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Scientific
Computing
[SciC 6300] Scientific Computing I,
[SciC 6301] Scientific Computing II,
[SciC 6302] Mathematical Modeling and Simulation,
[SciC 6303] Numerical Solution of Differential Equations,
[SciC 6304] Scientific Computing Tools,
[SciC 6307] Independent Study,
[SciC 6308] Special Topics in Scientific Computing.
[SciC 8300] Seminar I,
[SciC 8301] Seminar II.
[SciC 8600] Master's Thesis.
Applied and Computational Mathematics
[SciC 7310] Principles of Applied Mathematics I,
[SciC 7311] Principles of Applied Mathematics II,
[SciC 7312] Numerical Optimization,
[SciC 7313] Discrete Dynamical Systems and Chaos,
[SciC 7318] Special Topics in Applied and Computational Mathematics.
Computational
Engineering
[SciC 7320] Finite Elements Methods,
[SciC 7321] Computational Fluid Mechanics,
[SciC 7322] Real Time Systems,
[SciC 7323] Information Theory and Coding,
[SciC 7324] Digital Signal Processing,
[SciC 7328] Special Topics in Computational Engineering.
Computational Physical
Sciences
[SciC 7330] Quantum Mechanics and Spectroscopy,
[SciC 7331] Statistical Mechanics,
[SciC 7332] Atomistic and Molecular Simulations,
[SciC 7333] Computer Aided Molecular Design,
[SciC 7334] Advanced Electronic Structure,
[SciC 7338] Special Topics in Computational Physical Sciences.
Applied Computer
Science
[SciC 7340] Information Systems and Software Development,
[SciC 7341] System Design Methods,
[SciC 7342] Object Oriented Analysis and Design,
[SciC 7343] Software Maintenance,
[SciC 7348] Special Topics in Applied Computer Science.
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COURSE DESCRIPTION
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Scientific
Computing Courses:
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6300 Scientific
Computing I
(Object Oriented Programming & Databases -OO):Introduction
to the concepts of object-oriented programming, key concepts of OO
(modularity, encapsulation, inheritance and polymorphism), practical
work using an object-oriented language (e.g. C++ or Java),
introduction to databases, database design and implementation using
Query Languages (e.g. SQL), overview of database applications (GIS,
spatial, temporal DB, etc)
6301
Scientific
Computing II
(High performance computing & parallel
processing): Introduction to
computer architecture, RISC computers, memory management (virtual
memory, cashes, etc), porting and tuning software (optimizing
compilers, timing and profiling, loop optimizations etc), introduction
to parallel processing, classification of computer architectures (SISD,
SIMD, MISD, MIMD), parallel processing topologies and models (mesh,
pyramid, butterfly etc), analysis of parallel algorithms (Bitonic sort
algorithm etc).
6302 Mathematical Modeling and Simulation
Programming and interactive environment, modeling
with differential and difference equations, optimization and search,
simulation, selected topics, and applications, math packages:
6303 Numerical Solution of Differential
Equations
Iterative methods for systems of equations,
approximation of eigenvalues and eigenvectors, numerical solution of
initial and boundary value problems.
6304 Scientific
Computational Tools
Introduction to scientific computing, Unix
Operating systems, Unix installation, administration and networking,
networks and the Internet for use in science. Editing (emacs, Tex,
latex), programming languages under Unix, Visualization and graphic
plotting packages, Symbolic mathematical programming (Maple,
Mathematica, Mathcad, Matlab, Scilab).
6307 Independent
Study
Independent study or research conducted by the student
under the supervision of a staff member. A written report is required.
6308 Special
Topics in Scientific Computing
Study of a specified topic in scientific computing,
selected according to the interests and needs of students and the
availability of a faculty member or a visiting scientist.
8300 Seminar
I
An advanced study in a scientific computing
concentration for non-thesis students. Students taking this option must
submit by the end of the course a substantial report or develop a
project and document it. (Prerequisite: Passing all compulsory courses.)
8301 Seminar
II
An advanced study in a scientific computing
concentration for non-thesis students. Students taking this option must
submit by the end of the course a substantial report or develop a
project and document it. (Prerequisite: Passing all compulsory courses.)
8600 Master
Thesis
Students in the Master with thesis track must submit
and successfully defend a Masters thesis in a field of interest in
scientific computing. The program council must have approved the topic
of the thesis. (For students with thesis track only. (Prerequisite:
Passing all compulsory courses.)
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Applied
and Computational Mathematics
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7310 Principles
of Applied Mathematics I
Finite dimensional vector spaces, function spaces,
integral equations, differential operators, and calculus of variation,
transform and spectral theory.
7311
Principles of Applied Mathematics II
Complex variable theory, partial differential
equations, inverse problems, asymptotic expansions, regular
perturbation theory, singular perturbation theory.
7312
Numerical Optimization
Optimization problem and illustrative examples,
convexity, optimality conditions and duality, line and
multidimensional search methods, penalty and Barrier functions,
methods of feasible directions, linear complementary problem,
quadratic, separable, fractional and geometric programming.
7313 Introduction
to Discrete Dynamical Systems and Chaos
Stability
and chaos in one and two-dimensional maps, Sharkowsk’s theorem and
bifurcation, Julia and Mandelbrot sets, introduction to fractal
geometry.
7318
Special Topics in Applied and Computational Mathematics.
Selected topics from the field of applied and
computational mathematics of interest to both faculty members and
students.
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Computational
Engineering Courses:
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7320 Finite Elements Methods
Physical problem formulation, Finite element
modeling in generalized coordinates and natural (simplex) coordinates,
numerical solution of the finite element equations in linear and
nonlinear systems, solution methods for eigenvalue problems.
7321 Computational Fluid Mechanics
Dynamics of a body moving through a fluid medium,
inviscid fluid flow, inverse methods applied to superposition of
elementary flows, viscous fluid flow, self similar laminar boundary
layer flows, pipe and open channel flows, flat plate, Instability of
fluid flow, numerical solution of Orr-Sommer Feld equation, Galerkin
method.
7322 Real Time Systems
An overview of real time systems and their applications,
terminology, problems and architectures, sensors and actuators,
modeling of real-time systems, real-time operating system kernels,
architecture of micro-controllers, real-time communications,
scheduling algorithms, and applications.
7323 Information Theory and Coding
Information measures, information sources, entropy, source coding,
unique optimal codes, the First and second Shannon’s Theorem,
discrete channel, mutual
information, conditional entropy, channel capacity, continuous
channel, Galois field, error detection and correction codes,
transmission strategies, linear block codes, cyclic codes, convolution
codes.
7324 Digital Signal Processing (DSP)
Signals, Gram-Schmidt orthogonalization, linear
time invariant systems (LTI), the sampling theorem, modeling of
discrete systems in t, z, and w-domain, design and
implementation of FIR and IR digital filters, linear
filtering methods algorithms, DFT discrete convolution, FFT-algorithms,
spectrum estimation, multirate DSP, linear prediction, optimal
filters, Least square methods.
7328 Special topics in Computational Engineering
Selected topics from the field of applied sciences
of interest to both faculty members and students.
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Computational
Physical Sciences Courses:
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7330 Quantum Mechanics and Spectroscopy
Standard methods of quantum mechanics. Perturbation
theory, approximation techniques for bound and scattering problems,
eigenvalues and eigenfunctions. Soluble bound state and continuum
state problem, spin and identical particles, atoms and molecules in
time-dependent electric and magnetic fields.
7331 Statistical Mechanics
Thermodynamic equilibrium and statistical
mechanics, ensemble theory, partition functions, applications to ideal
gas and crystals, theories of simple liquids, Monte Carlo and
molecular dynamics simulations, reaction dynamics from a microscopic
viewpoint.
7332 Atomistic and Molecular
Simulations
Potentials for atomistic simulations: pair
potentials, Leonard-Jones, and the embedded atom method, Monte Carlo
simulations, classical and quantum molecular dynamics, applications of
simulation methods to selected problems in various fields.
7333 Computer Aided Molecular
Design (CAMD)
Computer graphics, towards realistic images, 3D
objects, displaying molecular shapes (representation of structural and
property shapes), access to experimental geometrical parameters (x-ray
diffraction, NMR Cambridge Database, Brookhaven Protein data bank),
emperial force field methods and molecular mechanics, Monte Carlo and
molecular dynamics simulations, exploring conformation space model
builders, quantum chemistry methods used in CAMD, modeling proteins,
drug receptor interactions.
7334 Advanced Electronic Structure Theory
Methods for band structure calculations and their
role in condensed matter research, simple band structures like the
augmented plane wave methods, Ab intio calculations, etc..
7338 Special Topics in Computational Physical
Sciences
Selected topics from the
field of physical sciences of interest to both faculty members and
students.
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Applied
Computer Science Concentration:
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7340 Information Systems and
Software Development
Introduction to information systems, requirement
gathering and feasibility study, phases of development and system life
cycle, communication with users, system design, system implementation,
case study
7341 System Design Methods
Approaches in system design (user interface,
databases and applications), structured design, object-oriented
design, physical systems, notations and tools, case study
7342 Object Oriented Analysis
and Design
Introduction to OO-Methods (UML, OMR, BOOCH), using
the Unified Modeling Languages (UML), applying patterns and building
frameworks, business modeling using the UML, case study
7343 Software Maintenance
Project planning and management, quality metrics,
design of software measurement programs, testing (unit, module, and
system levels), software re-use, case study
7348 Special Topics in Applied
Computer Science
Selected topics from the field of applied computer
science of interest to both faculty members and students.
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