COURSES GIVEN BY DEPARTMENT OF MATHEMATICS

MTH1101 CALCULUS I (ANALİZ I)

Calculus I includes functions, limits, continuity, differentiation of algebraic and trigonometric functions, mean value

theorem, various applications, Riemann sums and integrals, techniques and applications of integration and improper

integrals.

MTH 1103 LINEAR ALGEBRA I (LİNEER CEBİR I)

Systems of linear equations, Matrices, Matrix Operations, Algebraic properties of matrix operations, Special Types of

Matrices and Partitioned Matrices, Echelon Form of a Matrix, Finding inverse of a matrix by Elementary Matrices,

Determinants, Properties of Determinants and Cofactor Expansion, Bir matrisin tersi, Applications of Determinants,

Characteristic polynomial and eigenvalue of a matrix, Vectors, Real Vector Spaces.

MTH1105 ABSTRACT MATHEMATICS I (SOYUT MATEMATİK I)

Communicating mathematics and using symbols Sets, subsets and set operations Indexed collection of sets, partitions

of sets and cartesian products of sets Statements, the negation of statement, the disjunction and conjuction of

statements The implication, the biconditional, tautologies and contradictions Logical equivalence, some fundamental

properties of logical equivalence, characterization of statements Direct proof Proof by contrapositive Existence Proof

by contradiction Prove or disprove Eqivalence relations Partial order and total orders Maximum, maximal, minimum,

minimal elements of ordered sets.

MTH1107 ANALYTIC GEOMETRY I (ANLİTİK GEOMETRİ I)

Orthogonal coordinate system in plane and space, line equation in plane and space, plane equation in space, relations

of line and plane, cross product, projection of a point to a line, distance between two lines,projection and distance of a

point on a plane, half-space, angle between two planes, general definition of conic curves, circle, tangent of circle,

family of circle, special circles, ellipse, hyperbola, asymtotes of hyperbola, parabola, equation and tangent of parabola,

polar equation of conic curves.

MTH1102 CALCULUS II (ANALİZ II)

Calculus II includes series and series, vectors and their derivatives and integrals, functions of several variables and

their limits, continuity, differences, partial derivatives, multiple integrals and their applications, curvilinear and

surface integrals.

MTH 1104 LINEAR ALGEBRA II (LİNEER CEBİR II)

Real Vector Spaces, Subspaces, Spanning set and linear independency, Basis and Dimension, Coordinates,

Isomorphism and Linear.

MTH1106 ABSTRACT MATHEMATICS II (SOYUT MATEMATİK II)

The definition of a function, One-to-one and onto functions Bijective functions and composition of functions Inverse

functions and permutations Binary operations and properties of binary operations Cayley table and examples of binary

operation Construction of natural numbers Addition and multiplication for natural numbers Mathematical induction

Construction of integers, addition and multiplication for integers Division algorithm, least common multiple, greatest

common divisor Construction of rational numbers, addition and multiplication for rational numbers Properties of

rational numbers Cardinalities of sets, numerically equivalent sets, uncountable sets Comparing cardinalities of sets

and Schröder-Bernstein Theorem.

MTH1108 ANALYTIC GEOMETRY II (ANLİTİK GEOMETRİ II)

Geometric transformations, translations, rotations in plane, specified as a locus of conics in plane, examination of

second-degree surfaces in space, sphere surface, ruled surface, revolution surface, cylinder and cone surfaces,

homogeneous coordinates, definition of a curve in space.

PHY2201 PHYSICS I (FİZİK I)

Physics and measurements, vectors, one dimensional motion, instantanous velocity, acceleration, one dimensional

motion under constant acceleration, feely falling bodies, two dimensional motion, Laws of motion, circular motion

and Newton’s laws of motion, motion in accelerated systems, friction, work, power and energy, potential and kinetic

energy, conservation of energy, linear momentum and collisions.

MTH2201 MATHEMATICAL ANALYSIS I (MATEMATİKSEL ANALİZ I)

This course includes sequenced and convergence of sequences, sequential compactness, continuity and uniform

continuity, mean value theorem, derivative, convergence of Riemann sums, Weierstrass approximation theorem,

power series and taylor series.

MTH2203 COMPUTER PROGRAMING (BILGISAYAR PROGRAMLAMA)

Definition and structure of computers, Computer processing system, The binary number system, Floating point

arithmetics, error, machine numbers, Hardware units ,Physical structure and function of hardware units, Software

Operating systems, structures of software and classification, Application software, Algorithms and flowcharts,

Algorithms, Introduction to BASIC, Constants and variables, Basic codes in BASIC, Conditionals in BASIC, loops,

sequences, functions, subroutines, programming applications.

MTH2205 TOPOLOGY I (TOPOLOJİ I)

Topological spaces, base and subbase for a topology. Open sets and topological neighbourhood systems. Interior,

closure, frontier of a set, accumulation points and isolated points. Topological subspaces, continuity, construction of

initial and final topologies. Homeomorphisms, topological equivalence, topological properties, open and closed

mappings. Convergence of sequences in topological spaces and Hausdorff spaces.

MTH2229 MATHEMATICS LABORATORY I (MATEMATİK LABORATUVARI I)

To investigate applications of the courses of the first year, and analyse solutions of important problems.

MTH2231 READING AND WRITING SKILLS FOR MATHEMATICIANS (MATEMATİKÇİLER

İÇİN OKUMA VE YAZMA BECERİLERİ)

English expressions used in mathematics, basic mathematical terms, Mathematical abbreviations and symbols,

numbers, arithmatical operations, algebraic operations, indexes, matrices, inequalities, polynomial equations,

geometrical concepts, mathematical expressions, algebraic concepts, functions, translation applications.

MTH2267 HISTORY OF MATHEMATICS (MATEMATİK TARİHİ)

Short history of numbers, mathematics in Mesopotamia, mathematics in ancient Egypt, Greek mathematics, Turkish-

Islamic world mathematicians. Fibonacci numbers. The renaissance of mathematics: the rebirth of European

mathematics, Solutions and results of cubic equations, The dawn of modern mathematics, Development of probability

theory, Development of limit concept: Newton and Leibniz Euler, Gauss and Cauchy's contributions, The father of

modern analysis: Weierstrass, The representation of complex numbers,Counting the infinite, countable and

uncountable sets, The paradoxes of set theory, Women in modern mathematics, Development in mathematics in the

20th century.

PHY2202 PHYSICS II (FİZİK II)

The properties of electric charge, Electric Field, insulators and conductors , Coulomb’s law, Gauss's law, electric

potential, potential difference, capasitors and dielectric, capasitor with dielectric , current and resistans, electric

cicuits, Kirchoff's rules, RC circuits, movement of a charged particle in magnetic field, magnetic field sources.

MTH2202 MATHEMATICAL ANALYSIS II (MATEMATİKSEL ANALİZ II)

This course includes linear structure of 𝑅𝑛, convergence of a sequences in 𝑅𝑛, continuous functions, multivariable

functions, directional derivative, Hessian matrices, chain rule, Inverse function Theorem, Dini's theorem, Fubini's

Theorem, line and surface integrals, Green and Stokes Theorems. Hessian matrices, chain rule, Inverse function

Theorem, Dini's theorem, Fubini's Theorem, line and surface integrals, Green and Stokes Theorems.

MTH2204 DIFFERENTIAL EQUATIONS (DİFERENSİYEL DENKLEMLER)

Classification of differential equatios, initial and boundary value problems, Existence and uniqueness theorems,

Separable equations, Homogeneous equations and equations reducible to this form, Exact differential equations,

Integrating factor, Linear, Bernoulli and Riccati differential equations, Substitution, Clairaut and Lagrange equations,

Applications of first order differential equations, Theory of higher order linear differential equations, Higher order

linear homogeneous equations with constant coefficiens, The method of undetermined coefficients, Operator method,

The method of variation of parameters, Cauchy-Euler differential equation.

MTH2206 TOPOLOGY II (TOPOLOJİ II)

Product topology, metric function and metric spaces. Continuity, uniform continuity, convergence and cauchy

sequences in the setting of metric spaces. Metrizable topological spaces, compact spaces, compact subsets of the real

line and the plane. To introduce compact metric spaces, completeness and local compactness.

MTH2230 MATHEMATICS LABORATORY II (MATEMATİK LABORATUVARI II)

To investigate applications of the courses of the third semester, and analyse solutions of important problems.

MTH2232 ADVANCED PROGRAMMING (İLERİ PROGRAMLAMA)

Problem analysis in C++ language, Character sets, data types, statements, Operators and expressions, Data input –

output functions, Program running and testing Control structures, library functions and creating functions, Program

structures and multi-files , Arrays, Pointers,

MTH2272 COMBINATORICS (KOMBİNATORİK)

Basics and Terminology, Introduction to Counting, Pigeonhole Principle, Integer and Set partitions, Inclusion-

exclusion Principle and its applications, Mobius Inversion, Recurrence Relations, Applications of Recurrence,

Relations, Generating functions: Power series and their algebraic properties, Generating functions:, Homogeneous and

non-homogeneous linear recursion, Stirling and Bell Numbers, Catalan Numbers, Advanced, Counting: Probabilistic

Method, Advanced Counting: Polya’s Theorem.

MTH3301 ALGEBRA I (CEBİR I)

Some properties of integers, divisibility, prime factors, congruance of integer, equivalence classes and solutions of

equations, groups, subgroups, permutation groups, groups which are generated by a set and cyclic groups,

homomorphisms and isomorphisms of groups, , cosets and Lagrange’s theorem, normal subgroups and quotient

groups, internal direct sum of groups, p-groups and Sylow Theorems, structure of finite abelian groups.

MTH3305 THEORY OF COMPLEX FUNCTIONS (KOMPLEKS FONKSİYONLAR TEORİSİ)

Complex numbers, topology of complex plane, complex variable functions, limits and continuity, differentiation,

analyticity, harmonic functions, elementary functions, introduction to complex integral, contour integration. Integral

representations for analytic functions, power series, uniform convergence, Taylor and Laurent series.

MTH3307 ELEMENTARY DIFFERENTIAL GEOMETRY (TEMEL DİFERENSİYEL

GEOMETRİ)

Euclidean space; curves in Euclidean space; arc-length and reparametrization of a curve; curves in plane; some special

plane curves; Frenet vectors and curvatures; Frenet planes; Serret-Frenet formulas; some special space curves; tangent

vectors, vector vector fields; integral curves; invers function theorem; regular surfaces; first fundamental form;

Gaussian, mean and normal curvatures; ruled surfaces and minimal surfaces; some special curves on the surface.

MTH3329 MATHEMATICS LABORATORY III (MATEMATİK LABORATUVARI III)

To investigate applications of the courses of the third semester, and analyse solutions of important problems.

MTH3331 KINEMATICS (KİNEMATİK)

Planar motions, spherical motions, space motions, screw motions, finding screw axis, expression of displacements

with quaternions; rotation, translation and screw operators, and their applications.

MTH3337 FRACTAL GEOMETRY (FRAKTAL GEOMETRİ)

The notion of fractal, its history and some fractal examples; Sierpinski triangle, fractal examples; Koch snowflake,

inverse snowflake, polygon and circle fractals, space-filling curves, historic parks fractal, transformations in the plane

I, scale, reflections, transformations in the plane II, translations and contractions, fractal dimension, self-similarity,

dimensions of some fractals, fractional dimension, Hausdorff dimension, iteration methods, L-systems with

computers, Mandelbrot ve Julia sets, dimension with the box counting method, similarity dimension, Moran equation,

finding fractal decompositions, applications of the fractals in the nature, geometry of honeycomb fractal, geometry of

spiderweb fractal.

MTH3339 LINEAR PROGRAMING (LİNEER PROGRAMLAMA)

Introduction to Linear Programming, Applied Examples, Graphical Methods, Basic Concepts, Linear Algebra, Convex

Sets, Simplex Method, Duality.

MTH3341 ADVANCED DIFFERENTIAL EQUATIONS (İLERİ DİFERENSİYEL DENKLEMLER)

Higher order linear differential equations with variable coefficients, higher order nonlinear differential equations,

Laplace Transforms, inverse Laplace transforms, Convolution and integral equations, solution of differential equations

systems with Laplace transform, linear boundary value problems, Green's function, series solutions of differential

equations.

MTH3345 SYMBOLIC PROGRAMING LANGUAGES (SEMBOLİK PROGRAMLAMA DİLLERİ)

Introduction to Symbolic Languages (Maple, Matlab, Sage etc.) Integers, Rational Numbers, Irrational Numbers,

Exact and Floating Point Number Algebraic and Complex Numbers Assignment, Unassignment, Evaluation and

Names of Variables Functions, Polynomials and Graphing Solving Equations, Substitution, Expansion, Factorization

Limits, Differentiation, Integration and Summation Series and Approximations Sequences, Sets and Lists Array and

Table Differential Equation Applications Linear Algebra Applications Number Theory Applications Cryptography

and Coding Theory Applications

MTH3302 ALGEBRA II (CEBİR II)

Rings, subrings, integral domains and fields, the field of quotients of an integral domain, ordered integral domains,

ideals and qoutient rings, ring homomorphisms, the characteristic of a ring, maximal and prime ideals, polynomial

rings, divisibility for polynomials, factorization over polynomial rings, zeros of polynomials, finite fields.

MTH3304 NUMERICAL ANALYSIS (NÜMERİK ANALİZ)

Number representation and programming techniques, loss of significance. Locating roots of equations, bisection

method, Newton method, secant method. Interpolation and numerical differentiation, polynomial interpolation and

errors, estimating derivatives, Richardson extrapolation. Numerical integration, trapezoid rule, Romberg algorithm,

Simpson and Gauss quadrature formulas.

MTH3306 ADVANCED MATHEMATICAL ANALYSIS (İLERİ MATEMATİKSEL ANALİZ)

This course includes vector spaces and linear dependence of vectors, Normed spaces and Banach spaces, convergence

in normed spaces, operators and functionals, Hilbert spaces, concept of measure and measurability, Lebesgue measure

and L_ {p} spaces.

MTH3330 NUMBER THEORY (SAYILAR TEORİSİ)

Representations of integers, The fundamental theorem of arithmetic, Modular Arithmetic, Polynomial Congruences.

MTH3330 MATHEMATICS LABORATORY IV (MATEMATİK LABORATUVARI IIV)

To investigate applications of the courses of the fifth semester, and analyse solutions of important problems.

MTH3332 ADVANCED THEORY OF COMPLEX FUNCTIONS (İLERİ KOMPLEKS

FONKSİYONLAR TEORİSİ)

Singularities, zeros and poles, Residue Theorem and its applications, Argument Principle, Rouche Theorem, inverse

Laplace transform, linear transformation.

MTH3334 DIFFERENTIAL GEOMETRY (DİFERENSİYEL DENKLEMLER)

Fundamental forms; isometries and conformal maps; Gauss theorem; Gauss Bonnet Theorem and applications;

exponential maps; complete surfaces; Jacobi fields; surfaces of constant Gaussian curvature.

MTH3336 OPTIMIZATION (OPTİMİZASYON)

Concept of Optimiziation, Unconstrained and constrained Optimization, Linear and Nonlinear Programming, Solution

Methods, Applications.

MTH3338 PARTIAL DIFFERENTIAL EQUATIONS (KISMİ TÜREVLİ DENKLEMLER)

Curves and Surfaces in 3- dimensional space, Classification of partial differential equations, solution, Pfaffian systems

and their solutions, Origins of First order partial differential equations, Cauchy problem for first-order partial

differential equations, First order linear partial differential equations, Surfaces orthogonal to a given system of

surfaces, First-order nonlinear partial differential equations, Compatible systems, Charpit's method, First-order special

type partial differential equations and partial differential equations transformed special type equations, Applications of

first order partial differential equations, Higher order partial differential equations, Second order linear partial

differential equations with constant coefficients

MTH3340 SPECTRAL THEORY (SPEKTRAL TEORİ)

Boundary conditions and definition of Sturm-Liouville Operators. Lagrange Identity. Positive, symetric and

selfadjoint Sturm-Liouville Operators. Eigenvalues and eigenfunctions of selfadjoint operators. Examples of

eigenvalues and eigenfunctions. Integral equations and obtaining their solutions by consecutive approximation.

Getting the asymphtotics of eigenvalues. Getting the asymphtotic equality. Calculating the asymphtotics of

eigenfunctions and orthonormal eigen functions. Resolvent set and obtaining the resolvent operator. Spectral

expansion of Green Function and Resolvent operator by the method of integral equations, Spectral expansion on the

definition of the operator and spectral expansion of the resolvent operator. Karleman Formula.

MTH3344 TRANSFORMATIONS AND GEOMETRIES (DÖNÜŞÜMLER VE GEOMETRİLER)

Transformations, transformation groups, linear transformations in the plane, transformations that maintain distances,

motions in the Euclidean plane, kinds of motion in the plane, transformations that maintain the ratio of distances,

similarity transformations, non-metric geometries, affine transformations, affine geometry, geometry of projections.

MTH3348 INTEGRAL EQUATIONS (İNTEGRAL DENKLEMLER)

Definition and history of integral equations. Classify the integral equations. Relationship between differential and

integral equations. Fredholm integral equations and their solution methods. Volterra integral equations and their

solution methods.Integro - differential equations and their solution methods. Singular integral equations and their

solution methods. Nonlinear integral equations and their solution methods.

MTH3362 PROJECTIVE GEOMETRY (PROJEKTİF GEOMETRİ)

Affine plane, finite affine planes, obtaining affine plane with the help of object, projective planes, finite projective

planes, obtaining projective plane with the help of object, affine plane, and projective plane relations, real projective

planes, projective transformations, double ratio, projective conics, Dezarg and Pappus planes.

MTH3364 ALGORITHMS AND GRAPH THEORY (ALGORİTMALAR VE ÇİZGELER

KURAMI)

Introduction to algorithms, Growing rates and comparisons of algorithms, Sorting algorithms, Basics and Terminology

of graphs, Subgraphs and Graph Isomorphisms, Paths and Trees, An algorithm for vertex coloring, Trees and sorting

algorithms, Depth-first algorithm, Breadth-first algorithm, An algorithm for shortest path problem , Bipartite graphs,

Hall’s Theorem, Hierholzer's algorithm.

MTH3366 CODING THEORY (KODLAMA TEORİSİ)

Overview and Introduction to Coding Theory History of Coding Theory and Goals for Encoding and Decoding ISBN

Number, ZIP Bar Codes, Basic Replication Code and Basic Definitions Who is Hamming? Hamming’s Square codes

Hamming’s [7,4]-Code Finite Fields Vector Spaces Over Finite Fields Introduction to Linear Codes Properties of

Linear Codes Encoding and Decoding with a Linear Code Dual Codes Parity Check Matrix Syndrome Coding

Hamming Codes Perfect Codes.

MTH3376 SPECIAL FUNCTIONS (ÖZEL FONKSİYONLAR)

Definition of Gamma function and integral representation, The uniform convergence of integral representation and

sketching the graph of gamma function, Problem solving about gamma functions, Legendre duplication formula and

Weierstrass' infinite product, Applications of gamma function, Beta function and its properties, Error function and its

properties, Applications of error function: Heat Conduction in Solids, Elliptic integrals and its properties, Some

problems solving, Definition of Legendre polynomials, its genarating function and Legendre differential equation,

Legendre series, Applications of Legendre polynomials: Electric Potential due to a Sphere.

MTH4401 FUNCTIONAL ANALYSIS (FONKSİYONEL ANALİZ)

Hilbert Adjoint Operators, Hahn-Banach's Theorem, Reflexive Spaces, Strong and Weak Convergences, Open

Mapping and Closed Graph Theorem , Banach's Fixed Point Theorem.

MTH4403 CRYPTOLOGY (KRİPTOLOJİ)

Basics in Cryptology Caesar Cipher Mathematical description of a Cryptosystems The Substitution Cipher The Affine

Cipher The Vigenere Cipher The Hill Cipher The Permutation Cipher Stream Ciphers Cryptanalysis of some

cryptosystems Cryptanalysis of some cryptosystems Public-key Cryptosystems The RSA system ElGamal and Diffie-

Hellman cryptosystems.

MTH4405 MATHEMATICAL METHODS AND APPLICATIONS (MATEMATİKSEL

YÖNTEMLER VE UYGULAMALARI)

Coordinate systems and Calculus, Dirac delta function and its applications, algebra of vector, infinite series, vector

analysis, conservative vector field, Maxwell equations, complex analysis and its applications, Sturm separation and

Sturm comparison theorems, oscillating solutions, physical problems related with Sturm-Liouville systems, Bessel

functions and their applications, green function for heat equation, green function for wave equation, problem solving

MTH4407 REAL ANALYSIS (REEL ANALİZ)

Semiring, Ring, algebra, sigma-algebra, measure, outer measures, measurable sets, measurable functions, definition

of integration of measurable functions over measurable sets and investigation of related theorems.

MTH4409 SCATTERING THEORY (SAÇILIM TEORİSİ)

Fourier transform and its properties. Examples of Fourier transformation. Jost solution. Integral representation for Jost

solution. Properties of the kernel of Jost solution. Asymptotics of Jost solution. Jost function and its zeros. Scattering

function. Scattering data and its properties. Finding the Gelfand-Levitan equation. Existence and uniqueness of the

solution of the Gelfand-Levitan equation. Solution of invers problem. Parseval equation. Levinson equation.

MTH4411 INTRODUCTION TO DIFFERENTIABLE MANIFOLDS

((DİFERENSİYELLENEBİLİR MANİFOLDLARA GİRİŞ)

Differentiable maps; the inverse mapping theorem; topological manifolds; differentiable manifolds; differentiable

structure; submanifolds; immersion, submersion and embedding; vector fields; tensor and tensor product;

differentiable forms; Lie groups; Riemann metric; Riemann manifolds; exterior derivative and Stokes theorem.

MTH4413 SYSTEMS OF DIFFERENTIAL EQUATIONS (DİFERENSİYEL DENKLEM

SİSTEMLERİ)

Existence and uniqueness theorems, n-dimension linear differential equations systems, matrix method, linear systems

with periodic coefficients, nonlinear differential equations systems, Hamiltonian systems.

MTH4415 COMPLEX ANALYSIS (KOMPLEKS ANALİZ)

Mapping by elementary functions; mappings by w = 1/z,w = 𝑧2 and branches of w = 𝑧1/2; mapping by exponential

and logarithmic functions; mapping by trigonometric functions; successive mappings; linear fractional

transformations; conformal mapping; basic properties of conformal mappings; sequences of analytic functions; series

of analytic functions; uniform convergence, normal convergence; analytic continuation; Schwarz reflection principle;

Riemann surfaces.

MTH4417 ADVANCED TOPOLOGY (İLERİ TOPOLOJİ)

Product and box topology, countable product of metrizable spaces, uniform topology, order topology, quotient

topology, quotient space, limit point compact and sequential compact spaces, fundamental seperation axioms, normal

and reguler topological spaces, completely regular topological spaces, connectedness.

MTH4429 MATHEMATICS LABORATORY V (MATEMATİK LABORATUVARI V)

To investigate applications of the courses of the sixth semester, and analyse solutions of important problems.

MTH4437 HARMONIC ANALYSIS (HARMONİK ANALİZ)

Observation of some situations in applications that one has encountered Fourier series of a 2π-periodic and integrable

function, such as heat transfer, moreover, sufficient conditions for the uniform convergence of Fourier series of a

continuous 2π-periodic function, the Fejer and Poisson kernels, notion of convolution for the periodic and non-

periodic cases, Gauss-Weierstrass, Abel-Poisson kernels, L1, L2 spaces, pointwise or norm convergence of the family

of convolution operators in the appropriate spaces, degree of the convergence.

MTH4441 FRACTIONAL DIFFERENCE EQUATIONS (KESİRLİ FARK DENKLEMLERİ)

The function of Gamma and Beta The function of Mittag-Leffler Fractional integral and derivatives Fractional

derivatives of Riemann-Liouville Fractional derivatives of Caputo Left and right fractional differential equations

Properties of fractional derivatives Fractional Laplace transform Linear fractional differential equations Evaluation

Existence and uniqness theorems Laplace transform methods Fractional Green’s function Some applications on

fractional differential equations

MTH4443 DIFFERENCE EQUATIONS (FARK DENKLEMLERİ)

Difference operator, Properties of difference and shift operators, Analogies between the difference operator and

differential operator, Antidifference operator and its properties, Approximate summation, Theory of linear difference

equations, First order linear difference equations, Second order linear difference homogeneous equations,Second order

difference equations with variable coefficients, Higher order linear homogeneous difference equations with constant

coefficients, Methods of undetermined coefficients,The method of variation of constants, Nonlinear scalar difference

equations, Some applications on difference equations.

MTH4447 NON-EUCLIDEAN GEOMETRIES (ÖKLİD DIŞI GEOMETRİLER)

Non-Euclidean geometry, geometry and mechanics, distance and angle, Lorentzian circles, Galilean circles, Inversion,

Lorentz-Minkowski geometry, Frenet formulas, Loboçevski geometry, hyperbolic geometry, Galilean geometry, Other

non-Euclidean geometries.

MTH4451 OTHOGONAL POLYNOMIALS (ORTOGONAL POLİNOMLAR)

Basic concepts and definitions, construction of orthogonal polynomial system, moment functional and orthogonality,

existence theorems for orthogonal polynomials; recurrence formula, Favard's theorem and Christoffel-Darboux

formula for orthogonal polynomials, the roots of orthogonal polynomials, Rodrigues formulas, differential equations,

generating functions and norms of classical orthogonal polynomials, series expansions in terms of orthogonal

polynomials, asymptotic properties of orthogonal polynomials, applications of orthogonal polynomials in physics,

application of roots of Jacobi polynomials in potential theory, application of Hermite polynomials in quantum

mechanics , orthogonal polynomials on unit disc.

MTH4461 THEORY OF GROUPS (GRUPLAR TEORİSİ)

Basic isomorphism theorems, Simple groups, Characterizations of simple groups, To construct a new group, Divisible

groups, Group decompositions, Free groups, Finitely generated free abelian groups, direct product of groups, semi-

direct product of groups, inner and outer automorphisms, composion series, normal and subnormal series, Nilpotent

groups.

MTH4487 MATHEMATICAL MODELLING (MATEMATİKSEL MODELLEME)

Models and Classifications, Scale, Size, Power output, Motion, Running,Diving, Jumping, Hovering, Walking on

water, optimal gait, Number of legs, Posture and stability, Cost of packaging, Dimensional Analysis, Dimensional

homogeneity, Buckingham Pi theorem, Transformations of dimensionless products, Simple pendulum, Graphical

methods, Arm races, stability analysis, Leslie Age-structured model, epidemic model, Population models, Preditor-

Prey model, Measles Model with vaccination, Differential equations, Stability analysis, Phase-Plane equation, Orbits,

Ecological model for one species, Preditor-Prey model, Competition model, Spruce Budworm model, Epidemic

models

MTH4489 INTRODUCTION TO OPERATOR THEORY (OPERATÖR TEORİYE GİRİŞ)

Definition of operator and its properties, finite dimensional operators, compact operators, nuclear, Hilbert-Schmidt

operators, product operayors, positive and shift operators also spectrum and resolvent of these operators, infinite

determinants, maximal ideals, invariant subspaces.

MTH4400 GRADUATION PROJECT (BİTİRME PROJESİ)

To make an investigation on a specific subject, to plan a project and write a report on this subject, to encourage the

students to make research.

MTH4402 SYSTEMS OF DIFFERENCE EQUATIONS (FARK DENKLEM SİSTEMLERİ)

Systems of linear difference equations, Putzer algorithm, Method of Jordan canonical form, Linear periodic systems,

Stability theory of vector difference equations, Behavior of the solutions of the higher order scalar linear

homogeneous equations, Stability criterions for linear systems, Phase space analysis, Lyapunov’s direct method,

Linear autonomous systems and Sylvester’s criterion, Linear approximation and stability, Applications of difference

equation systems, Boundary value problems for difference equations, Lagrange identity, Green’s theorem, Liouville’s

formula.

MTH4404 FIELD EXTENSIONS (CİSİM GENİŞLEMELERİ)

Vector Space, Bases and Dimension, Linear transformations, Field extension, Algebraic and transcendental numbers,

Degree of an extension, Algebraic extensions, Monomorphisms, Tests for Primality of polynomials, Splitting Fields,

Cyclotomic Fields, The ring of algebraic integers, Norm, Trace and Discriminant, Integer Bases, Quadratic Number

Fields.

MTH4408 FOURIER ANALYSES (FOURIER ANALİZİ)

Fourier series, Fourier series for even and odd functions, complex form of Fourier series, Fourier series on general

interval, half-range expansions, term-by-term differentiation of Fourier series, term-by-term integration of Fourier

series, Fourier series of two-variable functions, Fourier integral, Fourier sine and cosine integrals, complex form of

Fourier integral, Fourier transforms, Fourier sine and cosine transforms, properties of Fourier transforms and

applications.

MTH4414 DYNAMICAL SYSTEMS (DİNAMİK SİSTEMLER)

Autonomous systems, critical points and their stability analysis, Lyapunov method, critical points for nonlinear

systems, energy conservation systems, some mathematical models.

MTH4430 MATHEMATICS LABORATORY VI (MATEMATİK LABORATUVARI VI)

To investigate applications of the courses of the fundamental courses, and analyse solutions of important problems.

MTH4432 APPLIED PARTIAL DIFFERENTIAL EQUATIONS (UYGULAMALI KISMİ TÜREVLİ

DENKLEMLER)

Partial differential equations with variable coefficient, Characteristic curves, Cauchy problems, Clasiffication of

partial differential equations, Heat equation, Solution of Heat equation with boundary conditions, Laplace equation,

Wave equation, Vibrating String with fixed end points, D'alembert 's solution, Sturm-Liouville eigenvalue problems,

Problems with a boundary condition of the third type.

MTH4436 THEORY OF MODULES (MODÜLLER TEORİSİ)

Modules and examples, submodules, cyclic modules and finitely generated modules, quotient modules, annihilators

and faithful modules, module homomophisms, isomorphisms and exact sequences, endomorphism rings, direct sums

and products of modules, free modules and vector spaces.

MTH4448 DISCRETE FRACTIONAL EQUATIONS (KESİRLİ FARK DENKLEMLERİ)

Preliminaries, Delta fractional exponential function, Delta fractional trigonometric functions, Delta fractional Taylor

polinomial, Delta fractional sum and differences, Initial value problems and solutions for delta fractional equations ,

Examples, The method of Laplace transform, Delta fractional Laplace transform, Evaluation, Discrete nabla fractional

exponential function, Discrete nabla fractional trigonometric functions, Discrete fractional sum and differences,

Discrete nabla fractional Laplace transfom.

MTH4452 INTRODUCTION TO TOPOLOGICAL VECTOR SPACES (TOPOLOJİK VECTOR

UZAYLARA GİRİŞ)

Convex, absorbent and balanced subsets in a vector space. Semi-norms, semi-metrics and their relations, quotient

vector space, Minkowski functional, topological vector spaces and their fundamental properties.

MTH4472 APPLIED COMPLEX ANALYSIS (UYGULAMALI KOMPLEKS ANALİZ)

Invariance of Laplace's equation. Finding a harmonic function to provide specific boundary conditions. Dirichlet

problem. Poisson's integral formula for the upper half-plane. Two-dimensional mathematical models. Steady state

temperature. Two-dimensional electrostatics. Two-dimensional fluid flow. The Fourier transform. The Laplace

transform. Shifting theorems. The z-transform. Cauchy integrals. The Hilbert transform.

MTH4490 THEORY OF RINGS (HALKALAR TEORİSİ)

Rings and subrings, ideals and rings of quotients, homomorphisms and isomorphisms, Boolean rings, regular rings,

direct sums of rings, maximal, prime and primary ideals, Jacobson radical, prime radical, simple rings and semisimple

rings, prime rings and semiprime rings, Noetherian and Artinian rings, rings of matrices, extensions of rings.

COM0405 ARTIFICIAL INTELLIGENCE

what is artificial intelligence, propositional logic, first-order predicate logic, search games and problem solving,

reasoning with uncertainity, machine learning and data mining, neural networks.

COM446 FUZZY LOGIC (FUZZY MANTIK)

Fuzzy Sets, Fuzzy Relations, Fuzzy Numbers, Fuzzy Functions, Uncertainity and Probability, Fuzzy Logic, Fuzzy

Inferences, and Fuzzy Control Systems.