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. DivideandConquer algorithms and recurrence relations. Generating Functions. InclusionExclusion. Applications of InclusionExclusion. 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, HigherOrder 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, MaxMin. 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.500A.D.1700), Negative numbers and invention of zero, Introduction of HinduArabic 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 alKashi A.D.1430, Law of Cosine), Translation of Arabic works, learning’s preserved by the Arabs slowly transmitted to Europe, Fibonacci’s book about HinduArabic numeral system (A.D.1202, an adaptation of alKhowarizmi’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 (4501683), Modern Period (A.D.1900 present) , (18281908 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 GramSchmidt 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  Existenceuniqueness 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. CauchyEuler 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 HeineBorel theorem, Nested set property, Pathconnected 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 Mtest, 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 StoneWeierstrass 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 topdown and bottomup 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 EulerLagrange 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. Firstorder logic. Interpretations of formulas in the firstorder 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 firstorder 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, tDistribution, FDistribution

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 CauchyGoursat 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  MittlagLeffler Functions; RiemannLiouville fractional integrals and derivatives; Caputo fractional derivatives; GrünwaldLetnikov fractional derivative; Riesz fractional integrodifferentiation 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. RungeKutta 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 GaussSeidel 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. Predatorprey 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 Ztransform, 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, SelfAdjoint 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, PrivateKey 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. PublicKey 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  Multitasking realtime 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 HahnBanach , Baire Category and uniform boundedness theorem, bounded and continuous linear operators.

MCS 458
Elective Course 
EGovernment  Policy and management issues specific to egovernment and egovernance; issues in effective IT adoption and diffusion in the public sector; information society, digital gap; methods and tools for the development and implementation of egovernment projects; maturity level of egovernment services; concepts of etransformation

MCS 476
Must Course 
Differential Geometry  Curves in R3. The local theory of curves parametrized by arc length. FrenetSerret 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 DecisionTree based classifiers, AssociationRule 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.
