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The graduate program in Scientific Computing is an interdisciplinary
program in spirit which focuses on numerical methods and techniques
relevant to the solution of scientific or engineering problems. It also
includes computational experiments demonstrating the effectiveness of a
proposed technique. Typically,
research work includes numerical simulation of physical phenomena using
state of the art numerical methods; efficient implementation of a new
numerical scheme by using high performance computing techniques; analysis
of theoretical aspects of a numerical method and its validation through
numerical experimentation; design and analysis of efficient data
structures to solve a scientific problems; development of mathematical
software for solving scientific and engineering problems using modern
techniques of software development.
Although computation is one of the key
components, this program is NOT a Computer Science program. The
Scientific Computing program consists of three major components:
1.
Application: research focuses on
solving numerically a practical problem or designing new methods or
techniques for solving a specific problem.
2.
Theory: the work should include an analysis
and discussion of theoretical aspects of the proposed techniques and/or
the problem to be solved.
3.
Computation: research work should
use efficient implementation by using high performance techniques such as
parallel programming or modern techniques of software development, for
example object oriented programming.
For more information about our academic and research activities Scientific Computing Research
Applicants for admission should have an undergraduate degree in
Mathematics, Science, Engineering
or an equivalent. Candidates are expected to have approved courses in
multivariable calculus, differential equations, linear algebra, numerical
analysis and data structures, as well as having programming experience
using a high level language such as FORTRAN or C\C++.
In addition
to the requirements of the Office of Graduate Studies, the Master of
Science degree in Scientific Computing with Thesis, Option I, requires a
minimum of 32 credits distributed as follows:
1.
12 credits in core courses
·
MATE 6672,
Numerical Mathematical Analysis
·
MATE 6025, Numerical
Linear Algebra
·
COMP 6785,
Analysis of Algorithms
·
COMP 6786,
High Performance Computing
2.
9 credits from the following (area of
specialization)
·
COMP 5050,
Parallel Computing
·
COMP 5045,
Automata and Formal Languages
·
COMP 6025,
Scientific Visualization
·
COMP 6838,
Topics in Scientific Computing
·
COMP 6839,
Topics in Scientific Computing
·
ESMA 5015,
Stochastic simulations
·
ESMA 6665,
Computational Statistics
·
MATE 5016,
Game Theory
·
MATE 5047,
Intermediate Differential Equations
·
MATE 5049,
Calculus of Variations
·
MATE 5055,
Vector Analysis
·
MATE 5150,
Linear Algebra
·
MATE 6005,
Combinatorics
·
MATE 6026,
Numerical Optimization
·
MATE 6674,
Numerical Methods for Partial Differential Equations
·
MATE 6675,
Mathematics in the Modern Sciences I
·
MATE 6676,
Mathematics in the Modern Sciences II
·
CIIC 6005,
Foundations of Computing
3.
6 credits outside the area of specialization or
major. The requirement of a
minimum of two out-of-discipline courses is to ensure cross-disciplinary
breadth. The courses must be related to mathematics and should be chosen
in a coherent way. These should be of level 5000 or higher. It is
recommended that student choose these courses with the help of their
advisor.
·
6000 or
5000 level courses not listed in the major or
·
6000 or
5000 level courses outside the math department
4.
2 credits in Internship or Seminar
·
COMP 6787,
Internship (2 credits)
or
·
MATE 6991,
Seminar I
(1 credit)
·
MATE 6692,
Seminar II
(1 credit)
5.
3 credits in Thesis
·
COMP
6998 (3
credits)
In addition, the candidate must
pass one qualifying exam from
·
Algorithms
·
Numerical Analysis
·
Numerical Linear Algebra
Option II: project option: the course and examination
requirements are similar to Option I, however the 3 Thesis credits must
be replaced by 3 Project credits. An oral examination on the project is
also required.
Option III, no project, no thesis: the student should approve a
minimum of 36 course credits:
·
A minimum
of 27 credits at graduate level
·
A minimum
of 21 credits in the area of specialization
·
A minimum
of 6 credits in courses related to, but outside the area of specialization.
In addition the student must pass two (2) exams from
the above list.
List of faculty associated with this program and their research
interests
Robert Acar, (Numerical
Analysis, Partial Differential Equations, Inverse problems)
Edgar Acuña, (Computational
Statistics, Data Analysis)
Dorothy Bollman, (Parallel
Algorithms, High Performance Computing)
Lev Steinberg, (Mathematical
Modeling, Nonlinear Mechanics)
Alexander Urintsev, (Fluid
Dynamics, Stability, Symbolic Computation)
Xuerong Yong, (Graph
theory with applications, Combinatorics,
algorithms)
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