Research in Scientific Computing in Undergraduate Education

MTH499 (02) COMPUTATIONAL MATHEMATICS SEMINAR

Instructor: Dr. Alfa Heryudono

Welcome students! I am happy that you sign up for my MTH499 Spring 2009 CSUMS class. This class is going to be different than regular class in the sense that you choose a topic, learn it as deep as you can, and present what you have learned to other students. You are expected to :

  • Do some numerical experiments with problem solving environment such as MATLAB, Mathematica, Maple, or other open source tools.
  • Read references to learn about history, interesting phenomena, and numerical techniques.
  • Write your research diary in your blog.
  • Make research presentation.
  • Make report in LaTeX.
  • Make a poster.

Hopefully, by the end of the semester, you will learn something useful (Introductory level). The topics that I provide are listed below. However, you are free to bring your own topics based on your research interest and math level. Feel free to discuss things with me.

The list below (choose any one of them) complements the list of topics on the left (Bullets 7, 8, and 9).

Group I

  • Radial Basis Functions (One of the themes of our department).
  • Pseudospectral Methods.
  • Barycentric Lagrange Interpolation.
  • Fast Fourier Transform.
  • Fast Gauss Transform.
  • Singular Value Decomposition.
  • QR Algorithm.
  • Gaussian Elimination and its Growth Factor.
  • Iterative methods for solving Ax=b.
  • Wavelets.
  • Finite Difference Method.
  • Toeplitz Matrix.

Group II

  • Self Reproduction Automata.
  • Digital Half Toning in Printer.
  • Bread Crust Formation.
  • Sudoku.
  • Nearest Neighbor Search.
  • Random Packing.
  • Delaunay Triangulation

Group III (software packages)

Other interesting topics are also available in books by Cleve Moler.

Syllabus

Useful resources for students

Participating students research blogs

  1. Christopher Bresten (poster) (final report) (code)
  2. Katie Cakounes (poster) (final report)
  3. Adam Callahan (poster) (final report)
  4. Daniel Katz (poster) (final report)
  5. Ann Kimball (poster) (final report)
  6. James Knuuttila (poster) (final report)
  7. Robert LeBoeuf (poster) (final report)
  8. Andrew Perry (poster) (final report)
  9. Elise Rapoza (presentation)  (python codes) (movie) (final report)
  10. Aimee Ross (poster) (final report)
  11. Leanne Silvia (poster) (final report)
  12. Daniel Higgs (poster) (final report)
  13. Shelly-Ann Bernard (presentation) (final report)
  14. Christina DiStefano (poster) (final report)
  15. Carter Chamberlain (poster) (final report)

Important Deadlines

I strongly encourage you to participate in the poster sessions in the conferences below.

For undergraduate students.

1.  Massachusetts Statewide Undergraduate Research Conference at UMass Amherst. (Conference date: Friday, May 1 2009). Deadline for Abstract: Passed.

2. UMass Dartmouth Sigma Xi Exhibition. (Conference date: April 28 & 29 2009). Deadline for Abstract: Monday, April 13 2009.

3. SIAM Annual Conference 2009 in Denver. (Conference date: July 7 2009). Deadline for Abstract: Monday, April 20 2009.

Students’ abstracts for Sigma Xi and Amherst Conference can be found here

Conference photos can be found here

For Graduate Students

1. Frontiers in Applied and Computational Mathematics at NJIT. (Conference date: June 1-2 2009). Deadline for Abstract: Wednesday, April 15 2009

2. Graduate Student Mathematical Modeling Camp (GSMMC) at RPI. (Workshop date: June 9-12 2009). Deadline for registration: Friday, April 17 2009

3. Mathematical Problems in Industry at University of Delaware. Follow up of GSMMC (June 15-June 19 2009). Deadline for registration: May 25 2009

Field Trips (for Undergrad/Grad)

1. New England Numerical Analysis Day 2009. April 4 2009. Please register online for free.

2. Fifth M.I.T Conference. (Conference date, June 17-19 2009). Registration Deadline: April 4 2009

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