Mathematical Modeling and Numerical Methods
Math 350, Fall 2009

This course explores the process of building, analyzing, and interpreting mathematical descriptions of physical processes. Topics may include feature extraction, partial differential equations, neural networks, statistical models. The course will involve some computer programming, so previous programming experience is helpful, but not required. Prerequisite: Math 300 (Linear Algebra)

There is no required text for this course. Class notes will be provided.

Coursework and Handouts

  1. Sep 01-03: Introduction, Matlab and some Statistics
  2. Sep 08-10: Finish up stats and Matlab (See notes above)
  3. Sep 15-17: Linear Algebra and perhaps some Linear Programming
  4. Sep 22-24: Linear Algebra, continued.
  5. Sep 29-Oct 1: Exam passed out this week. Due on Monday, Oct 5th at 4PM.
  6. Oct 6-8: On Oct 6, we assigned Exercises 1(e) (write code called Line1.m), 1(f) (See the scan below for the setup), Exercise 3 (write the Median-Median line code as Line3.m), and apply the lines to the data in Exercise 5. On Oct 8, we continued in the notes, and assigned Exercises 1-4 on p. 6. Due: Oct 15.
  7. (Short week!) Oct 15: Run the experiment on page 11.
  8. Oct 20-22: The Widrow-Hoff learning rule. Applications to time-series analysis. Gradient descent for minimization.
  9. Oct 27-29
  10. Nov 3-5
  11. Nov 10-12: Exam week. In class exam on Nov 10, we spent Thursday in the lab (see Exam 2 materials below).
  12. Nov 17-19: Begin discussion of nonlinear regression. First up: The Radial Basis Functions.
  13. Dec 1-3: Lab materials for this week:
  14. Dec 8-10
    Here are some sample files that show you how to train a set of Radial Basis Functions to do some classification:

Final Exam Materials

  1. Data file: Photos of some people.
  2. Final Exam details, Part I

Exam 2 Materials

  1. Exam 2 (Take-Home part)
  2. Items for Question 2:
    1. Data for classification (Right click and save)
    2. MODIFIED data file (Exam2Ques2DataE.mat)
    3. Run this script file to get a plot of the data and to construct your targets.
    4. MODIFIED script file (Exam2Ques2PlotB.m)
  3. Items for Question 3:
    1. Faces data for Question 3. When you load the data (load Faces.mat), you will have a matrix Y that is 77028 x 30. Change it to double format (like we did for the movie data). See the exam for more instructions.