INSTITUTE OF APPLIED MATHEMATICS
Last Updated:
06/02/2018 - 13:15

2017-2018 Spring

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

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

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

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

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: 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

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 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

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

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

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

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

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

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: 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

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.

See the course in IAM Catalogue or METU Catalogue

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: 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(3-3); 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

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.

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

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

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

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.

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

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.

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

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