# Courses

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**MATH111** - Basic Logic and Algebra
(3 + 0) 6

Logic, sets, induction, relations, functions, elementary number theory, elementary examples of groups, rings and fields, the real numbers.

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**MATH121** - Analytic Geometry I
(2 + 1) 4

Fundamental principles of analytic geometry, cartesian coordinates, lines in plane, trigonometry, polar coordinates, rotation and translation in plane, conics.

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**MATH135** - Mathematical Analysis I
(4 + 2) 8.5

Preliminaries, functions and graphs, limits and continuity, derivatives, mean value theorem, applications of derivatives: monotonicity, local and absolute extrema, concavity, L?Hospital?s rule, graphs of functions.

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**MATH112** - Discrete Mathematics and Combinatorics
(3 + 0) 6

Numbers and counting, countable and uncountable sets, continuum, the Pigeonhole Principle and its applications, permutations and combinations, combinatorial formulas, recurrence relations, principle of inclusion and exclusion, binary relations, elementary graph theory.

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**MATH122** - Analytic Geometry II
(3 + 0) 6

Cartesian coordinates in 3-space, vectors, lines and planes, basic surfaces, cylinders, surface of revolutions.

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**MATH136** - Mathematical Analysis II
(4 + 2) 8.5

Riemann integral, the fundamental theorem of calculus, integration techniques, applications of integrals: area, volume, arc length, improper integrals, sequences, infinite series, tests for convergence, functional sequences and series, interval of convergence, power series, Taylor series and its applications.

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**MATH231** - Linear Algebra I
(4 + 0) 7

Matrices and linear equations, determinants, vector spaces, linear transformations.

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**MATH251** - Advanced Calculus I
(3 + 2) 8

Vector and matrix algebra, functions of several variables: limit, continuity, partial derivatives, chain rule; implicit functions. inverse functions, directional derivatives, maxima and minima of functions of several variables, extrema for functions with side conditions.

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**MATH232** - Linear Algebra II
(4 + 0) 7

Eigenvalues and eigenvectors, elementary canonical forms, the rational and Jordan forms, inner product spaces, operators on Inner product spaces, bilinear forms.

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**MATH252** - Advanced Calculus II
(3 + 2) 8

Vector and scalar fields. Double integrals. Triple integrals. Integral of vector functions. Improper İntegrals. Line İntegrals. Green?s theorem. Surface integrals. The divergence Theorem. Stoke?s Theorem

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**MATH262** - Ordinary Differential Equations
(4 + 0) 6

First-order, higher-order linear ordinary differential equations, applications of first-order differential equations, series solutions of differential equations, Laplace transforms, linear systems of ordinary differential equations.

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**MATH331** - Abstract Algebra
(4 + 0) 7

Groups: subgroups, cyclic groups, permutation groups, Lagrange Theorem, normal subgroups and factor groups, homomorphisms, isomorphism theorems, rings and fields: subrings, integral domains, ideals and factor rings, maximal and prime ideals, homomorphisms of rings,field of quotients, polynomial rings, principal ideal domain (PID), irreducibility of

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**MATH351** - Introduction to Real Analysis
(4 + 0) 7

A review of sets and functions, real numbers (or system), countable and uncountable sets, sequences of real Numbers (Cauchy sequences), Uniform Convergence of Sequences of functions, Metric Spaces, Compactness and Connectedness, Contraction Mapping Theorem, Arzela-Ascoli Theorem, Extension Theorem fo Tietze, Baire?s Theorem.

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**MATH392** - Probability Theory and Statistics
(4 + 0) 7

Probability spaces, conditional probability and independence, random variables and probability distributions, numerical characteristics of random variables, classical probability distributions, random vectors, descriptive statistics, sampling, point estimation, interval estimation, testing hypotheses.

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**MATH313** - Introduction to Mathematical Finance
(3 + 0) 6

Introduction to theory of interest: simple and compound interest, time value of money, rate of interest, rate of discount, nominal rates, effective rates, compound interest functions, generalized cash flow modelling, loans, present value analysis, accumulated profit, and internal rate of return for investment projects, annuities, perpetuities, meas

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**MATH316** - Mathematics of Financial Derivatives
(3 + 0) 6

Introduction to options and markets, European call and put options, arbitrage, put call parity, asset price random walks, Brownian motion, Ito?s Lemma, derivation of Black-Scholes formula for European options, Greeks, options for dividend paying assets, multi-step binomial models, American call and put options, early exercise on calls and puts on a

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**MATH318** - Hıstory of Mathematics I
(3 + 0) 6

Prehistoric mathematics, Ancient Near East mathematics (Mesopotamia-Egypt, 3rd millenium BC?500 BC), Greek and Hellenistic mathematics (c. 600 BC?300 AD), Chinese mathematics (c. 2nd millenium BC?1300 AD), Indian mathematics (c. 800 BC?1600 AD), Islamic mathematics (c. 800?1500).

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**MATH325** - Elementary Number Theory
(3 + 0) 6

Divisibility, congruences , Euler, Chinese Remainder and Wilson?s Theorems, arithmetical functions, primitive roots, quadratic residues and quadratic reciprocity, diophantine equations.

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**MATH326** - Coding Theory
(3 + 0) 6

Error detection, correction and decoding, finite fields, linear codes, bounds in coding theory, construction of linear codes, cyclic codes.

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**MATH332** - Finite Fields
(3 + 0) 6

Characterization of finite fields, roots of irreducible polynomials, trace, norm, roots of unity and cyclotomic polynomials, order of polynomials and primitive polynomials, irreducible polynomials, construction of irreducible polynomials, factorization of polynomials

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**MATH333** - Matrix Analysis
(3 + 0) 6

Preliminaries, eigenvalues, eigenvectors and similarity, unitary equivalence and normal matrices, Canonical forms, Hermitian and symmetric matrices, norms for vectors and matrices, location and perturbation of eigenvalues, positive definite matrices, nonnegative matrices.

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**MATH357** - Functional Analysis
(3 + 0) 6

Vector spaces, Hamel basis, linear operators, equations in operators, ordered vector spaces, extension of positive linear functionals, convex functions, Hahn-Banach Theorem, The Minkowski functional, Separation Theorem, metric spaces, continuity and uniform continuity, completeness, Baire Theorem, normed spaces, Banach spaces, the algebra of bounde

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**MATH360** - Theory of Ordinary Differential Equations
(3 + 0) 6

First-order ordinary differential equations, the Existence and Uniqueness Theorem, systems and higher-order ordinary differential equations, linear differential equations, boundary value problems and eigenvalue problems, oscillation and comparison theorems.

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**MATH363** - Calculus on Time Scales
(3 + 0) 6

The h-derivative and the q-derivative, the concept of a time scale, differentiation on time scales, integration on time scales, Taylor?s Formula on time scales.

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**MATH372** - Topology
(3 + 0) 6

Fundamental concepts, functions, relations, sets and Axiom of Choice, well-ordered sets, topological spaces, basis, the Order Topology, the Subspace Topology, closed sets and limit points, continuous functions, the Product Topology, Metric Topology, the Quotient Topology, connectedness and compactness, Countability and Separation Axioms, the fundam

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**MATH378** - Partial Differential Equations
(3 + 0) 6

Basic concepts; first-order partial differential equations; types and normal forms of second-order linear partial differential equations; separation of variables; Fourier series; hyperbolic, parabolic and elliptic equations; solution of the Wave Equation.

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**MATH381** - Numerical Analysis
(3 + 0) 7

Computational and mathematical preliminaries, numerical solution of nonlinear equations and systems of nonlinear equations, numerical solution of systems of linear equations, direct and iterative methods, the Algebraic Eigenvalue Problem, interpolation and approximation, numerical differentiation and integration, numerical solution of ODE`s.

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**MATH417** - Computational Methods of Mathematical Finance
(2 + 0) 6

Introduction to MATLAB, finite difference formulae, the explicit and implicit finite difference methods, The Crank-Nicolson method, European option pricing by the heat equation, pricing by the Black-Scholes equation, pricing by an explicit, an implicit and Crank-Nicolson method, pricing American options, projected SOR and tree methods, pseudo-rando

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**MATH419** - History of Mathematics II
(3 + 0) 6

Early Middle Ages European mathematics (c. 500?1100), mathematics of the Renaissance: rebirth of mathematics in Europe (1100?1400), early modern European mathematics (c. 1400?1600): solution of the cubic equation and consequences, invention of logarithms, time of Fermat and Descartes, development of the limit concept, Newton and Leibniz, the age of

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**MATH427** - Introduction to Crytopgraphy
(3 + 0) 6

Basics of cryptography, classical cryptosystems, substitution, review of number theory and algebra, public-key and private-key cryptosystems, RSA cryptosystem, Diffie-Hellman key exchange, El-Gamal cryptosystem, digital signatures, basic cryptographic protocols.

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**MATH437** - Statistical Methods and Financial Applications
(3 + 0) 6

Central tendency/dispersion measures, moments, maximum likelihood estimation, correlation and simple linear regression, multi-regression model, autocorrelation and multi-collinearity on regression models, portfolio theory, CAPM and ARMA approaches.

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**MATH463** - Applied Mathematics
(4 + 0) 8

Calculus of variations and applications, integral equations and applications.

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**MATH467** - Dynamical Systems and Chaos
(4 + 0) 6

One-dimensional dynamic systems, stability of equilibria, bifurcation, linear systems and their stability, two-dimensional dynamic systems, Liapunov?s direct method and method of linearization, 3-dimensional dynamic systems.

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**MATH482** - Numerical Methods for Ordinary Differential Equations
(3 + 0) 6

Existence, uniqueness and stability theory; IVP: Euler?s method, Taylor series method, Runge-Kutta methods, explicit and implicit methods; multistep methods based on integration and differentiation; predictor?corrector methods; stability, convergence and error estimates of the methods; boundary value problems: finite difference methods, shooting me

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**MATH483** - Special Functions of Applied Mathematics
(3 + 0) 6

Gamma and Beta functions; Pochhammer`s symbol; hypergeometric series; hypergeometric differential equation; generalized hypergeometric functions; Bessel function; the functional relationships, Bessel`s differential equation; orthogonality of Bessel functions.

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**MATH484** - Classical Orthogonal Polynomials
(3 + 0) 6

Generating functions; orthogonal polynomials; Legendre polynomials; Hermite polynomials; Laguerre polynomials; Tchebicheff polynomials; Gegenbauer polynomials.

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**MATH485** - Theory of Difference Equations
(3 + 0) 6

The difference calculus, linear difference equations, linear systems of difference equations, self-adjoint second-order linear equations, the Sturm-Liouville eigenvalue problem, boundary value problems for nonlinear equations.

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**MATH486** - Mathematical Modeling
(3 + 0) 6

Differetial equations and solutions, models of vertical motion, single-species population models, multiple-species population models, mechanical oscillators, modeling electric circuits, diffusion models.

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**MATH447** - Computer Algebra
(3 + 0) 6

Introduction to Maple, complexity of arithmetic operations, computing with algebraic numbers, bit operations, computer arithmetic with big integers; Euclidean and extended Euclidian algorithms, polynomial interpolation, factorization and applications, primality testing, arithmetic on finite fields, operations in linear algebra, computing in lattice

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**MATH495** - Stochastic Processes
(3 + 0) 6

Basic notions of probability theory; reliability theory; notion of a stochastic process; Poisson processes, Markov chains; Markov decision processes.

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**MATH346** - Complex Analysis
(4 + 0) 7

Complex Nnumbers and elementary functions, analytic functions and integration, sequences, series and singularities of complex functions, residue calculus and applications of contour integration, conformal mappings and applications.

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**MATH374** - Differential Geometry
(3 + 0) 6

Curves in the plane and space, curvature and torsion, global properties of plane curves, surfaces in space, the First Fundamental Form, curvatures of surfaces, Gaussian curvature and the Gauss Map, geodesics, minimal surfaces, Gauss`s Theorema Egregium, the Gauss-Bonnet Theorem.

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**MATH448** - Algorithms
(2 + 0) 6

Design and analysis of algorithms, O,o,?,?,? notations, lower and upper bound theory, divide and conquer algorithms, recurrences, dynamic programming, complexity of sorting and searching algorithms, Greedy algorithms, Greedy algorithms versus dynamic programming, elementary graph algorithms, NP-completeness

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**MATH380** - Numerical Methods for Engineers
(3 + 1) 5

Solution of nonlinear equations, solution of linear systems, eigenvalues and eigenvectors, interpolation and polynomial approximation, least square approximation, numerical differentiation, numerical integration.

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**MATH400** - Undergraduate Research Project
(1 + 0) 6

Preparation and presentation of a graduation project.

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**MATH411** - Seminar Studies
(1 + 2) 7

Research on a mathematical topic by literature survey and investigation, report writing by observing scientific ethical rules and oral presentations.