INSTITUTE OF APPLIED MATHEMATICS
Last Updated:
26/09/2017 - 10:47

2017-2018 Fall

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

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

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

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

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

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

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

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

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

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

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

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

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.

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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: 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: 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

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: 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.

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.

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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

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.

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