Education

Scope of the Program and the Disciplines Included

The Computational Science and Engineering Master’s Program, which is presented with a thesis, includes theoretical and applied studies that can contribute to the process of solving problems with mathematical modeling and simulation for problems that are tried to be solved in all areas of basic sciences and engineering. The fields of science it includes are Physics, Chemistry, Photonics, Mathematics, Bioengineering, Chemical Engineering, Computer Engineering, Energy Systems Engineering, Materials Science and Engineering.

 

Student Admission Requirements

Admissions to the Computational Science and Engineering Master’s program are made according to the rules and criteria determined by the Institute.

 

The Total Number of Credits Required and the Required and Elective Courses to be taken in the Program (Course Code, Title, Content and Credits)

Students who are accepted to the Computational Science and Engineering Master’s program with a bachelor’s degree must take at least 7 credit courses, provided that a total of not less than 21 credits. Courses taken must have a total of 120 ECTS points. The training plan of the program is given below. In addition, the list of courses that are opened in other graduate programs of our institute and will be enrolled in this program can be taken as an elective course with the approval of the head of the department or the thesis advisor.

 

CURRICULUM OF THE M.S. PROGRAM IN COMPUTATIONAL SCIENCE AND ENGINEERING

Program Core Courses
Credit ECTS
CSE 500 MS Thesis (0-1) NC 26
CSE 501 Numerical Methods and Scientific Programming I (3-0)3 9
CSE 502 Numerical Methods and Scientific Programming II (3-0)3 9
CSE 598* Research Seminar (0-2) NC 7
CSE 599* Ethical Issues in Research Methods (0-2) NC 7
CSE 8xx Special  Studies (8-0) NC 4

* All M.S. students must register the course until the beginning of their 4th semester.

 

Program Selective Courses
Credit ECTS
MATH 505 Fundamental Methods in Discrete Mathematics (3-0)3 7
MATH 527 Basic Abstract Algebra (3-0)3 8
MATH 533 Ordinary Differential Equations (3-0)3 8
MATH 534 Partial Differential Equations (3-0)3 8
ME 515 Finite Element Analysis in Solid Mechanics (3-0)3 8
ME 516 Finite Element Analysis in Vibrations (3-0)3 8
ME 536 Computational Fluid Dynamics (3-0)3 8
ME 570 Computational Intelligence (3-0)3 8
CENG 112* Data Stuctures (3-0)3 5
CENG 113* Programming Fundamentals (3-2)4 7
CENG 218* Analysis and Design of Algorithms (3-0)3 6
CENG 441* Introduction to Parallel Programming (3-0)3 5
CENG 443* Heterogeneous Parallel Programming (3-0)3 5
CENG 463* Introduction to Machine Learning  (3-0)3 5
CENG 501 Introduction to Statistical Data Processing (3-0)3 9
CENG 504 Optimization Methods (3-0)3 9
CENG 506 Deep Learning (3-0)3 9
CENG 507 Introduction to Biometric Recognition (3-0)3 9
CENG 508 Digital Image Processing (3-0)3 9
CENG 509 Vision Based Tracking and Modeling (3-0)3 9
CENG 516 Advanced Programming Languages (3-0)3 9
CENG 533 Probabilistic Reasoning (3-0)3 9
CENG 608 3D Photography (3-0)3 9
MSE 509 Atomistic Simulation of Materials -I (3-0)3 7
MSE 519 Atomistic Simulation of Materials -II (3-0)3 7
MSE 520 Transport in Nanostructures (3-0)3 7
PHOT 508 Mathematical Methods in Photonics (3-0)3 7
PHOT 518 Low Dimensional Materials (3-0)3 7
ENE 512 Wind Turbine Aerodynamics I (3-2)4 8

* Maximum 2 of the undergraduate courses in the program can be taken.

Total credit (min): 21

Number of courses with credit (min): 7

Total ECTS credit (min): 120

* All M.S. students must register this course until the beginning their fourth semester.

Core Courses:
Code Credit ECTS Name Content
CSE 500 (0-1) NC 26 MS Thesis Student prepares a master’s thesis under the supervision of a faculty member, by conducting an independent study on experimental and/or theoretical research on the basis of the courses he/she has taken.
CSE 501 (3-0)3 9 Numerical Methods and Scientific Programming I Preliminary Information: Limit andContinuity, Differentiation, Integral, Taylor Polynomials and Series, Rounding Errors, Decimal Machine Numbers and Convergence Rate, Bisection Method; Fixed Point Iteration, Newton and Secant Methods,Regula Falsi Method, Interpolation, Lagrange Interpolation Polynomials, Neville Method, Reverse Interpolation.
CSE 502 (3-0)3 9 Numerical Methods and Scientific Programming II Divided Differences, Forward, Reverse and Central Differences, Numerical Differential, Richardson Extrapolation, Numerical Integration, Open and Closed Newton-Cotes Formulas, Compound Numerical Integration and Compound Integral Calculations, Rounding Errors, Romberg Integration, Numerical Solutions of Initial Value Problems: Euler , Mid-Point Method, Modified Euler, Heun and Runge-Kutta Methods,
CSE 598 (0-2) NC 7 Research Seminar The course consists of activities involving the study of literature on the subject that the student wishes to work under the supervision of his/her advisor, data evaluation, analysis and reporting the results.
CSE 599 (0-2) NC 7 Ethical Issues in Research Methods The course covers the following topics: Basic scientific research methodology. Research questions and experimental questions. Experimental evaluation. Examination of scientific ethics and ethical theories.
CSE 8xx (8-0)NC 4 Special  Studies Graduate students work on special topics related to their thesis under the supervision of the thesis supervisor.

 

Elective Courses:
Code Credit ECTS Name Content
MATH 505 (3-0)3 7 Fundamental Methods in Discrete Mathematics Counting methods and techniques; generating functions; formal power series; binomial theorem; recurrence relations and their solutions; graph terminology; adacency and incidence matrices; isomorphism; matchings; planar graphs; chromatic number; stable sets and cliques; connectivity; growth of functions; running times; complexity classes.
MATH 527 (3-0)3 8 Basic Abstract Algebra Integers. Sets. Linear Algebra. Groups. Subgroups. Factor groups. Isomorphism theorems. Finitely generated Abelian groups. Rings. Ideals. Maximal, prime ideals. PID. Irreducible polynomials. Fields. Algebraic extensions. Modules. Exact sequences.
MATH 533 (3-0)3 8 Ordinary Differential Equations This course develops techniques for solving ordinary differential equations. Topics covered include: introduction to First-Order Linear Differential Equations; Second-Order Differential Equations, existence and uniqueness theory for first order equations, power series solutions, nonlinear systems of equations and stability theory, perturbation methods, asymptotic analysis, confluent hyper geometric functions. Mathieu functions. Hill’s equation.
MATH 534 (3-0)3 8 Partial Differential Equations General theory of partial differential equations; first order equations; classification of second order equations; theory and methods of solution of elliptic, parabolic, and hyperbolic types of equations; maximum principles; Green’s functions; potential theory; and miscellaneous special topics.
ME 515 (3-0)3 8 Finite Element Analysis in Solid Mechanics Hybrid-mixed formulation. Beam elements, plate elements, flat-shell elements. Modelling of laminated composites. Small-strain large deflection problems, rigidplastic large deformation problems, large elastic-plastic deformation problems.
ME 516 (3-0)3 8 Finite Element Analysis in Vibrations Formulation of the equation of the motion. Element energy functions. Finite element displacement method. In-plane vibration of plates. Vibration of solids. Flexural vibration of plates. Analysis of free vibration. Forced response.
ME 536 (3-0)3 8 Computational Fluid Dynamics Governing equations of fluid dynamics, dimensionless form of equations, boundary conditions, simplification of governing equations based on flow type, mathematical classification of flows, vorticity-stream function approach, primitive variable approach, pressure equation, finite difference method, finite difference form of diffusion, convection and source terms, implementation of boundary conditions, finite volume method, SIMPLER algorithm and related procedure,  turbulent flows and governing equations, standard k-Є model, grid generation.
ME 570 (3-0)3 8 Computational Intelligence Introduction to conventional AI topics, and recently surging intelligent optimization schemes. From the theory of Neural Networks, to the scheduled cooling in parameter optimization in SA. Inductive and Deductive decision making, simulation of natural processes where nature is at her best : The evolution. It is intended to cover a range of topics from classical to modern computational intelligence.
CENG 112 (3-0)3 5 Data Stuctures Basic concepts of data, data structures and data types: arrays, strings, linear structures, sequential searching and sorting techniques, stacks, queues, pointers, linked lists. Various forms of m-way search and B-trees.
CENG 113 (3-2)4 7 Programming Fundamentals

 

 

Fundamentals of computer programming: sequence, decision, repetion, syntax, compilation, debugging and maintenance, procedures, parameters, arrays, object, top-down structured design, layout and style. The emphasis is on an engineering “right-first-time” approach to solving large problems using computers. Basic concepts of algorithmics and algorithmic terminologies.
CENG 218 (3-0)3 6 Analysis and Design of Algorithms The role of algoritms in computing, Growth of functions, recurrences, probabilistic analysis and randomized algorithms, dynamic programming, greedy algorithms, advanced data structures, graph algorithms, NP-Completeness.
CENG 441 (3-0)3 5 Introduction to Parallel Programming Introduction to the programming techniques to effectively utilize modern multicore computers. Identifying the parallelism, naming shared data, synchronizing threads, the latency and bandwidth associated with communication, analyzing & improving parallel performance, parallel programming tools, miscallenous lab works & exercises.
CENG 443 (3-0)3 5 Heterogeneous Parallel Programming The course covers the following topics: Heterogeneous GPU architecture, GPU programming models and methods, CUDA programming.
CENG 463 (3-0)3 5 Introduction to Machine Learning An Introduction to the machine learning with examples in different application areas. Bayesian decision theory. Supervised learning techniques. Model selection. Dimensionality reduction. Clustering. Support vector machines. Graphical models. Introduction to neural networks. Reinforcement learning.
CENG 501 (3-0)3 9 Introduction to Statistical Data Processing Organization and application of computers and statistical techniques to data processing. Data handling in terms of coding, preparation, acquisition (with and without computers), screening and reduction; summarization, tabulation and analysis; random variables, statistical estimation and hypothesis testing, enumerated data analysis, linear models (regression, correlation, analysis of variance).
CENG 504 (3-0)3 9 Optimization Methods Linear programming, nonlinear programming, iterative methods and dynamic programming are presented, especially as they relate to optimal control problems. Discrete and continuous optimal regulators are derived from dynamic programming approach which also leads to the Hamilton-Jakobi-Bellman Equation and the Minimum Principle. Linear quadratic regulators, linear tracking problems and output regulators are treated. Linear observer and the separation theorem are developed for controller implementation.
CENG 506 (3-0)3 9 Deep Learning This course covers methods for designing and training deep neural networks. The course content includes the historical evolution of deep neural networks, their fundamental working principles and image classification and object detection and recognition in images using convolutional neural networks.
CENG 507 (3-0)3 9 Introduction to Biometric Recognition This course covers biometric recognition and identification methods and systems. The course content includes the historical evolution of biometric recognition, the fundamental principles of biometric recognition systems and basic face and fingerprint recognition algorithms
CENG 508 (3-0)3 9 Digital Image Processing This course covers the materials required to process and enhance photographic images, remote sensor multispacial scanner data and others. Topics include transform techniques, records and discriminate function.
CENG 509 (3-0)3 9 Vision Based Tracking and Modeling This course covers the tracking of object and camera positions from images and videos by using computer vision techniques. Course contents include the mathematical theory and the algorithms used in practice necessary for modeling the objects and scene to be tracked.
CENG 516 (3-0)3 9 Advanced Programming Languages Design and implement new language features, to precisely understand the rationale for existing features in modern languages, and to understand how design decisions can impact implementations.
CENG 533 (3-0)3 9 Probabilistic Reasoning Graphical Probability Models. Bayesian Reasoning. Bayesian Networks. Learning in Bayesian Networks. Knowledge Engineering. Temporal Models. Inference in Dynamic Bayesian Networks. Markov Decision Processes.
CENG 608 (3-0)3 9 3D Photography This course covers algorithms and applications to extract 3D information (especially shape) from images. It starts with the camera model and calibration, 2D and 3D projective geometries and extracting feature points. Then it covers passive 3D reconstruction techniques such as single view reconstruction, structure from motion, shape from silhouettes. Active sensing techniques (time of flight cameras, structured light, laser scanners etc.) that directly obtain 3D data are also briefly covered.
MSE 509 (3-0)3 7 Atomistic Simulation of Materials -I In this course, the students will be introduced with the basic concepts in modeling and simulation of materials; and they will make a fast introduction to the applications of density functional theory, which is one of the leading methods in quantum mechanical modeling of materials. Approximately half of the lectures will be reserved for hands-on tutorials.
MSE 519 (3-0)3 7 Atomistic Simulation of Materials -II In this course, the students will be introduced with the concepts in modeling and simulation of materials. Computation of elastic, vibrational, thermal, optical and magnetic properties of materials will be reviewed using state-of-the-art tools. Approximately half of the lecture hours will be reserved for computations.
MSE 520 (3-0)3 7 Transport in Nanostructures In this course, the students will be introduced with the fundamental concepts of the nano-scale transport. They will learn about the basics of electronic, spintronic and thermal transport at the quantum limit. Transport regimes ranging from ballistic transport to diffusive transport and localization regimes will be visited. Recent advances in the literature will be addressed.
PHOT 508 (3-0)3 7 Mathematical Methods in Photonics Complex analysis, Fourier transform theory, linear algebra, vector algebra, ordinary and partial differential equations (e.g., wave equation), special functions (e.g., Bessel functions),  numerical methods for solving ODE’s and PDE’s, eigensystems.
PHOT 518 (3-0)3 7 Low Dimensional Materials What is dimension, quantum confinement, low-dimensional structures, formation and synthesis of low-dimensional structures, structural, electronic, magnetic, vibrational, optical and transport properties of materials in two, one and zero dimensions.
ENE 512 (3-2)4 8 Wind Turbine Aerodynamics I The content of the course is design to connect the knowledge that the students gets from generic fluid mechanics courses and carry it to the aerodynamic design of the wind turbines. With the methodology that is followed in the course – Blade Element Momentum (BEM) – the student can get the necessary knowledge for wind turbine prototype. Furthermore, students also get extra attention on important sub-topics of the wind turbine aerodynamics (e.g. vortex, tip loss, rotor and tower effects). The course naturally also includes large amount of knowledge on introduction to windturbine aeroelasticty.