Mathematical Fundamentals, basic cryptologic techniques, crypto analysis, elliptic curve cryptology, quantum cryptology.

Meaning, importance and aim of the research. Types of the research. Defining the research problem and approaches to the problems and their solutions. Design of the research. Sampling design. Measurement techniques. Data collecting techniques. Analysis of data. Presentation and preparation of research document. Ethic.

Meaning, importance and aim of the research. Types of the research. Defining the research problem and approaches to the problems and their solutions. Design of the research. Sampling design. Measurement techniques. Data collecting techniques. Analysis of data. Presentation and preparation of research document. Ethic.

The course will deal with problems of ethics as a field of philosophy and, on the basis of these
problems, will discuss the ethical aspects of human rights.

Infinite set theory, ordinal and cardinal, numbers, topological spaces, bases, functions, theory of convergence, seperation, and first countable topological space, and second countable topological spaces, compactness and paracompactness

Basic concepts, LaTeX input files, text and language structure, page structure and the environment. Mathematical formulas. The structures of theorems, definitions, examinations and results. Bibliography preparation, internal references, the preparation of the footer and header, to prepare documents in PDF format. Graphic drawing.Adding new commands and environments. Fonts and typefaces.

Sets, functions, real and complex numbers, sequences of real and complex numbers, series, metric spaces, compakt spaces, vektor spaces, continuity, uniform continuitry, compactness, integrals of complex valued functions, differentiationof complex valued functions, sequences of functions and series of functions, differantial equations and exponantial function, trigonometric functions and logaritm, functions with two variables, infinitely differantiable certain functions, continuous periodical functions, uniform periodical functions, translation,convulation, approximation, Weierstrass approximation theorem,periodical distrubitons, convulation of distrubitions, operations on periodical distrubitions.

Hilbert spaces, Hilbert spaces of sequences, orhonormal bases, orthonormal distrubitions, Periodical expansions and FUrier series of uniformly periodical functions, convulations, heat equation, complex differantial, complex integration, Cauchy integral Formula, holomorf functions, isoleted singularities, rationel functions, Laurent expansions, rezidues, holomorf functions on unit square, Laplace transforms of functions, Laplace transforms of distrubitions, differantial equations.

Unbounded sets, properties of sets, Limit points, measure concept in real line, measure concept in plane; generalized measure conceptı, measurable sets, measure of sets, Measuable functions, sequences of functions and convergence in measure, concept of measure space, definition of properties of measurable functions, Lebesgue, B.Levi,Fatou theorems; monoton, bounded variation, absolute continuous functions, Lebesgue integral of bounded functions.

Metric spaces, open, closed set, neighbourhood, convergence, Cauchy sequence, completeness, proofs of completenessı, completion of metric spaces, vector spaces, normed spaces, Banach spaces, examples of normed spaces, Finite dimensional normed spaces and subspaces,
, kompactness and fineite dimension, linear operators, bounded and continuous operators, linear operators, linear functionals, linear operators and functionals in finite dimensional linear spaces, normed spaces and operators, dual spaces, iner product spaces, Hilbert spaces, Properties of iner product spaces, orthonormal sets and sequences, properties of orthonormal sequences and sets, complete orthonormal and sequences, Legendre, Hermite Laguerre sequences, presentation of functionals in Hilbert spaces, Hilbert adjoint operator, Self-adjoint, unit and normal operators, main theorems in normed and Banach spaces, Reflexible spaces, uniform boundedness theorem, strong and weak convergence, convergence sequences of operators, summability of sequences, closed linear operators.

Symetric sets, balanced sets, convex sets, absolute convex sets, Minkowsky functionals, topological vector spaces induced by a sequence of semi-norms, bounded sets, local convex topological vector spaces, Frechet spaces, continuous functions in topological vector spaces, linear functionals and related theorems.

Summability and infinite matrices, Cesaro and Holder matrices, Abel?s method, Tauberian theorems.

The aim of the course is to teach the main importance of the differential equations, and give the applications of the systems.

Complex Numbers, The complex plane, The sequences of complex numbers, The functions of a complex variable, Connectedness, Connected set, Continuous curves, Domains, The Jordan curve theorem, The extended complex plane, Differentiation and Cauchy-Riemann equations, Analytic functions, Geometric interpretation of the modulus and the argument of the derivative, Conformal mappings, Möbius transformation and its properties, Polynomials, The exponential function, The logarithm, Trigonometric functions, Examples of Riemann Surface, Integrals of complex functions and their properties, Cauchy?s Integral theorem and its applications, The formula of Cauchy?s Integral, Integrals of Cauchy Type, Cauchy Formula for derivatives, Morera?s Theorem, Cauchy?s Inequality, Liouville?s theorem, Power series representation of analytic functions and its uniqueness, The zeros of analytic functions and their degrees, The uniqueness theorem, The maximum modulus princible, The theorems of Phragmen Lindelöf, Laurent series, The isolated singular points, The residue theorem, The argument princible, The theorems of Rouche and Hurwitz, The calculus of residue and its applications

Ortogonal Polinomlar, Ortogonal Polinomların Genel Özellikleri, Açılım Teoremleri, Klasik Ortogonal Polinom Aileleri, Legendre Fonksiyonları, Geliştirilmiş Legendre Fonksiyonları, Bessel Fonksiyonları, Bessel Fonksiyonlarının Önemli Bazı Özellikleri.

Topological spaces, Product topology, Metric topology, Quotient topology, Connectedness, Compactness, Differentiable manifolds, Tangent spaces, Vector fields, Lie brackets, Hypersurfaces of Euclidean space, Standard connection of Euclidean space, Weingarten and Gauss maps, Gauss and Codazzi equations, Tensors, Differential forms, Lie derivative, Riemannian connection, Riemannian curvature tensor.

Introduction to basic concepts and motivation, Hamiltonian systems on symplectic manifolds, Canonical Hamiltonian systems on the cotangent bundles, Lagrangian mechanics, Variational Principles and Constraints, Differentiable manifolds, Differentiable mappings, submanifolds, Tangent bundle, vector fields, Jacobi-Lie bracket of vector fields, Cotangent bundle, Differential forms, Interior and exterior derivative, Lie derivative

The axioms of probability, random variables, probability distributions, statistical decision theory, estimation, hypothesis testing, data analysis, regression and corelation, analysis of variance

Vectors in space, matrices, linear equations, determinants, matrix inversion and Cramer's rule, eigenvalue, eigenvectors, first order linear and separable differential equations, higher order differential equations, Laplace transformation and solution of differential equations.

Meaning, importance and aim of the research. Types of the research. Defining the research problem and approaches to the problems and their solutions. Design of the research. Sampling design. Measurement techniques. Data collecting techniques. Analysis of data. Presentation and preparation of research document. Ethic.