Program Description
Graduate education in computational science and engineering (CMSE) at Koç University is offered through an interdisciplinary program among the Departments of the College of Arts and Sciences and the College of Engineering . In this program graduate students are trained on modern computational science techniques and their applications to solve scientific and engineering problems. New technological problems and associated research challenges heavily depend on computational modeling and problem solving. Because of the availability of powerful and inexpensive computers model-based computational experimentation is now a standard approach to analysis and design of complex systems where real experiments can be expensive or infeasible. Graduates of the CMSE Program should be capable of formulating solutions to computational problems through the use of multidisciplinary knowledge gained from a combination of classroom and laboratory experiences in basic sciences and engineering.
Individuals with B.S. degrees in biology, chemistry, physics, and related engineering disciplines should apply for graduate study in the CMSE Program.
Research Areas of Interest
Computational Biology & Bioinformatics
Computational Chemistry
Molecular Dynamics and Simulation
Parallel and High Performance Computing
Computational Electromagnetics
Computational Fluid Dynamics
Dynamical and Stochastic Systems
Computational Physics
Quantum Mechanics of Many Body Systems
Electronic Design Automation
Numerical Methods
Simulation of Material Synthesis
Structural Dynamics
Biomedical Modeling and Simulation
Virtual Environments
Faculty and Research Areas
Yaman Arkun ; Chemical & Biological Engineering
Research Area: Nonlinear modeling and dynamics, optimal control, control of biological and chemical processes, bioinformatics.
Cagatay Basdogan ; Mechanical Engineering
Research Area: Man-machine interfaces, computer graphics, virtual environments, robotics, medical simulation and visualization, and computational modeling for biological systems.
Nihat Berker ; Physics
Research Area:
Elvan Ceyhan ; Mathematics
Research Area: Probabilistic Inference, spatial statisitics, random graphs, medical image analysis.
Mine Caglar ; Mathematics
Research Area: Stochastic flows and data traffic in telecommunications.
Alper Demir ; Electrical & Electronics Engineering
Research Area: Computational prototyping and design technologies for electronic and opto-electronic systems, electronic design automation.
Tekin Dereli ; Physics
Research Area: Quantum information theory. Qubits and qutrits. Measures of entanglement. Quantum gates and circuits.
Burak Erman ; Chemical & Biological Engineering
Research Area: Computational studies of polymers, proteins and complex biological systems.
Engin Erzin ; Electrical & Electronics Engineering
Research Area: Signal processing and its applications in bioinformatics, speech processing.
Attila Gursoy ; Computer Engineering
Research Area: Bioinformatics, protein interaction networks, parallel algorithms for computational biology.
Alkan Kabakcioglu ;Physics
Research Area: Statistical physics of complex systems, conformational properties of biopolymers.
Halil Kavaklı ; Chemical & Biological Engineering
Research Area: Plant biology and genomics, biological clock in human.
Ozlem Keskin ; Chemical & Biological Engineering
Research Area: Protein structure and function, bioinformatics, protein folding.
Metin Muradoglu ; Mechanical Engineering
Research Area: Multiphase flows in bio/micro fluid systems, turbulent combustion, scientific computing.
Ceyda Oguz ; Industrial Engineering
Research Area: Machine scheduling, logistics, bioinformatics, metaheuristics, mathematical programming, operations research, and production planning and inventory control.
Lerzan Ormeci ; Industrial Engineering
Research Area: Applied probability, stochastic processes, stochastic optimization.
Oznur Ozkasap ; Computer Engineering
Research Area: Distributed computing, computer networks, simulation/modeling/evaluation of distributed systems.
Sibel Salman ; Industrial Engineering
Research Area: network models and optimization with applications in telecommunication, distribution logistics, and disaster management.
Mehmet Sayar ; Mechanical Engineering
Research Area: Simulation of soft-condensed matter, polymer physics, biologically inspired materials, mechanics of single molecules.
Alphan Sennaroglu ; Electrical & Electronics Engineering
Research Area: Solid state lasers, ultrafast lasers, spectroscopy, nonlinear optics.
Metin Turkay ; Industrial Engineering
Research Area: Computational drug synthesis, discrete-continuous optimization.
Ersin Yurtsever ; Chemistry
Research Area: Molecular quantum chemistry, molecular simulations, dynamics and thermodynamics of clusters.
Curriculum
Required core courses (3 credit each):
- Cmse 501 Introduction to Computational Science
- Math 503 Applied Mathematics
- Math 504 Numerical Methods I
- Math 506 Numerical Methods II
Elective courses (3 credit each):
- CHEM 420 Quantum Chemistry
- CHBI 406 Bioinformatics
- PHYS 408 Optical and Laser Spectroscopy
- PHYS 409 Topics in Condensed Matter Physics
- ENGR 500 Applied Optimal Control
- MATH 551 Partial Differential Equations
- MATH 552 Partial Differential Equations II
- INDR 501 Optimization Models and Algorithms
- MECH 522 Computational Fluid Dynamics and Heat Transfer
- MECH 534 Computer Based Simulation and Modeling
- ECOE 510 Computer Graphics
- ECOE 515 Distributed Computing Systems
- ECOE 518 Numerical Analysis of Circuits and Systems
- ECOE 519 Advanced Computer Architecture
- ECOE 529 Parallel Computing
- ECOE 554 Machine Learning
- ECOE 570 Bioinformatics and Algorithms in Computational Biology
- CMSE 520 Biomolecular Structure, Function and Dynamics
- CMSE 581 Selected Topics in Computational Chemistry
- CMSE 582 Selected Topics in Computational Physics
- CMSE 583 Selected Topics in Computational Biology
Courses are selected by the students from the above list and from other courses not listed here in accordance with their areas of specialization and subject to the approval of their advisors. In addition, each student has to take a seminar course, CMSE 590 Seminar. Students also register for the thesis course.
- CMSE 590 Seminar
- CMSE 595 MS Thesis
Students who have TA assignments must take TEAC 500: Teaching Experience during the semester of their assignments. Students must also take ENGL 500: Graduate Writing course.
Course Descriptions
CMSE 501
Introduction to Computational Science
An introduction to methods and software tools used in scientific computing. Software development, data abstraction and the concept of object oriented programming. Hands-on exploration of some of the principal modern software tools of computational science including computing environments, symbolic computing, numerical libraries and software repositories. An introduction to high performance computing and parallel programming.
Math 503
Applied Mathematics
Review of Linear Algebra and Vector Fields: Vector Spaces, Eigenvalue Problems, Quadratic Forms, Divergence Theorem and Stokes' Theorem. Sturm-Liouville Theory and Orthogonal Polynomials, Methods of Solution of Boundary Value Problems for the Laplace Equation, Diffusion Equation and the Wave Equation. Elements of Variational Calculus.
Math 504
Numerical Methods I
Review of Linear Algebra: linear spaces, orthogonal matrices, norms of vectors and matrices, singular value decomposition. Projectors, QR Factorization Algorithms, Least Squares, Conditioning and Condition Numbers, Floating Point Representation, Stability, Conditioning and Stability of Least Squares, Conditioning and Stability Analysis of Linear Systems of Equations.
Math 506
Numerical Methods II
Numerical Solution of Functional Equations, the Cauchy Problem and Boundary Value Problems for Ordinary Differential Equations. Introduction to the Approximation Theory of One Variable Functions. Finite - difference Methods for Elementary Partial Differential Equations. Monte Carlo Method and Applications.
ENGR 500
Applied Optimal Control
Optimization problems for dynamical systems. Pontryagin's Maximum Principle. Optimality conditions for nonlinear dynamical systems. Linear Quadratic Optimal Control of continuous and discrete linear systems using finite and infinite time horizons. Stability and performance analysis of the properties of the optimal feedback solutions. Moving horizon optimal control of constrained systems using Model Predictive Control formulation. Applications from different disciplines and case studies.
Prerequisite: Consent of the Instructor.
CHBI 406 Bioinformatics
The principles and computational methods to study the biological data generated by genome sequencing, gene expressions, protein profiles, and metabolic fluxes. Application of arithmetic, algebraic, graph, pattern matching, sorting and searching algorithms and statistical tools to genome analysis. Applications of Bioinformatics to metabolic engineering, drug design, and biotechnology.
Prerequisite: BIOL 200 and ENGR 200 or consent of the instructor.
CMSE 520 Biomolecular Structure, Function and Dynamics
(Also CHBİ 420)
Relationship between structure, function and dynamics in biomolecules. Overview of the biomolecular databases and application of computational methods to understand molecular interactions; networks. Principles of computational modeling and molecular dynamics of biological systems.
Prerequisite: Consent of the instructor
CHEM 420 Quantum Chemistry
Quantum mechanical description of the molecular structure; exact solution of simple systems, approximate solutions to molecular problems; variational solutions, molecular orbital theory, Hückel approximation, self-consistent-field theory, semiempirical and ab-initio methods, and electron correlation. Properties such as interaction potential functions, electrostatic potential maps, and population analysis will be analyzed using MOPAC, GAUSSIAN 98.
Prerequisite: CHEM 203 or consent of the instructor.
PHYS 408 Optical and Laser Spectroscopy
(Also PHYS 508,MASE 550)
Interaction of electromagnetic radiation with atoms and molecules, rotational spectroscopy, vibrational spectroscopy, electronic spectroscopy, spectroscopic instrumentation, lasers as spectroscopic light sources, fundamentals of lasers, nonlinear optical spectroscopy, laser Raman spectroscopy.
Prerequisite: Consent of the instructor.
PHYS 409 Topics in Condensed Matter
(Also PHYS 509)
Introduction of statistical mechanical concepts; statistical thermodynamics; structure dependent properties of condensed matter; dielectric and magnetic properties; chemical equilibrium conditions; transport phenomena; normal mode analysis; structure and energy minimizations; classical and quantum numerical molecular simulation methods; superconductivity; superfluidity.
Prerequisite: PHYS 203 or consent of the instructor.
MATH 551 Partial Differential Equations I
First order equations, method of characteristics; the Cauchy-Kovalevskaya theorem; Laplace ’s equation: potential theory and Greens’s function, properties of harmonic functions, the Dirichlet problem on a ball; heat equation: the Cauchy problem, initial boundary-value problem, the maximum principle; wave equation: the Cauchy problem, the domain of dependence, initial boundary-value problem.
MATH 552 Partial Differential Equations II
Review of functional spaces and embedding theorems; existence and regularity of solutions of boundary-value problems for second-order elliptic equations; maximum principles for elliptic and parabolic equations; comparison theorems; existence, uniqueness and regularity theorems for solutions of initial boundary-value problems for second-order parabolic and hyperbolic equations.
Prerequisite: MATH 551 or consent of the instructor.
INDR 501 Optimization Models and Algorithms
Convex analysis, optimality conditions, linear programming model formulation, simplex method, duality, dual simplex method, sensitivity analysis; assignment, transportation, and transshipment problems. Prerequisite: Consent of the instructor.
MECH 522 Computational Fluid Dynamics
(Also MECH 422)
Numerical methods for elliptic, parabolic, hyperbolic and mixed type partial differential equations arising in fluid flow and heat transfer problems. Finite-difference, finite-volume and some finite-element methods. Accuracy, convergence, and stability; treatment of boundary conditions and grid generation. Review of current methods. Assignments require programming a digital computer.
Prerequisite: MATH 204 and MECH 301 or consent of the instructor.
MECH 534 Computer Based Simulation and Modeling
(Also MECH 434)
Geometric, physics-based, and probabilistic modeling methodology and associated computational tools for interactive simulation: computer programming, numerical methods, graphical modeling and programming, physics-based and probabilistic modeling techniques.
Prerequisite: Consent of the instructor.
ECOE 510 Computer Graphics
(Also COMP 410)
Theory and practice of 3D computer graphics. Topics covered include 3D display techniques, representations and transformations; illumination and color models; 3D passive and active reconstruction techniques; animation and rendering; scientific visualization; surface simplification; multiresolution and progressive object modeling; mesh compression and subdivision surfaces, Web3D/VRML.
Prerequisite: COMP 202 or consent of the instructor.
ECOE 515 Distributed Computing Systems
(Also COMP 415)
Introduction to distributed computing, overview of operating systems, process synchronization and deadlocks, threads and thread synchronization, communication protocols, synchronization in distributed systems, management of time, causality, logical clocks, consistent global states, distributed mutual exclusion, distributed deadlock detection, election algorithms, agreement protocols, consensus, multicast communication, distributed transactions, replication, shared memory model, scheduling, distributed file systems, fault tolerance in distributed systems, distributed real-time systems.
Prerequisite: COMP 304 or consent of the instructor.
ECOE 518 Numerical Analysis of Circuits and Systems
Introduction to mathematical formulations and computational techniques for the analysis and numerical simulation of circuits and systems. Applications are drawn from the time-frequency domain and noise analysis of electronic circuits at the transistor level; electromagnetic analysis for interconnect in VLSI circuits; analysis of wave propagation in integrated optics and optical fibers; simulation of communication systems; circuit and system macro-modeling. Topics include sparse direct and iterative matrix-implicit solution techniques for linear systems of equations, solution of eigenvalue problems, Newton methods for nonlinear problems, numerical methods for the solution of ordinary and partial differential equations, reduced-order modeling. Prerequisite: Consent of the instructor.
ECOE 519 Introduction to Artificial Intelligence
A graduate-level introduction to artificial intelligence with the goals of understanding human intelligence from a computational point of view and building applied systems that can reason, learn, and adapt. Review of seminal work on language, vision, robotics, game playing with an emphasis on machine learning techniques.
Prerequisite: Consent of the instructor.
ECOE 529 Parallel Computing
Overview of parallel architectures: interconnection networks, memory hierarchy. Parallel programming models and languages: shared address space, message passing, data driven, and data parallel models. Performance modeling and scalability analysis, sources of parallel overhead. Design of parallel algorithms and programs: partitioning, fundamental communication operations, mapping, load balancing. Study of parallel matrix, graph, and search algorithms.
Prerequisite: COMP 202 or consent of instructor .
ECOE 554 Machine Learning
An introduction to the fields of machine learning and data mining from a statistical perspective. Machine learning is the study of computer algorithms that improve automatically through experience. Vast amounts of data generated in many fields from biology to finance to linguistics makes a good understanding of the tools and techniques of machine learning indispensable. Topics covered include regression, classification, kernel methods, model assessment and selection, boosting, neural networks, support vector machines, nearest neighbors, and supervised learning.
Prerequisite: Consent of the instructor.
ECOE 570 Bioinformatics and Algorithms in Computational Biology
Algorithms, models, representations, and databases for collecting and analyzing biological data to draw inferences. Overview of available molecular biological databases. Sequence analysis, alignment, database similarity searches. Phylogenetic trees. Discovering patterns in protein sequences and structures. Protein 3D structure prediction: homology modeling, protein folding, representation for macromolecules, simulation methods. Protein-protein interaction networks, regulatory networks, models and databases for signaling networks, data mining for signaling networks.
CMSE 590 Seminar
A series of lectures given by faculty or outside speakers. Participating students must also make presentations during the semester.
CMSE 595 M.S. Thesis
Independent research towards M.S. degree with thesis option.
TEAC 500 Teaching Experience
Provides hands-on teaching experience to graduate students in undergraduate courses. Reinforces students' understanding of basic concepts and allows them to communicate and apply their knowledge of the subject matter.
ENGL 500 Graduate Writing
This is a writing course specifically designed to improve academic writing skills as well as critical reading and thinking. The course objectives will be met through extensive reading, writing and discussion both in and out of class. Student performance will be assessed and graded by Satisfactory/Unsatisfactory