is to give the students an introduction to model order reduction techniques for solving problems in the engineering and the sciences described by systems of differential equations. The modeling of complex physical and technical processes often leads to systems of differential equations with several millions of equations and variables. The numerical simulation, real-time and optimal control of such large-scale systems is very time consuming and expensive due to high computing times and high memory requirements, and sometimes impossible. The goal of model order reduction is to approximate highly dimensional systems with systems of smaller dimension. Hereby, crucial physical properties of the system should be preserved in the reduced order model, while simultaneously the approximation error should be small, and the methods should be stable and efficient.

This course is designed for graduate students majoring in mathematics as well as mathematically inclined graduate engineering students. At the end of this course, the student will:

- learn the fundamental concepts of model order reduction techniques such as proper orthogonal decomposition, active subspaces method, and dynamic mode decomposition;
- learn the fundamental concepts of partial differential equation (PDE) constrained optimization;
- learn how to solve large-scale systems efficiently by preserving their crucial physical properties;
- develop proficiency in the applications of model order reduction (modeling, analysis, and interpretation of results) to realistic engineering problems through the use of major commercial general purpose MATLAB codes.

Course Learning Outcomes

Upon successful completion of this course, the student will be able to

- formulate and solve (with a computer) partial differential equations efficiently by using various model order reduction methods;
- formulate and solve linear-quadratic optimal control problems;
- solve large-scale systems efficiently by preserving their crucial physical properties;
- apply model order reduction techniques in their thesis and understand the current research in this area;
- tackle real-life applications in science, engineering, and finance using state of art model order reduction techniques.

Tentative (Weekly) Outline

- Reduced Order Modeling: proper orthogonal decomposition (POD)
- Reduced Order Modeling: evolution problems
- Active Subspaces: parametrized models in physics and engineering
- Active Subspaces: discover the active subspaces
- Active Subspaces: exploit the active subspaces
- Active Subspaces: active subspaces in action
- Dynamic Mode Decomposition: introduction to DMD
- Dynamic Mode Decomposition: Koopman analysis
- PDE-constrained optimization: motivation and introduction
- PDE-constrained optimization: unconstrained problems
- PDE-constrained optimization: control constraints
- PDE-constrained optimization: boundary control problems
- PDE-constrained optimization: parabolic control problems
- Reduced Order Modeling: optimal control of linear quadratic problems

Course Textbook(s)

- P. Benner, M. Ohlberger, A. Cohen and K. Willcox, Model Reduction and Approximation Theory and Algorithms, SIAM 2017.
- P. G. Constantine, Active Subspaces Emerging Ideas for Dimension Reduction in Parameter Studies, SIAM, 2015.
- J. N. Kutz, S. L. Brunton, B. W. Brunton and J. L. Proctor, Dynamic Mode Decomposition: Data- Driven Modeling of Complex Systems, SIAM, 2016.
- A. Quarteroni, A. Manzoni and F. Negri, Reduced Basis Methods for Partial Differential Equations, Springer, 2015.
- F. Tröltzsch, Optimal Control of Partial Differential Equations-Theory, Methods and Applications, AMS, 2010.
- S. Volkwein, Proper Orthogonal Decomposition: Theory and Reduced Order Modeling, Uni Konstanz, 2013.

Supplementary Materials and Resources

- Resources:
- MATLAB
- htps://odtuclass.metu.edu.tr

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#### IAM761 - Special Topics: Networks and Graphs

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Course Objectives

Course Learning Outcomes

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IAM762 - Adaptive Finite Elements and Optimal Control

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Adaptive Finite Elements and Optimal Control.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Adaptive Finite Elements and Optimal Control.

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#### IAM763 - Special Topics: Numerical Simulation in Fluid Dynamics

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Description of fluids and flows. Derivation of Navier-Stokes equations (conservation of mass, conservation of momentum and conservation of energy). Numerical treatment of the Navier-Stokes equations by finite difference method. Applications: lid driven cavity problem, flow over a backward-facing step, free boundary problems, heat flow, natural convection with heated lateral walls, chemical transport. Extension to three-dimensions with examples from environmental sciences, architecture and engineering. Finite element method and applications.

Course Objectives

At the end of the course, the student will learn:

- modelling fluid flows
- discretization of fluid dynamic equations
- efficient numerical algorithms
- fast solvers for fluid flow problems
- flow simulations

Course Learning Outcomes

Student, who passed the course satisfactorily will be able to:

- model fluid flow problems
- discretize using numerical techniques the PDEs
- write their own computer programs to solve Navier-Stokes equations
- apply the methods learnt to problems in natural and applied sciences

Tentative (Weekly) Outline

- Derivation of fluid flow equations
- Finite Difference Method, discretization
- Finite Difference solution of Navier-Stokes equation in velocity-pressure and vorticity-stream function formulations
- Applications: lid-driven cavity problem, flow over a backward-facing step, free boundary problems, heat flow, natural convection with heated lateral walls, chemical transport
- Finite Element Method
- Applications on environmental sciences, architecture and engineering

Course Textbook(s)

- Numerical Simulation in Fluid Dynamics - A Practical Introduction, M. Griebel, T. Dornseifer, T. Neunhoeffer, SIAM, 1998

Supplementary Materials and Resources

- Books:
- Computational Fluid Dynamics, T. J. Chung, Cambridge University Press, 2002
- Computational Fluid Dynamics, K. A. Hoffmann, S.I, Chiang, Engineering Education System, 2000

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#### IAM765 - Special Topics: Finite Elements: Adaptivity

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Variational formulation of differential equations, ﬁnite element spaces and ﬁnite elements discretization, a posteriori error estimators for elliptic problems, residual error estimators, parabolic problems, spacetime adaptivity, implementation and numerical examples.

Course Objectives

This course aims to Introduce students into concepts of a posteriori error estimation techniques and their application to design adaptive ﬁnite elements needed in various applications in science and engineering. The students have to be able to apply the adaptive ﬁnite element methods in their thesis and understand the current research in this area.

Course Learning Outcomes

At the end of the course students should be able to analyze and implement adaptive FEM methods to PDEs and optimal control problems.

Tentative (Weekly) Outline

Variational formulation of differential equations, ﬁnite element spaces and ﬁnite elements discretization, a posteriori error estimators for elliptic problems, residual error estimators, parabolic problems, spacetime adaptivity, implementation and numerical examples.

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#### IAM766 - Special Topics: Optimal Control With Partial Differantial Equations

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Course Objectives

The objective of this course is to introduce the optimal control of partial differential equations and computational techniques.

Course Learning Outcomes

At the end of this course students should be able to tackle optimal control problems of in science, engineering and finance using state of art numerical methods. Both lectures and computer exercises serve for this aim of learning, deepening, applying and preparing for thesis work.

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#### IAM767 - Special Topics: Iterative Methods for Large Scale Linear and Nonlinear Equations

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Iterative Solvers for linear and nonlinear systems of equations, precondtioning technics, analysis and implementation of the algorithms

Course Objectives

Large scale systems of equations arising in the discretization of linear and nonlinear partial differential equations lie at the heart of many algorithms in scientiﬁc computing and require highly efﬁcient solvers. The course will be based around understanding the mathematical principles underlying the design and the analysis of effective methods and algorithms.

Course Learning Outcomes

At the end of the course students will become familiar with concepts and ideas related to theoretical basis for algorithms, assessing algorithms with respect to computational cost, conditioning of problems and stability of algorithms.

Tentative (Weekly) Outline

Iterative Solvers for linear and nonlinear systems of equations, precondtioning technics, analysis and implementation of the algorithms

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#### IAM768 - Special Topics: Methods and Applications of Uncertainty Quantification

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Probability, Random Processes, and Statistics; Markov Chains; Sampling and Monte Carlo Methods; Parameter Estimation; Uncertainty Propagation in Models; Stochastic Spectral Methods; Surrogate Models and Advanced Topics.

Course Objectives

Students are expected to gain, besides theoretical concepts, programming skills that are related to Uncertainty Quantification and related applications.

Course Learning Outcomes

By the end of this course, students should be equipped with fundamental methods of Uncertainty Quantification, and related concepts from Scientific Computing, Finance and Statistics, and Physics and Engineering.

Tentative (Weekly) Outline

Probability, Random Processes, and Statistics; Markov Chains; Sampling and Monte Carlo Methods; Parameter Estimation; Uncertainty Propagation in Models; Stochastic Spectral Methods; Surrogate Models and Advanced Topics.

Weekly Outline / Tentative Course Schedule

- Introduction and Preliminaries
- Motivating Applications and Prototypical Models
- Probability, Random Processes, and Statistics; Markov Chains
- Sampling and Monte Carlo Methods
- Computing Expectations/Integrals, Moments; Moment Approximations using Limit Theorems
- Monte Carlo Methods, variance reduction techniques; importance sampling
- Parameter Estimation
- Frequentist Techniques: Linear Regression, Nonlinear Parameter Estimation, Optimisation and Algorithms (related content from least squares, regularization, etc.)
- Bayesian Techniques: Markov Chain Monte Carlo, Metropolis-Hasting Algorithms, and Sequential Monte Carlo and Particle Filter; Delayed Rejection Adaptive Metropolis (DRAM), DiffeRential Evolution Adaptive Metropolis (DREAM)
- Stochastic Spectral Methods
- Orthogonal Polynomials, Piecewise Polynomial Approximation, Interpolation, Projection, (Gaussian) Quadrature Rules; Finite Elements (and, possibly, Finite Differences), Galerkin (Finite Element) Methods, (Polynomial) Spectral Methods
- Spectral Expansion and Stochastic Spectral Methods: Karhunen-Loève Expansion, (generalised) Polynomial Chaos Expansion (gPC); Stochastic Galerkin Methods, Collocation, and Discrete Projection
- Surrogate Models and Advanced Topics

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#### IAM769 - Special Topics: Reaction-Diffusion systems: Applications and Numerics

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Introduction into dynamical systems concepts and numerical methods for solving reaction-diffusion equations occurring in biology, chemistry and physics.

Course Objectives

Introduction into dynamical systems concepts and numerical methods for solving reaction-diffusion equations occurring in biology, chemistry and physics.

Course Learning Outcomes

Student will learn dynamical system properties of reaction-diffusion and equations and efficient solvers by performing several projects.

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#### IAM770 - Special Topics: Discontinuous Galerkin Methods

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

DG in One Spatial Dimension: linear system, implementation in MATLAB; Higher Dimensional Elliptic Problems: interior penalty methods, variational formulation, a priori error estimates, implementation in MATLAB, local discontinuous Galerkin method; DG for Convection Diffusion Problems: upwind scheme; Construction of Finite Element Spaces: Lagrange, Hermite, etc.; A Posteriori Error Analysis: residual-based, goal-oriented, hierarchical, equilibrated error estimators; Hybrid Discontinuous Galerkin Methods.

Course Objectives

The aim of the course is to give the students an introduction to discontinuous Galerkin methods for solving problems in the engineering and the sciences described by systems of partial differential equations. These methods, most appropriately considered as a combination of finite volume and finite element methods, have become widely used during the last decade as a powerful tool for the simulation of challenging problems in the sciences and engineering.

The course covers both an overview of the theoretical properties of the methods, their efficient implementation, and more applied problems related to the multi-dimensional problems, an a posteriori error analysis, and adaptive refinement, illustrated using Matlab. We shall draw on application examples and illustrations from fluid dynamics but the focus on the course is on understanding the methods in sufficient depth to apply them to a broad range of problems.

- understand the mathematics behind discontinuous Galerkin methods: formulations, assembly for implementations, discrete spaces, approximation theory, error estimates;
- implement adaptive mesh refinement using various a posteriori error estimates;
- develop proficiency in the applications of the discontinuous Galerkin methods (modeling, analysis, and interpretation of results) to realistic engineering problems through the use of major commercial;
- general-purpose discontinuous Galerkin finite element code implement such methods and extensions in MATLAB or any programming language.

Course Learning Outcomes

Upon successful completion of this course, the student will be able to

- formulate and solve (with a computer) higher order partial differential equations in multi–dimensional problems using discontinuous Galerkin method;
- derive a priori and a posteriori error estimates using discontinuous Galerkin method;
- generate adaptive meshes using various a posteriori error estimates;
- apply the discontinuous Galerkin method in their thesis and understand the current research in this area;
- evaluate different techniques for solving problems and be able to motivate when to use existing software and when to write new code.

Tentative (Weekly) Outline

- Introduction and DG in One Spatial Dimension
- DG in One Spatial Dimension: linear System, implementation in MATLAB
- Higher Dimensional Elliptic Problems: interior penalty Methods, variational formulation
- Higher Dimensional Elliptic Problems: a priori error estimates
- Higher Dimensional Elliptic Problems: implementation in MATLAB
- Higher Dimensional Elliptic Problems: local discontinuous Galerkin method
- DG for Convection–Diffusion Problems: upwind Scheme
- Construction of Finite Element Spaces: Lagrange, Hermite, etc.
- A Posteriori Error Estimates: residual-based error estimator
- A Posteriori Error Estimates: goal-oriented and hierarchical estimator
- A Posteriori Error Estimates: equilibrated estimators
- Hybrid Discontinuous Galerkin Methods
- Direct Discontinuous Galerkin (DDG) Methods
- Review of the Topic Material

Course Textbook(s)

- Béatrice Riviére, Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations: Theory and Implementation, SIAM, 2008.
- D. Di Pietro and A. Ern, Mathematical Aspects of Discontinuous Galerkin Methods, Springer 2012.

Supplementary Materials and Resources

Book(s)

- J. S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin methods, Springer, 2008.

Resources

- L. Chen iFEM: an innovative finite element methods package in MATLAB. Tech. rep.:Department of Mathematics, University of California, Irvine, CA 92697-3875; 2008.
- MATLAB (https://www.mathworks.com/)

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#### IAM771 - Special Topics: Optimization Methods for Machine Learning

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent to the Instructor

Course Catalogue Description

Convexity; Gradient Descent; Stochastic Gradient Methods; Noise Reduction Methods; Second-Order Methods; Adaptive Methods; Methods for Regularized Models; Introduction to Machine Learning: support machine vector, neural network.

Course Objectives

The interplay between optimization and machine learning is one of the most important developments in modern computational science. Optimization formulations and methods are proving to be vital in designing algorithms to extract essential knowledge from huge volumes of data. Machine learning, however, is not simply a consumer of optimization technology but a rapidly evolving field that is itself generating new optimization ideas. Optimization approaches have enjoyed prominence in machine learning because of their wide applicability and attractive theoretical properties. The increasing complexity, size, and variety of today's machine learning models call for the reassessment of existing assumptions. This course is designed for graduate students majoring in mathematics as well as mathematically inclined graduate engineering students. At the end of this course, the student will:

- capture the state of the art of the interaction between optimization and machine learning.
- understand the various optimization methods that underlie machine learning methods that have become so popular today in real-world applications.
- use the computational tools available to solving optimization problems on computers once a mathematical formulation has been found.

Course Learning Outcomes

Upon successful completion of this course, the student will be able to

- assess/evaluate the most important algorithms, function classes, and algorithm convergence guarantees.
- compose existing theoretical analysis with new aspects and algorithm variants.
- formulate scalable and accurate implementations of the most important optimization algorithms for machine learning applications.

Tentative (Weekly) Outline

- Background of machine learning
- Convexity and nonsmooth calculus tools
- Gradient descent
- Projected gradient descent
- Stochastic gradient methods
- Variance reduction methods: SAG, SAGA, SVRG
- Accelerated gradient descent
- Mirror descent
- Second-order methods
- Second-order methods: stochastic quasi-Newton
- Dual methods: stochastic dual coordinate ascent methods
- Conditional gradient method
- Adaptive methods
- Methods for regularized models

Course Textbook(s)

There will be no explicit textbook for the course; rather, the instructor will provide some hand-written lecture notes along with the progress of the course. However, the following monographs on this topic are recommended:

- S. Suvrit, S. Nowozin, and S. J. Wright, Optimization for Machine Learning, MIT Press, 2012.
- J. Nocedal and S. J. Wright, Numerical Optimization, Second Edition, Springer, 2006.
- S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
- L. Bottou, F. E. Curtis, J. Nocedal: Optimization Methods for Large-Scale Machine Learning, arXiv:1606.04838v3
- W. Hu, Nonlinear Optimization in Machine Learning, Lecture Notes
- E. Hazan, Optimization for Machine Learning, arXiv:1909.03550v1
- S. Bubeck, Convex Optimization: Algorithms and Complexity, arXiv:1405.4980v2
- M. Jaggi and B. Gärtner, Optimization for Machine Learning, Lecture Notes

Supplementary Materials and Resources

- Python: https://www.python.org/

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#### IAM781 - Special Topics: Functional Analysis

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Properties of real numbers, limits and convergence of sequences of numbers, exponential and logarithm function, continuity and uniform continuity of functions, intermediate value theorem, Hölder and Lipschitz continuity, differentiability, and differentiation rules.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Properties of real numbers, limitsand convergence of sequences of numbers, exponential and logarithm function, continuity and uniform continuity of functions, intermediate value theorem, Hölder and Lipschitz continuity, differentiability, and differentiation rules.

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#### IAM782 - Special Topics: Extreme Values in Insurance and Finance

Credit: 3(0-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Course Objectives

Course Learning Outcomes

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#### IAM783 - Special Topics: Life Insurance: Products, Finance and Modeling

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Short review of basic concepts, terminology, definitions in life insurance and the types of life insurance. Product development, pricing strategy, preliminary and final product design, product implementation and management, pricing assumptions and life insurance cash flows, reserves, reinsurance, investment income, profit measurement, financial modeling, asset/liability modeling, and matching, stochastic modeling and financial management.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Short review of basic concepts, terminology, definitions in life insurance and the types of life insurance. Product development, pricing strategy, preliminary and final product design, product implementation and management, pricing assumptions and life insurance cash flows, reserves, reinsurance, investment income, profit measurement, financial modeling, asset/liability modeling, and matching, stochastic modeling and financial management.

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#### IAM784 - Special Topics: Pension Systems and Their Financial Management

Credit: 3(0-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Types of pension systems, the nature of interrelationship between social security schemes, their demographic, economic and fiscal environments, the valuation of public pension systems, structural reform considerations, the valuation of short-term cash benefits.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Types of pension systems, the nature of interrelationship between social security schemes, their demographic, economic and fiscal environments, the valuation of public pension systems, structural reform considerations, the valuation of short-term cash benefits.

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#### IAM785 - Special Topics: Survival Models in Actuarial Science

Credit: 3(3-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Forms of survival models, survival distributions, parametric survival models, introduction to demography and life tables, force of mortality, estimation of parametric survival models, actuarial estimation with survival models.

Course Objectives

Course Learning Outcomes

Tentative (Weekly) Outline

Forms of survival models, survival distributions, parametric survival models, introduction to demography and life tables, force of mortality, estimation of parametric survival models, actuarial estimation with survival models.

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#### IAM8XX - Special Studies

Credit: 0(0-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Please, ask Secretary to IAM, or your advisor/supervisor about the details.

Course Objectives

Course Learning Outcomes

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#### IAM9XX - Advanced Studies

Credit: 0(0-0); ECTS: 8.0

Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Please, ask Secretary to IAM, or your advisor/supervisor about the details.

Course Objectives

Course Learning Outcomes

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