Doctor of Philosophy (Ph.D.) in Computational Sciences and Engineering
Program tanımlarıProgram 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.
Degree Requirements
Students can apply to the Ph.D. programs with a B.S. or M.S. degree. The Ph.D. degree requires successful completion of 14 courses beyond the B.S. degree or 7 courses beyond the M.S. degree. All students must pass the Ph.D. Qualifying Examination in the first year after they have been admitted to the Ph.D. program. Students are encouraged to begin research early. Students who have passed the Ph.D. qualifying examination are assisted in matters pertaining to their thesis research by a faculty thesis advisory committee. The research advisor serves as the chair of this committee. The committee meets with the student at least once each semester. Ph.D. students must submit a satisfactory written Ph.D. thesis proposal in their second year of study. At the completion of the Ph.D. research, the students must submit a written Thesis and pass an oral defense to complete the degree requirements.
Research areas of interest
Computational Biology & Bioinformatics
Computational Chemistry
Computational Physics
Molecular Dynamics and Simulation
Parallel and High Performance Computing
Computational Fluid Dynamics
Dynamical and Stochastic Systems
Quantum Mechanics of Many Body Systems
Electronic Design Automation
Numerical Methods
Simulation of Material Synthesis
Structural Dynamics
Biomedical Modeling and Simulation
Virtual Environments
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):
ChBi 503 Thermodynamics
ChBi 505 Polymer Engineering
ChBi 506 Bioinformatics
ChBi 507 Advanced Mass transfer
ChBi 516 Biotechnology
CHEM 420 Quantum Chemistry
CMSE 520 Biomolecular Structure, Function and Dynamics
CMSE 580 Selected Topics in Computational Science and Engineering
ECOE 501 Random Processes
ECOE 505 Linear Systems and Estimation Theory
ECOE 508 Computer Vision and Pattern Recognition
ECOE 510 Computer Graphics
ECOE 515 Distributed Computing Systems
ECOE 518 Numerical Analysis of Circuits and Systems
ECOE 529 Parallel Computing
ECOE 554 Machine Learning
ECOE 556 Algorithms and Computational Complexity
ECOE 570 Bioinformatics and Algorithms in Computational Biology
ENGR 500 Applied Optimal Control
INDR 501 Optimization Models and Algorithms
INDR 520 Network Models and Optimization
INDR 551 Advanced Optimization Methods
INDR 553 Advanced Stochastic Processes
INDR 564 Dynamic Programming
INDR 568 Heuristic Methods
MASE 503 Thermodynamics & Kinetics
MASE 538 Intermolecular and Surface Forces
MASE 540 Surface & Interface Properties of Materials
MASE 542 Biomaterials
MATH 545 Mathematics of Finance
MATH 551 Partial Differential Equations
MATH 552 Partial Differential Equations II
MECH 521 Advanced Fluid Dynamics
MECH 522 Computational Fluid Dynamics and Heat Transfer
MECH 534 Computer Based Simulation and Modeling
MECH 552 Introduction to Biomechanics
PHYS 408 Optoelectronics
PHYS 509 Condensed Matter Physics I
PHYS 510 Condensed Matter Physics II
PHYS 521 Photonics and Lasers
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 596 PhD Thesis
Students who have TA assignments must take TEAC 500: Teaching Experience during the semesters 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.
ChBi 503 Thermodynamics
Classical thermodynamics: enthalpy, entropy, free energies, equilibria; introduction to statistical thermodynamics to describe the properties of materials; kinetic processes; diffusion of mass, heat, energy; fundamentals of rate processes in materials, kinetics of transformations.
ChBi 505 Polymer Engineering
Polymers, their synthesis and properties. Relationships between molecular structure and properties. Rheology in polymer processing. Fabrication methods and applications.
ChBi 506 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.
ChBi 507 Advanced Mass Transfer
Fundamentals of diffusion; primary mechanisms for mass transfer; mass transfer coupled with chemical reactions; membrane processes and controlled release phenomena.
ChBi 516 Biotechnology
Recombinant DNA, enzymes and other biomolecules. Molecular genetics. Commercial use of microorganisms. Cellular reactors; bioseparation techniques. Transgenic systems. Gene therapy. Biotechnology applications in environmental, agricultural and pharmaceutical problems.
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.
CMSE 520 Biomolecular Structure, Function and Dynamics
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.
ECOE 501 Random Processes
Discrete random variables, continuous random variables, functions of random variables, multiple random variables, vector random variables, independence of random variables, functions of multiple random variables, Central Limit Theorem. Discrete-time random processes, continuous-time random processes, stationary random processes, ergodicity, auto and cross correlation functions, power spectral density; spectral estimation, white noise processes, Markov chains
ECOE 505 Linear Systems and Estimation Theory
Linear functions and linear dynamical systems, Multiple Input Multiple Output (MIMO) Systems, State Space Descriptions, Quadratic Forms, Maximum Likelihood and Maximum A posteriori Estimation, SVD and Its Applications, Deterministic and Stochastic Least Squares, Wiener and Kalman Filtering, Spectral Factorization.
ECOE 508 Computer Vision and Pattern Recognition
(Also ELEC 408)
Study of computational models of visual perception and their implementation in computer systems. Topics include: image formation; edge, corner and boundary extraction, segmentation, matching, pattern recognition and classification techniques; 3-D Vision: projection geometry, camera calibration, shape from stereo / silhouette / shading, model-based 3D object recognition; color texture, radiometry and BDRF; motion analysis.
ECOE 510 Computer Graphics
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.
ECOE 515 Distributed Computing Systems
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.
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.
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.
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.
ECOE 556 Algorithms and Computational Complexity
Advanced topics in data structures, algorithms, and their computational complexity. Asymptotic complexity measures. Graph representations, topological order and algorithms. Forests and trees. Minimum spanning trees. Bipartite matching. Union-find data structure. Heaps. Hashing. Amortized complexity analysis. Randomized algorithms. Introduction to NP-completeness and approximation algorithms. The shortest path methods. Network flow problems.
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.
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.
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.
INDR 520 Network Models and Optimization
Network flow models and optimization problems. Algorithms and applications. Minimum spanning tree problems. Shortest path problems. Maximum flow problems, minimum cuts in undirected graphs and cut-trees. The minimum cost network flow problem. Matching problems. Generalized flows. Multicommodity flows and solution by Lagrangean relaxation, column generation and Dantzig-Wolfe Decomposition. Network design problems including the Steiner tree problem and the multicommodity capacitated network design problem; their formulations, branch-and-cut approaches and approximation algorithms.
INDR 551 Advanced Optimization Methods
Combinatorial optimization, structure of integer programs, pure integer and mixed integer programming problems, branch and bound methods, cutting plane and polyhedral approach, convexity, local and global optima, Newton-type, and conjugate gradient methods for unconstrained optimization, Karush-Kuhn-Tucker conditions for optimality, algorithms for constrained nonlinear programming problems, applications in combinatorial and nonlinear optimization.
Prerequisite: INDR 501 or consent of the instructor.
INDR 553 Advanced Stochastic Processes
Brief review of basic processes like Poisson, Markov and renewal processes. Markov renewal processes and theory. Regenerative and semi-regenerative processes. Random walk, Wiener process, Brownian motion and martingales. Stochastic differential equations and integrals. Applications in queueing, inventory, reliability and financial systems.
Prerequisite: INDR 503 or consent of the instructor.
INDR 564 Dynamic Programming
Theory and practice of dynamic programming, sequential decision making over time; the optimal value function and Bellman's functional equation for finite and infinite horizon problems; Introduction of solution techniques: policy iteration, value iteration, and linear programming; General stochastic formulations, Markov decision processes; application of dynamic programming to network flow, resource allocation, inventory control, equipment replacement, scheduling and queueing control.
Prerequisite: INDR 501 and INDR 503 or consent of the instructor.
INDR 568 Heuristic Methods
Constructive heuristics; improving heuristics; metaheuristics: simulated annealing, genetic algorithms, tabu search, scatter search, path relinking, ant colony optimization, variable neighborhood search, and their hybrids; heuristic methods based on relaxation and decomposition; applications: routing, scheduling, cutting and packing, inventory and production management, location, assignment of resources, bioinformatics, and telecommunications.
Prerequisite: INDR 501 or consent of the instructor
MASE 503 Thermodynamics & Kinetics
Classical thermodynamics: enthalpy, entropy, free energies, equilibria; introduction to statistical thermodynamics to describe the properties of materials; kinetic processes; diffusion of mass, heat, energy; fundamentals of rate processes in materials, kinetics of transformations.
MASE 538 Intermolecular and Surface Forces
Intermolecular forces which govern self-organization of biological and synthetic nanostructures. Thermodynamic aspects of strong (covalent and coulomb interactions) and weak forces (dipolar, hydrogen bonding). Self-assembling systems: micelles, bilayers, and biological membranes. Computer simulations for “hands-on” experience with nanostructures.
MASE 540 Surface & Interface Properties of Materials
Fundamental physico-chemical concepts of surface and interface science; interaction forces in interfacial systems; surface thermodynamics, structure and composition, physisorption and chemisorption; fluid interfaces; colloids; amphiphilic systems; interfaces in polymeric systems & polymer composites; liquid coating processes.
MASE 542 Biomaterials
Materials for biomedical applications; synthetic polymers, metals and composite materials as biomaterials; biopolymers, dendrimers, hydrogels, polyelectrolytes, drug delivery systems, implants, tissue grafts, dental materials, ophthalmic materials, surgical materials, imaging materials.
Prerequisite: At least one semester of organic chemistry or consent of the instructor.
MATH 545 Mathematics of Finance
From random walk to Brownian motion, quadratic variation and volatility, stochastic integrals, martingale property, Ito formula, geometric Brownian motion, solution of Black-Scholes equation, stochastic differential equations, Feynman-Kac theorem, Cox-Ingersoll-Ross and Vasicek term structure models, Girsanov’s theorem and risk neutral measures, Heath-Jarrow-Morton term structure model, exchange-rate instruments.
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.
MECH 521 Advanced Fluid Dynamics
Foundations of fluid mechanics introduced at an advanced level. Aspects of kinetic theory as it applies to formulation of continuum fluid dynamics. Introduction to tensor analysis and derivation of Navier Stokes equations and energy equation for compressible fluids. Boundary conditions and surface phenomena. Viscous flows, boundary layer theory, potential flows and vorticity dynamics. Introduction to turbulence and turbulent flows.
Prerequisite: MATH 204,and MECH 301 or consent of the instructor
MECH 522 Computational Fluid Dynamics
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.
MECH 534 Computer Based Simulation and Modeling
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.
MECH 552 Introduction to Biomechanics
Applications of mechanics to biological systems; basic principles of mechanics (force-moment, stress-strain, work, energy, rigid body dynamics), analysis of human movement, musculoskeletal mechanics, tissue mechanics, motor control system, sports biomechanics, and rehabilitation engineering.
Prerequisite: MECH 201 or consent of the instructor.
PHYS 408 Optical and Laser Spectroscopy
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.
PHYS 509 Condensed Matter Physics I
Free electron theory of metals. Crystal lattices. Reciprocal lattice. Classification of Bravais lattices. X-ray diffraction and the determination of crystal structures. Electrons in a periodic potential. Tight binding method. Band structures. Semi-classical theory of conduction in metals. Fermi surface. Surface effects.
PHYS 510 Condensed Matter Physics II
Classification of solids. Theory of harmonic crystals. Phonons and phonon dispersion relations. Anharmonic effects in crystals. Phonons in metals. Dielectric properties of insulators. Semiconductors. Diamagnetism and paramagnetism. Electron interactions and magnetic structure. Magnetic ordering. Superconductivity.
PHYS 521 Photonics and Lasers
Review of electromagnetism; electromagnetic nature of light, radiation, geometrical optics, Gaussian beams, transformation of Gaussian beams; electromagnetic modes of an optical resonator, interaction of light with matter, classical theory of absorption and dispersion, broadening processes, Rayleigh scattering, quantum theory of spontaneous and stimulated emission, optical amplification, theory of laser oscillation, examples of laser systems, Q switching and mode locking of lasers. Prerequisite: ELEC 206 or consent of the instructor.
CMSE 590 Seminar
A series of lectures given by faculty or outside speakers. Participating students must also make presentations during the semester.
CMSE 596 Ph.D. Thesis
Independent research towards Ph.D. degree.
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.