Research in Scientific Computing in Undergraduate Education

Courses currently assigned to the project team for Spring 2009 that form part of a coherent offering in computational mathematics include the following:

MTH 112 (2) Calculus II

Topics from integral calculus, including techniques of integration (including numerical methods), and infinite series.  Numerical explorations on Taylor series and numerical integration will be incorporated into the relevant sections of the course.

Time: Monday, Wednesday & Friday, 1-1:50 and W 2-2:50.

Professor: Dr. Alfa Heryudono

MTH 204 Computational Experiments in  Mathematics

Designed for Freshman and Sophomores to develop the skills necessary to do research in the mathematical sciences by exploring areas or applications of mathematics using software tools such as MATLAB or Maple. Typical topics include: iterations and fixed points, Fibonacci numbers, fractals, the Google PageRank, magic squares and mathematical recreations, predator prey models, and computer animation.

Textbook: Experiments with MATLAB by Cleve Moler.

Time: Tuesday and Thursday, 11:00-12:15.

Professor: Dr. Steven Leon

MTH 212 Differential Equations

Ordinary differential equations of the first order, linear differential equations, some nonlinear second order equations, series solutions and Laplace transforms. Professional standard numerical algorithms for approximating solutions to system of non-linear differential equations,  will be empasized, as will the qualitative behavior of flows, and of numerical approximation to differential equations, and systems of equations that cannot be solved exactly.

Time: Monday, Wednesday & Friday, 8:00-8:50 or 10:00-10:50.

Professor: Dr. Gary Davis

MTH 332 Statistics

This course will cover descriptive statistics, including quantile plots; simple random sampling, including confidence intervals; estimation and testing, including goodness-of-fit tests; regression, including prediction; analysis of variance; stratified sampling including parametric bootstrap; Poisson counts and rates; ecological regression. The course will emphasize computational explorations and techniques.

Time: Monday, Wednesday & Friday, 12:00-12:50.

Professor: Dr. Gary Davis

MTH 353 Applied Linear Algebra

For upper level students and for sophomores who have successfully completed MTH 221. Orthogonality and least square problems. Other topics include applications of eigenvalue, quadratic forms, numerical linear algebra.

Time: Tuesday  & Thursday, 12:30-1:45.

Professor: Dr. Steven Leon

MTH 362 Numerical Analysis II

Numerical methods for solving initial value problems. Topics include: numerical differentiation and integration, Euler method and Taylor’s series method, Runge- Kutta methods, multi-step methods, and stiff equations, and an introduction to numerical methods for partial differential equations.

Time: Tuesday & Tuesday, 8:00-9:15

Professor: Dr. Sigal Gottlieb

MTH 472 Numerical Solution of Partial Differential Equations

Numerical methods for solving parabolic, hyperbolic, and elliptic partial differential equations. The course emphasizes the concepts of consistency, convergence, and stability. Topics include: implicit and explicit methods, truncation error, Von Neumann stability analysis, and the Lax equivalence theorem.

Time: Monday, Wednesday & Friday,  9:00-9:50.

Professor: Dr. Cheng Wang

MTH 499 (1) Scientific Programming

The Department of Mathematics intends to make this course an alternative to the current programming requirement of either CIS 261 or CIS 265. If you have not already taken either of the two CIS courses you should plan on taking MTH 499 instead.

Time: Monday, Wednesday & Friday, 2:00-2:50 PM

Professor: Dr. Adam Hausknecht

MTH 499 (2) Computational Mathematics Seminar

This CSUMS research seminar is designed for all mathematics majors, Freshman through Senior. A prerequisite for enrollment in the seminar is Calculus I, and permission of the instructor. The topic of the course is computational mathematics and scientific computing. Students will work on a research topic under the guidance of the instructor. The work includes reading some papers, written progress in student’s blog, MATLAB/Octave programming projects, presentations, and making a poster. Students will be taught the skills they need to carry out the research, such as programming in MATLAB or writing in LaTex.

Time: Monday, Wednesday & Friday 3:00-3:50.

Professor: Dr. Alfa Heryudono.

MTH 499 (3) Mathematical Aspects of Quantum Mechanics

A mathematical perspective on various topics in a first course on quantum mechanics, which will include a hands-on computational science component in which students will use Monte Carlo and other methods to help visualize key aspects of quantum mechanics, particularly its probabilistic nature.

Time: Monday, Wednesday & Friday, 11:00-11:50.

Professor: Dr. Dana Fine.

MTH 499 (4) Cryptology

An introduction to the mathematical foundations of modern cryptography, focusing on public key cryptosystems and digital signeture schemes.  We will use available computer packages (Maple, MATLAB, Octave) to do numerical computations and write our own codes for some basic number theoretic calculations.

Time: Monday, Wednesday & Friday, 2-2:50.

Professor: Dr. Saeja Kim.


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