INSTITUTE OF APPLIED MATHEMATICS
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All Courses @ IAM Actuarial Sciences Cryptography Financial Mathematics Scientific Computing

All Courses @ IAM

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

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.

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

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

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

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

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

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

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

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

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

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.

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

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

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

The aim of this course is to introduce the basic of quantum information theory with an emphasis on quantum cryptography and quantum algorithms. A short review of classical information theory. 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.

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

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.

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

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

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.

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

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.

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

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

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.

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

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

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.

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

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

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

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

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.

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

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

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

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

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.

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

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.

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

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

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

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

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

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

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

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

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.

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

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

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.

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

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.

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

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

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

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

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.

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

Introduction to statistical learning, simulation and supervised learning. Linear methods of regression and classification. Model assessment and selection. Model inference and averaging. Additive models, trees and related methods. Prototype methods and nearest neighbors. Cluster algorithms and support vector machines. Unsupervised learning. Computer applications and MATLAB exercises are important elements of the course.

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

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

This course is about densities. In the history of science, the concept of densities emerged only recently as attempts were made to provide unifying descriptions of phenomena that appeared to be statistical in nature. In view of the formal developments of probability and statistics, we have come to associate the appearance of densities with the description of large systems containing inherent elements of uncertainty. The aim of this course is to introduce the students into the theory of Markov operators, ergodic theory, and their applications to study of chaotic dynamical systems.

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

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.

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

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

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

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

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

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

Unconstrained optimization: line search methods, steepest descent, Newton and quasi Newton methods, the conjugate gradient method constrained optimization: equality and inequality constraints, linear constraints and duality, linear programming, the simplex method, Lagrange multiplier algorithms, interior point methods, penalty methods, large scale optimization.

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

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

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

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

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

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

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

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

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

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

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

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

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

Risk theory analysis of pension funds. Valuation of pension plans. Terminal funding. Multiple Decrement models. Actuarial cost methods for retired and for active and retired lives pension funding.

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

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

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

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

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

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

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.

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

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).

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

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

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

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

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

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

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.

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

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

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.

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

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

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.

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

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

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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Credit: 0(0-0); ECTS: 0.0

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.

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

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

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

See the course in IAM Catalogue or METU Catalogue

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

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.

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

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

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

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

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

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

See the course in IAM Catalogue or METU Catalogue

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

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.

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

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

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

The course’s aims consist in a deepened knowledge by he students, and that they are enabled and activated to a do their own scientific work in future. Therefore, the objective of this course is to guide students in their first steps as young researchers on modern areas of mathematical finance. For this purpose, course material will be presented and distributed whose understanding will demand a joint view and participation of the different mathematical foundations of finance. This necessitates further reading and deep reflection by all participants, a spirit of scientific entrepreneurship and willingness to become more mature. Approaches and results of the sources taught and distributed will become improved by the participants, and every participant will prepare a small paper on his/her findings that will be submitted.

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

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

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.

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

The focus of this course is on model order reduction methods for large-scale systems,which arise when partial differential equations are solved using numerical methods such as the finite element methods. Model order reduction techniques such as proper orthogonal decomposition and reduced basis provide an efficient and reliable way of solving these problems in the many-query or real-time context,such as optimization, characterization, and control.

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

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

See the course in IAM Catalogue or METU Catalogue

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

Adaptive Finite Elements and Optimal Control.

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

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 value problems,heat flow,natural convection with heated lateral wall, chemical transport. Extension to three-dimensions with examples from environmental, sciences, architecture end engineering. Finite volume method and applications.

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

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

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

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.

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

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

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

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.

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

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.

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

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

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

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

See the course in IAM Catalogue or METU Catalogue

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

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

See the course in IAM Catalogue or METU Catalogue