Course Code Course Name Course Content MCS 123 Must Course Discrete Mathematics Elements of logic. Basic proof techniques. Propositional Logic. Propositional equivalences. Predicates and Quantifiers. Set theory and operations on sets. Relations. Functions. Basics of counting. Permutations and combinations. Combinatorial arguments. Application to analysis of algorithms. Recurrence relations. Solving linear recurrence relations. Divide-and-Conquer algorithms and recurrence relations. Generating Functions. Inclusion-Exclusion. Applications of Inclusion-Exclusion. Graphs and Trees and their representation in computing. MCS 151 Must Course Calculus I Real numbers and the real line, intervals, absolute value, Equations and inequalities involving absolute value, Graphs of Quadratic Equations, circles, parabolas, shifting a graph, ellipses and hyperbolas, Functions, domain and range, graphs, even and odd functions, combining functions, composite functions, piecewise defined functions, Trigonometric functions, identities, graphs of trigonometric functions, Limits of functions, Limits at infinity and infinite limits, Continuity,   Tangent lines and their slopes, the derivative, Differentiation Rules, The Chain Rule, Derivatives of Trigonometric Functions, Higher-Order Derivatives, The Mean Value Theorem, Implicit Differentiation, Antiderivatives, Inverse Functions, The Natural Logarithm and Exponential, The Inverse Trigonometric Functions, Hyperbolic Functions, Related Rates, Finding Roots of Equations, Indeterminate Forms, Extreme Values, Concavity and Inflections, Sketching the Graph of Functions, Max-Min. Problems, Linear Approximations, Taylor Polynomials, Sums and Sigma Notation, Areas as Limits of Sums, The Definite Integral, Properties of the Definite Integral, the Fundamental Theorem of Calculus, The Method of   Substitution, Areas of Plane Regions, Integration by Parts MCS 152 Must Course Calculus II Integrals of Rational Functions, Inverse Substitutions, Improper Integrals, Volumes by Slicing, Solids of Revolution, Arc length, Surface Area, Polar Coordinates and Polar Curves, Arc Lengths for Polar Curves, Sequences and Convergence, Infinite series, Convergence Tests for Positive series, Absolute and Conditional Convergence, Power Series, Taylor and Mac Laurin Series The Binomial Theorem, Analytic Geometry in Three Dimensions, Vectors, The Cross Product, Planes and Lines, Vector Functions of One Variable, Curves and Parametrization, Functions of Several Variables, Limits and Continuity, Partial Derivatives, Higher order Derivatives, The Chain Rule, Differentiability and Differentials, Gradients and Directional Derivatives, Implicit Functions, Taylor Series, Extreme Values, Extreme Values of Functions Defined on Restricted Domains, Lagrange Multipliers, Double Integrals, Iteration of Double Integrals in Cartesian Coordinates, Improper Integrals, Double Integrals in Polar Coordinates, Triple Integrals, Cylindrical and Spherical Coordinates, Change of Variables in Triple Integrals, Line Integrals, Conservative Vector Fields, Gradients, Divergence, and Curl, Green’s Theorem in the Plane, Stoke’s Theorem. MCS 182 Must Course Computer Programming I Algorithmic approach to problem solving, pseudocodes, flow charts. Introduction to Java programming language. Using Java programming language, selection statements, loops, methods, single dimensional arrays, multidimensional arrays, characters and character sequences. Object oriented programming with Java. Inheritance. Polymorphism. MCS 183 Must Course Foundations of Mathematics and Computer Science Symbolic logic, set theory, Cartesian product, relations, functions, injective, surjective and bijective functions, equipotent sets, countability of sets, equivalence relations, partitions, quotient sets, order relations, partial order, total order, well ordering, mathematical induction and recursive definitions of functions. Introductory computer, science topics; Operating systems, Networking, Data structures, Database systems. Introductory Latex. MCS 193 Must Course Introduction to History of Mathematics Mathematical Periods, Egyptian and Babylonian Period (2000 B.C.- 500 B.C.) Introduction to early numeral systems, Simple arithmetic, Practical geometry, Decimal and Sexagesimal numeral systems, Sources: Ahmes (Rhind) papyrus; Moscow papyrus; Babylonian tablets, No theorems, no formulas, essentially empirical mathematics, Greek Mathematics Period, (500 B.C- A.D.500) Development of deductive geometry (Thales, Pythagoras), Start of number theory (Pythagorean school) Systematization of deductive logic (Aristotle, Platon or Eflatun; 340 B.C), Geometry of conic sections (Apollonius, 225 B.C), Axiomatic development of geometry (Euclid, 300 B.C), Germ of the integral calculus (Archimedes, 225 B.C), Hindu, Islamic and Period of Transmission (A.D.500-A.D.1700), Negative numbers and invention of zero, Introduction of Hindu-Arabic numeral system (before A.D 250), Preserves of Hindu arithmetic and Greek geometry, Book of Algebra and a book about the computation of Hindu numerals (Al- Khowarizmi, A.D.820), Geometric solution of cubic equations (Omar Hayyam, A.D. 1100, S. Al- Tusi A.D.1170), Trigonometric tables (Ulug Bey, A.D.1435, Jamshid al-Kashi A.D.1430, Law of Cosine), Translation of Arabic works, learning’s preserved by the Arabs slowly transmitted to Europe, Fibonacci’s book about Hindu-Arabic numeral system (A.D.1202, an adaptation of al-Khowarizmi’s book), First math. Book printed in Europe (Treviso Arithmetic, Italy 1478), First printed edition of Euclid’s “Elements” (A.D.1482), Growth of the Ottoman Empire (450-1683), Classic Period (A.D. 1700-A.D.1900) ,(1700-1827 Stagnation period of the Ottoman Empire), Logarithms (Napier1614), Modern Number Theory (Fermat,1635), Analytic Geometry (Descartes 1637), Mathematical Probability (Pascal 1654), Calculus (Leibniz 1684, Newton 1687), Applied Calculus (Bernoulli 1700, D’Alembert 1743, Euler 1750,Lagrange 1788, Laplace1805, Green 1828, Poisson 1831, Fourier, 1822), Topology (Riemann 1851, Möbius 1865,Poincaré 1895), Analysis (Lagrange 1797, Abel 1826, Cauchy 1827, Dirichlet 1840, Dedekind 1872,Weierstrass 1874, Lebesgue 1903), Abstract Spaces (Frechet 1906, Hausdorff 1914, Banach 1923), Set Theory (Cantor 1874, Boole 1847, De Morgan 1848, Hausdorff 1914), Abstract Algebra (Galois 1832, Hamilton 1843, Cayley 1857,Grassmann 1844) Electromagnetism (Edison, 1890, N.Tesla, 1900), Modern Period (A.D.1900- present) , (1828-1908 Decline period of the Ottoman Empire), Gödel ‘s Incompleteness Theorem (1958), Inner Product Spaces, Generalizations of R^n (Hilbert, 1925), Metric Spaces (Frechet, 1906), Topological Spaces (Kuratowski, 1922, Hausdorff 1914), Functional Analysis (S. Banach, 1932, Volterra 1930), Theory of Distributions (Sobolev 1935, Schwarz (1942), Neutrices (B.Fisher 1996), Fractional Calculus (S.Dugowson 1998), Computing Machines (Babbage 1832, Alan Turing (1936). MCS 200 Must Course Summer Training I Students are required to attend and successfully complete a minimum of 20 working days summer training. The summer internship should be carried out in accordance with the rules and regulations set by the department. In both internships, students are expected to observe, describe and report their practical experiences. MCS 231 Must Course Linear Algebra I Systems of linear Equations, Row Echelon Form, Matrix Algebra, Elementary Matrices, Determinants, Vector Spaces, Linear Independence, Basis and Dimension, Row Space and Column Space, Null Spaces and Ranges, Linear Transformations, Similarity MCS 232 Must Course Linear Algebra II Inner Product Spaces, Orthogonality, Orthonormal Sets, The Gram-Schmidt Orthogonalization Process, Eigenvalues and Eigenvectors, Diagonalization, Hermitian Matrices, Positive Matrices, Normal Matrices, Real Symmetric Matrices, Unitary and Orthogonal Matrices, Bilinear and Quadratic Forms, Canonical Forms, Decompositions. MCS 245 Must Course Differential Equations Existence-uniqueness theorem of first order initial value problems. First order equations (Separable, exact, linear, etc.). Higher order linear ordinary differential equations. Constant coefficient equations. Reduction of order method, method of undetermined coefficients, method of variation of parameters. Cauchy-Euler equations. Power series solutions. The Laplace transform. Convolution integral. Solution of initial value problems using Laplace transform. Solution of systems of linear differential equations by simple elimination and by the Laplace transform. MCS 251 Must Course Advanced Calculus I The Real line and Euclidean space (ordered field, distance, Schwarz Inequality), The topology of Euclidean space (open sets, Interior of a set, closed sets, accumulation points, closure of a set, boundary of a set, sequences, completeness), Compact and Connected sets (compactness, the Heine-Borel theorem, Nested set property, Path-connected sets, connected sets), Continuous Mappings (continuity, Images of compact and connected sets, operations on continuous mappings, the boundedness of continuous functions on compact sets, Uniform continuity, Differentiation and Integration of functions of one variable), Uniform convergence (pointwise and uniform convergence, the Weierstrass M-test, Integration and differentiation of series, the space of continuous functions, the Arzela – Ascoli theorem. MCS 252 Must Course Advanced Calculus II The space of continuous functions, the Arzela – Ascoli theorem, the contraction mapping principle and its applications, the Stone-Weierstrass theorem, Differentiable Mappings, Differentials of transformations, Matrix representation, Continuity of differentiable mappings, Differentiable paths, Conditions for differentiability, The chain rule, Product rule and gradients, Higher derivatives, Maxima and Minima of the functions defined on R^n, The Inverse and Implicit Function Theorems and Related Topics, Constrained extrema and Lagrange Multipliers, Integration, Integrable functions, Volume and sets of measure zero, Properties, Improper Integrals, Some convergence theorems, Fubini’s Theorem and the change of variables formula, Fourier Analysis, Inner Product Spaces, Orthogonal Families of Functions, Convergence Properties of Fourier Series MCS 281 Must Course Computer Programming II Using Java programming language, developing algorithms using top-down and bottom-up analysis method, fundamentals of visual programming, programming in GUI, subprograms, Java graphics tools and libraries, opening and closing files. MCS 282 Must Course Numerical Analysis Roundoff errors, algorithms and convergence, bisection method, fixed point iteration, Newton’s method, error analysis, accelerating convergence. Interpolation and Lagrange polynomial, divided differences. Cubic splines. Numerical differentiation, Richardson’s extrapolation. Numerical integration, trapezoid, Simpson’s and Boole’s rules. Romberg integration, adaptive quadrature. Gaussian quadrature. Multiple integrals MCS 288 Elective Course Data Structures with Java Algorithmic problem solving. Basic data structures. Queues. Stacks. Hash tables. Searching and sorting techniques, utilizing different data structures.  In this course Java programming language will be used. MCS 311 Elective Course Calculus of Variations Lagrange multipliers, Maxima and minima, the first variation. The Euler-Lagrange equations. Constraints. Natural and boundary conditions.Transversality conditions. The Hamiltonian formulation. MCS 315 Must Course Partial Differential Equations First order equations; linear, quasilinear, and nonlinear equations; classification of second order linear partial differential equations; canonical forms; the Cauchy problem for the wave equation; Laplace and heat equations MCS 321 Elective Course Symbollic Logic Propositional logic: interpretations of formulas in the propositional logic, normal forms. First-order logic. Interpretations of formulas in the first-order logic, prenex normal forms. Skolem standard forms. Herbrand universe of a set of clauses. Semantic trees. Herbrand’s theorem. Resolution principle for the propositional logic and resolution principle for the first-order logic. MCS 322 Elective Course Fuzzy Sets The notion of membership. The concept of fuzzy subsets. Simple operations on fuzzy sets. Properties of the set of fuzzy subsets. Product and algebraic sum of two fuzzy subsets. Fuzzy graphs.Fuzzy relations. Properties of fuzzy binary relations. MCS 323 Must Course Abstract Algebra Review: Mappings, Mathematical Induction, Basic Tools from Number Theory, Groups, Subgroups, Cyclic Groups, Permutation Groups, Cosets and Lagrange Theorem, Direct Products, Normal Subgroups and Factor Groups, Group Homomorphisms, Fundamental Theorem of Finite Abelian Groups, Rings, Integral Domains, Ideals, Factor Rings, Ring Homomorphisms. MCS 324 Must Course Introduction to Probability and Statistics Statistical Inference, Sampling Procedures, Measures of Location, Measures of variability, Statistical Modeling, Graphical Methods, Data Description, Sample Spaces, Events, Algebra of Events, Probability of Events, Conditional Probability, Bayes’ Rule, Random Variables, Joint Random Variables, Mathematical Expectation, Variance, Covariance, Discrete Random Variables: Binomial, Hypergeometric, Negative Binomial, Geometric and Poison Distribution, Continuous Random Variables: Normal, Gamma and Exponential Distribution, Random Sampling, Sampling Distributions, Central Limit Theorem, t-Distribution, F-Distribution MCS 352 Must Course Complex Calculus Basic properties of the complex numbers. Complex functions and linear mappings of regions in the complex plane. Limits and continuity. Branches of functions. Differentiable and analytic functions. Harmonic functions. Elementary functions. Contours and contour integrals. The Cauchy-Goursat theorem. Cauchy integral formula and its extensions. Taylor and Laurent series representations. Singularities, zeros, and poles. The residue theorem and its applications to evaluation of trigonometric and improper integrals. The argument principle and Rouché’s theorem. MCS 366 Elective Course Elementary Number Theory Divisibility. The linear Diophantine equation. Primes. Congruences. Euler, Fermat, Wilson, Lagrange and Chinese Remainder Theorems. Arithmetical functions. MCS 371 Elective Course Introduction to Fractional Differential Equations Mittlag-Leffler Functions; Riemann-Liouville fractional integrals and derivatives; Caputo fractional derivatives; Grünwald-Letnikov fractional derivative; Riesz fractional integro-differentiation ordinary differential equations; fractional Laplace transform; Cauchy type problems. MCS 381 Must Course Scientific Computation Ordinary differential equations and initial value problems. Euler’s method. Higher order Taylor methods. Runge-Kutta methods. Error control, systems of ordinary differential equations and higher order equations. Linear systems of equations. Operations of linear algebra. Gaussian elimination. Pivoting strategies, LU factorization. Eigenvalues. Iterative methods of Gauss-Seidel and Jacobi. Applications with MATLAB. MCS 386 Must Course Introduction to Mathematical Modelling Discrete dynamical systems. Optimization models and Linear Programming. Correlation and regression. Discrete and continuous probabilistic models. Predator-prey models, optimal harvesting, traffic flow. Verification and validation of models. MCS 388 Elective Course Database Management Systems with Java Introduction to databases. Relational data model. Entity Relationship (ER) diagrams. Relational Algebra. Relational calculus. Structured Query Language (SQL). Database Programming Techniques. Functional dependency and normalization for relational databases. Transaction processing. MCS 410 Elective Course Special Functions Gamma function. Beta function. Bessel’s and generalized Bessel’s function. Orthogonal polynomials. Chebyshev, Legendre, Hermite, Laguere, Jacobi polynomials, Hypergeometric functions MCS 417 Elective Course Introduction to Difference Equations The difference calculus, first order equations, linear equations, equations with constant coefficients, equations with variable coefficients, undetermined coefficients method, variation of parameters method, the Z-transform, linear systems, stability theory MCS 418 Elective Course Calculus on Time Scales Basic Definitions, Differentiation, Integration, First Order Linear Equations, Second Order Linear Equations, Laplace Transform, Self-Adjoint Equations, Boundary Value Problems and Green’s Function, Eigenvalue Problems. MCS 427 Elective Course Introduction to Cryptography History and overview of cryptography, The Basic Principles of Modern Cryptography, Private-Key Cryptography; One time pad and stream ciphers, Block ciphers, PRPs and PRFs, Attacks on block ciphers. Message Integrity; Collision resistant hashing, Authenticated encryption: security against active attacks. Public-Key Cryptography; Cryptography using arithmetic modulo primes, Public key encryption, Arithmetic modulo composites. Digital Signatures. MCS 437 Elective Course Computer Networks with Java Introduction to computer networks. LAN, WAN, bridges, routers, gateways, Ethernet. Protocol design. TCP/IP protocols and IP addressing. Digital data transmission, Error detection and correction. Routing algorithms. ISO reference layers, Network layer in the Internet. Internetworking. Elements of transport protocol. Network security. MCS 438 Elective Course Operating Systems with Java Multi-tasking real-time operating systems, batch systems, multiprogramming systems, time sharing systems, interactive systems, operating system services, file system, CPU scheduling, memory management, deadlocks, buffering and spooling concurrent process and concurrent programming languages. MCS 441 Elective Course Mobile Application Development I History of mobile software development; information about Android operating system; Android development tools: software development kit (SDK), Android virtual devices (AVD), debugging; activities; user interface (UI) design: views, layouts, resources, menus, handling events; intents; adapters; creating animations; Android data and SQLite. Java programming language will be used in all implementations. MCS 448 Elective Course Introduction to Pattern Recognition MCS 451 Must Course Topology Topological. Spaces; definitions, bases and subbases; continuous closed and open functions; homeomorphisms; countability axioms; separation axioms;compactness;product and quotient topologies; connectedness; metric and normed spaces; function spaces, Ascoli’s theorem, compact open topology. MCS 452 Must Course Functional Analysis To teach metric sequence spaces, Normed, Banach spaces and Hilbert spaces, the basic theorems in Hilbert spaces such as Riesz Representation Theorem, basic theorems in Banach spaces such as Hahn-Banach , Baire Category and uniform boundedness theorem, bounded and continuous linear operators. MCS 458 Elective Course E-Government Policy and management issues specific to e-government and e-governance; issues in effective IT adoption and diffusion in the public sector; information society, digital gap; methods and tools for the development and implementation of e-government projects; maturity level of e-government services; concepts of e-transformation MCS 476 Must Course Differential Geometry Curves in R3. The local theory of curves parametrized by arc length. Frenet-Serret formulas. Surfaces. The tangent plane. The first fundamental form. Normal curvature. Geodesics. MCS 485 Must Course Computer Graphics with Java Using Java programming language, Advanced application of computer graphics techniques. Shading. Deformation. Ray tracing. Radiosity. Texture mapping. Fractal representation. Concepts of motion are introduced for the generation of digital animation. Concepts of graphical workstation design. Especially with respect to user interfaces and window managers are introduced. MCS 488 Elective Course Introduction to Data Mining The course introduces principles and techniques of data mining from preprocessing to evaluation of results. It emphasizes the advantages and disadvantages of using these methods in real world systems. Topics include: preprocessing techniques, data mining using Decision-Tree based classifiers, Association-Rule mining, Clustering methods, Statistical methods (Probability, Maximum Likelihood, Bayesian methods), data warehousing and application examples like Text Mining, Web Mining. MCS 491 Must Course Graduation Project I A practical / theoretical training in mathematics / modelling / computer / simulation. A report and presentation are required for the completion of the course. MCS 492 Must Course Graduation Project II A practical / theoretical training in mathematics / modelling / computer / simulation. A report and presentation are required for the completion of the course. MCS 494 Elective Course Game Theory Strategic Games; Illustrations, Bayesian Games, Mixed Strategies, Maxminimization, Rationalizability, Evolutionary Equilibrium. Extensive Games; Illustrations, Signaling Games, Extensions, Repeated Games, Bargaining. Coalitional Games; Bargaining.