Course Description

**CENG 502 - Computer Networks and Communication (3 0 3)**

Basics of data communication, computer networks, ISO /OSI basic reference model, routing, flow control, congestion control, TCP/IP suite of protocols, data links, Internetworking, higher level protocols.

**CENG 535 - Database Management (3 0 3)**

Introduction to database systems, data storage and retrieval problems, data definition, relational database management systems, Tables, Queries, Relationships. Entity-Relationship models. Introduction to Sequential Query Language (SQL), Writing queries in Visual environments, Embedded SQL. Database programming with Visual Basic and MS-ACCESS.

**MCS 501 - Analysis (3 0 3)**

Elementary topology of Rn, continuous functions in Rn, uniform continuity, uniform convergence, differentiability and implicit function theorem, differentiation under an integral sign, Stone-Weierstrass theorem on the real line, measure spaces, Lebesgue measure and integral, convergence theorems for the Lebesgue integral, types of convergence for sequences of functions, product measures and Fubini's theorem, Lp spaces and the Riesz representation theorem, Radon-Nikodym theorem.

**MCS 502 - Ordinary Differential Equations (3 0 3)**

Basic theory: initial value problems. Linear systems: linear homogeneous and non homogeneous systems. Linear systems with constant and periodic coefficients. Oscillation theory. Stability: definitions of stability and its boundedness. Lyapunov functions. Lyapunov stability and instability. Domain of attraction. Perturbation of linear systems. Stability of an equilibrium point. The stable manifold. Stability of periodic solutions. Asymptotic equivalence.

**MCS 503 - Scientific Computation I (3 0 3)**

Gaussian elimination and its variants. Sensitivity of linear systems. Orthogonal matrices and the least squares problem. Eigenvalues and eigenvectors. The singular value decomposition. Solutions of Partial differential equations, solution of system of equations, Examples of time dependent events, and their solutions. Applications with MATLAB / Java.

**MCS 504 - Advanced Topics in Mathematical Modelling (3 0 3)**

Curve fitting, stability, bifurcation, predator-prey oscillations, optimal harvesting, Traffic flow, exponential growth, self-limiting growth, vibrations and resonance, random processes, Markov Chains, diffusion Equation. Design of models of real life events, verification and validation of models.

**MCS 505 - Computer Simulation (3 0 3)**

Computer simulations are methods which are commonly used by performance analysts to represent constraints and optimize performance, and to predict the future possible outcomes. In this course students will work on projects which are related to the real life problems during the semester, including design of the model, verification and validation of models; analysis and interpretation of the results.Good level of a programming language knowledge is required.

**ELECTIVE COURSES**

**CENG 501 - Operating Systems (3 0 3)**

Fundamentals of concurrent programming; multitasking operating systems with special emphasis on UNIX; mutual exclusion problem and critical sections; semaphores; ADA rendezvous; transporters; UNIX structure.

**CENG 503 - Image Processing (3-0-3) **

Discrete time signals, reconstruction, quantisation, digital image representation, image fundamentals, image transforms, image enhancement, image restoration, segmentation, description, sampling.

**CENG 508 - Artificial Intelligence I (3 0 3)**

Exploring natural events, goal reduction, finding solution paths, games, logic, advanced knowledge representation, natural language of understanding, matching, applications.

**CENG 514 - Computer Graphics (3 0 3)**

Review of hardware and software used in graphic systems. Introduction to programming with OpenGL/Java. Graphic primitives. 2D and 3D geometric transformations. Two dimensional viewing: Viewing pipeline, clipping, and windowing. Three dimensional viewing: Viewing pipeline, viewing parameters, projections, viewing transformations, clipping. Visible surface detection. Introduction to illumination models and surface rendering. Introduction to ray tracing.

**CENG 519 - Artificial Intelligence II (3-0-3)**

Knowledge representation. Uncertain knowledge and reasoning. Learning in neural and belief networks. Natural language processing.

**CENG 520 Information Security (3 0 3)**

Essentials of information security, determination of IT-security risks, specification of security objectives and security policy will be introduced. Furthermore, network packet capture and analysis, protocol decoding, security scanning, and attacks. Techniques and tools in penetration testing. Attends will learn to analyze security risks, design and test IT-security procedures and mechanisms, scan ÝP networks, discover and monitor intrusions and vulnerability within a specific range of threats.

**CENG 567 - Data Mining (3 0 3)**

What is data mining? Data mining strategies and techniques, Decision trees, Association rules, K-means algorithm, and statistical models. Tools used for data mining, Knowledge discovery in databases, Evaluation methods, Advanced data mining techniques, Intelligent systems.

**MCS 506 - Algebra (3 0 3)**

Groups: generalities, groups acting on a set, Sylow theorems, free group, direct product and sums. Rings: generalities, commutative rings, principle ideal domains, unique factorization domains, Euclidean domains. Noetherian rings. Hilbert’s theorem. Field of fractions. Localization.

**MCS 507 - Partial Differential Equations (3 0 3)**

Cauchy-Kowalevski theorem. Linear and quasilinear first order equations. Existence and uniqueness theorems for second order elliptic, parabolic and hyperbolic equations. Correctly posed problems. Green’s function.

**MCS 508 - Differentiable Manifolds (3 0 3)**

Differentiable manifolds. Smooth mappings. Tangent, cotangent bundles. Differential of a map. Submanifolds. Immersions. Imbeddings. Vector fields, tensor fields. Differential forms. Orientation on manifolds. Integration on manifolds. Stoke’s theorem.

**MCS 509 - Complex Analysis (3 0 3)**

The algebraic, geometric and topological properties of complex numbers. Limits and continuity. Analytic and harmonic functions. Elementary functions. Contour integrals. Cauchy's integral formula. The Theorems of Morera and Liouville, and Extensions. Sequences and series of analytic functions. Taylor and Laurent series representations. Singularities, zeros, and poles. Theory of integral residues. Applications of residues. The argument principle and Rouché’s theorem.

**MCS 510 - Applied Functional Analysis (3 0 3)**

Distribution theory and Green’s functions, the Delta function, basic distribution theory, convergence of distributions, The integral of a distribution, Applications of Green’s functions, The classical Fourier transform, Distributions of slow growth, generalized Fourier transforms, Banach spaces and fixed point theorems, the contraction mapping theorem, Application to differential and integral equations, Hilbert spaces, orthogonal expansions, bounded operators on normed spaces, eigenvalue problems for self-adjoint operators, variational methods, positive operators, the Rayleigh- Ritz method for eigenvalues, applications.

**MCS 511 - Topology (3 0 3)**

Topological spaces. Neighbourhoods. Basis. Subspace topology, product and quotient topologies. Compactness. Tychonoff’s Theorem. Heine-Borel theorem. Separation properties. Urysohn’s Lemma and Tietze Extension theorem. Stone-Cech compactification. Alexandroff one point compactification. Convergence of sequences and nets. Connectedness. Metrizability. Complete metric spaces. Baire’s theorem.

**MCS 512 - Scientific Computation II (3 0 3)**

Interpolation: Polynomial interpolation, Divided differences, Hermite interpolation, Spline interpolation. Approximation of functions. Numerical differentiation: Richardson extrapolation. Numerical integrations: Guassian Quadrature, Romberg integration. Root finding methods:Bisection, Newton, Secant methods, Fixed point iteration. Applications with MATLAB.

**MCS 513 - Nonlinear Dynamical Systems (3 0 3)**

Equilibrium solutions, Lyapunov Functions, Periodic Solutions, Poincare maps, center manifolds, normal forms, bifurcation.

**MCS 514 - Special Topics in Fractional Differential Equations (3 0 3)**

Fractional integrals and derivatives, Cauchy type problem for ordinary fractional linear equations, Fractional existence and uniqueness theorems, Fractional method of reduction to fractional Volterra integral equations, Fractional compositional method. Applications with MATLAB.

**MCS 515 - Special Topics in Applied Convex Functions (3 0 3)**

Convex functions on Intervals, the integral form of Jensen’s inequality, the Hermite-Hadamard Inequality, convexity and majorization, Comparative Convexity on Intervals, the Gamma and Beta functions, Multiplicative convexity of special functions, Convex functions on Banach spaces, Continuity, Differentiability of convex functions, the variational approach of Partial Differential Equations, the minimum of convex functionals.

**MCS 516 - Spectral Theory of Linear Operators (3 0 3)**

Compact operators, compact operators in Hilbert spaces, Banach Algebras, The spectral theorem of normal operators, unbounded operators between Hilbert spaces, The spectral theorem for unbounded adjoint operators, self-adjoint operators, self adjoint extentions.

**MCS 523 - Fundamentals of Pattern Recognition (3 0 3)**

Preprocessing of datasets, feature reduction and selection approaches, statistical methods like bayes decision theory, discriminant functions, linear and non-linear classifiers, clustering and combining classifiers.

**MCS 524 - Artificial Neural Networks (3 0 3)**

Human brain and biological neurons, artificial neuron models, the perceptron and the perceptron learning algorithm, multi-layer perceptrons and backpropagation algorithm. Recurrent neural networks and time delay neural networks. Unsupervised learning. Recent advances about image processing applications. Combining neural networks.

Central Campus : Eskisehir Yolu 29. Km Yukarıyurtcu Mahallesi Mimar Sinan Caddesi No:4 06790, Etimesgut/ANKARA/TURKEY Tel: +90 312 233 10 00 | Registrar's Office Fax: +90 312 233 10 24

Balgat Campus : Ogretmenler Cad, No: 14, 06530 100.Yil/ANKARA/TURKEY Tel: +90 312 284 45 00 Fax: +90 312 286 40 78

Balgat Campus : Ogretmenler Cad, No: 14, 06530 100.Yil/ANKARA/TURKEY Tel: +90 312 284 45 00 Fax: +90 312 286 40 78

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