Mathematical Modeling and Numerical Methods
Math 350, Spring 2008
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
- Chapter 2 (Introduction and Data)
- Chapter 3 (Learning)
- Chapter 4 (Statistics/Linear Regression, in
- Chapter 5 (Linear Alg)
- Appendix on Derivatives (in PDF format)
- First part of Chapter 6 (The Best Basis)
- Second part of Chapter 6 (Eigenfaces)
- Chapter 7 (Best Non-Orthogonal Basis)
- Chapter 8: Local Basis and Dimension (future chapter)
- Chapter 9: Data Clustering
- Chapter 10: Linear Networks
- Chapter 11: Radial Basis Functions
(new version, updated April 15, 2008).
Here is a copy of the old version, if needed.
- Chapter 12, part 1
- Jan 14-18: Work through Chapters 2 and start 3.
- Tuesday: Problems 2, 5, 7 (p. 16) and read to page 29
- Thursday: Exercise 1, p. 29 and Exercise 3, p. 30
- Friday: Intro to Matlab (Meet in the Computer Lab)
- Jan 21-25
- Thursday: Exercises 1-5, pg. 38
- Friday: Exercises 1-5, p. 44
Jan 28-Feb 1: Finish up Chapter 3 (Learning), Start Chapter 5 (Linear Algebra)
Thursday: Exercises 1-7, p 75 (in Ch 5)
- Tuesday: Last page of notes, code up the classification (Use
the code below as a template)
M-file for class
Take Home Quiz (Quiz 2)
Right-click and "Save Link As...". Print your solution (we'll talk
about how in class on Friday) and turn it in on/before class on
Feb 4-8: Finish up Chapter 5 (Linear Algebra)
- Tuesday: Finish Problem 6, p. 76. Do Exercise 19, p. 79
(this is a Matlab exercise). Be sure you understand the code!
- Thursday: Homework on
this handout. Also, read through to p. 87
- Friday: Appendix on Derivatives (See the link to the text above,
also handed out in class). Work through the 8 exercises, p. 240-241.
Feb 11-15: We'll be working through Chapter 4, Statistics
- Tuesday: Derivatives, p. 240-1 (We're a little behind).
- Thursday: Statistics (Chapter 4), p. 12-15 (Problems 1-12)
- Friday: HW: Finish up the stats stuff. Quiz 4 handouts below:
Feb 18-22: Finish Chapter 4, Review for Exam I
- Thursday: Review for Exam I
- Friday: Exam I. See the section below for the take home
exam materials (Due Tuesday at the beginning of class)
Feb 25-29: The Best Basis, Eigenfaces
Friday: Computer Lab materials:
- An set of points for today's lab
(900 points in the plane in an elliptical shape) Be sure to right-click
the mouse to "Save Link As..."
- Computer Lab Here
Mar 24 - Mar 28: Data Clustering.
Mar 31 - Apr 4:
Apr 7 - Apr 11: Radial Basis Functions
Apr 14 - Apr 18: Nonlinear Networks
Apr 21 - Apr 25
Apr 28 - May 2:
May 6: No class- Work on the Final Exam.
May 8th: Final Exam due at 5PM- No exceptions.
- Tuesday: HW is p. 173: 3, 4, 5, p. 176: 1-3; p. 179 1-6 (if we get there)
Class Example Links:
- Thursday: HW: Continue with previous HW.
Class Example Links:
- Friday: Quiz 9 is here
Here is the new code from today's session: