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
There is no required text for this course. Class notes will be provided.
Coursework and Handouts
- Sep 01-03: Introduction, Matlab and some Statistics
- Sep 08-10: Finish up stats and Matlab (See notes above)
- Sep 15-17: Linear Algebra and perhaps some Linear Programming
- Linear Algebra Fundamentals handout.
- Homework (9/15): Look at problems 1-4 on the last page of the previous handout.
- Passed out Quiz 2 on Thursday, due next Thursday once we've talked
a bit more.
- Sep 22-24: Linear Algebra, continued.
- Finish up projections and Matlab coding for projections. HW: Finish
- Continue with Linear Algbra.
- Sep 29-Oct 1: Exam passed out this week. Due on Monday, Oct 5th
- Worked on ``The Best Basis'' chapter. Defined the covariance
matrix and worked out how we will define the error for
optimization of the basis vectors.
- We will not be getting tested on Matlab this time around (ran
short of time).
- 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.
- (Short week!) Oct 15: Run the experiment on page 11.
- Oct 20-22: The Widrow-Hoff learning rule. Applications to
time-series analysis. Gradient descent for minimization.
- Oct 27-29
- Nov 3-5
- Nov 10-12: Exam week. In class exam on Nov 10, we
spent Thursday in the lab (see Exam 2 materials below).
- Nov 17-19: Begin discussion of nonlinear regression. First
up: The Radial Basis Functions.
- Dec 1-3: Lab materials for this week:
- 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
- Data file: Photos of some people.
- Final Exam details, Part I
Exam 2 Materials
- Exam 2 (Take-Home part)
- Items for Question 2:
- Data for classification (Right click and save)
- MODIFIED data file (Exam2Ques2DataE.mat)
- Run this script file to get a plot of
the data and to construct your targets.
- MODIFIED script file
- Items for Question 3:
- 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.