Math 625: Fall 2007
Computational Mathematics and C Programming

Course information

Course:	Math 625/0101 [catalog #7564]: Computational Mathematics and C Programming
Time & Place:	MW 4:00pm–5:15pm, MP 401
Instructor:	Dr. Rouben Rostamian
Office:	MP 402
Phone:	410–455–2458
Email:	rostamian@umbc.edu
Office hours:	MW 3:00–4:00 and by appointment
Course web page:	http://www.math.umbc.edu/~rouben/2007-09-math625/

Course Description

This is a hands-on computational mathematics course with emphasis on programming in C. The goal is quickly to impart the necessary algorithmic and programming skills to enable the students build moderate- to large-scale application programs and gain a mastery of the C programming language in the context of scientific computing.

Some programming knowledge is assumed. A substantial part of the course will consists of introduction to C with special emphasis on common idioms used in scientific computing. Through the semester the students will gradually build their own computing library and will successively apply it to solve increasingly complex computational projects.

Prerequisites: Math 221 (linear algebra), Math 251 (multivariable calculus)

Syllabus

• Dynamic memory allocation for vectors and matrices
• Linear system and the LU decomposition of matrices
• Haar wavelets applied to the image processing and compression
  • Assorted images for testing
• Minimizing functions of n variables with Nelder-Mead downhill simplex algorithm
  • Here is the rank-vertices.c program that I described in class.
• Analyzing statically indeterminate 2D trusses via minimization of energy
  • Files truss-material.h and truss-material.c specify the mechanical behavior of the trusse's material.
  • Files truss-to-eps.h and truss-to-eps.c allow to capture a drawing of the truss into a PostScript file. Documentation is in truss-to-eps.h. You may view a PostScript file by "gv filename".
  • Files cantilever.dat and bollman.dat are sample data files. Run programs as "truss-demo < input.dat > output.dat". Here are the output files: cantilever.out, bollman.out. I passed the following parameters for Nelder-Mead: double tol = 1.0e-3; double h = 0.1; int maxevals = 50000;. Iterations converged after 3174 and 5958 function evaluations for cantilever and Bollman, respectively.
• Integration over a triangulated mesh.
  • Files for TWB quadrature: twb-quad.c, twb-quad.h.
  • Sample ProblemSpec files: problem-spec.c, problem-spec.h, contain two predefined geometries. You add something like an annulus.
• A finite element solver for elliptic partial differential equations on irregular 2D domains with mixed Dirichlet and Neumann boundary conditions
• Using the UMFPACK library for solving large linear systems with sparse coefficients

Textbook

There is no textbook which covers the selection of topics planned for this course. I will provide plenty of reading material from various sources throughout the semester. Students are expected to take detailed notes.

Required reading: The C Programming Language by Brian Kernighan and Dennis Ritchie.

It would be a good idea to go over the book's errata collected in the book's website and insert fixes in the book.

You will find much interesting information about the book at http://cm.bell-labs.com/cm/cs/cbook.

Grading method

I will collect and grade the weekly programming assignments. Course grade will be based on cumulative performance on these assignments.

Sample image filtered with Haar wavelets

Original image	...with 10% of the original information
...with 5% of the original information	...with 1% of the original information

The Official UMBC Honors Code

By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal.

For detailed policies on academic integrity consult:

Undergraduate students:

Undergraduate Student Academic Conduct Policy

Graduate students:

Policy and Procedures for Student Academic Misconduct