Math 350, Fall 2016
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.
There is no required text for this course. Class notes will be provided.
- Week 1
- Wed, Aug 31: Ch 7.1 (Boyce and Diprima on CLEO), 1, 3, 7, 8, 15,
- Fri, Sep 2: Nothing new was assigned. Continue working on
- Week 2
- Mon, Sep 5:
Modeling Question (handed out last week):
- Wed, Sep 7
- Fri, Sep 9
- Week 3
- Mon, Sep 12: (Phase planes and the Poincare Diagram) HW is from
Section 9.1, exercises 1, 3, 7, 13, 17(*).
Here is another link to the Poincare
- Wed, Sep 14: (Local linearization) Read Appendix A,
and 9.2-9.3. HW is from Section 9.3,
Exercises 6, 8, and 20(*). For the drawings in 6 and 8, use the link
to the slope fields below.
Here is the link to Appendix A.
- Fri, Sep 16: Continued from last time, and take a look
at creating and analyzing three popular nonlinear models. HW: Look
at exercises 1, 3 in Section 9.4 and the same problems in Section
- Week 4
- Mon, Sep 19. Today we finish 9.4, 9.5. For homework, finish
the problems given on Friday. There will be a handout today as
Homework for Nonlinear Analysis.
Be prepared to turn in 1(a) and 2 for next week.
What's due for Wednesday? Turn in the starred problems from
last week (9.1, 17; 9.3, 20).
- Wed, Sep 21: Starting Discrete Dynamical Systems. See Section
2.9 from Boyce and Diprima (located on CLEO). Homework today: 2.9,
1, 3, 5(*), 6, 8(*), 9, 10.
- Fri, Sep 23. Continue with Boyce and Diprima.
- Week 5
- Monday, Sep 26: Class Notes
Here (finished discussion of discrete systems).
- Wednesday, Sep 28: Review Day
- Friday, Sep 30: Exam 1
- Week 6
- Monday, Oct 3: We're starting in on the notes for the class.
First up, we'll discuss reinforcement learning and recall some
basic facts about statistics. We're also introducing Matlab,
so the homework is a bit broken up:
Homework (about stats, Chapter 3 of the class notes): 1, 2, 4,
5-12. Turn in solutions to 5-12 (they'll go fast).
Furthermore, spend an hour or two looking at Matlab in the
computer lab. Take a look at Exercise Set 1 from the Matlab notes
- Wednesday, Oct 5: Finished the section on stats.
- Friday, Oct 7: No classes today.
- Week 7
- Monday, Oct 10: Linear regression, Matlab, start on n-armed
bandit from Chapter 2. Links from today:
- Wednesday, Oct 12: Matlab, the n-armed bandit. Here is some
Matlab code discussed in the text (Chapter 2).
- Friday, Oct 14: Continue n-armed bandit.
Homework for the n-armed bandit.
Be sure to read over the Matlab code to see if you can understand
what the code is doing.
- Week 8
- Monday, Oct 17: Softmax and Pursuit strategies for the
n-armed bandit. Introduction to Genetic Algorithms. Homework:
Work on the problems assigned on Friday to turn in on Wednesday.
Be sure to implement the code in Matlab. Here are some files:
- Wednesday, Oct 19: Start genetic algorithms.
- Friday, Oct 21: Genetic Algorithms, continued.
- Week 9
- Monday, Oct 24: Finish GA, start linear algebra notes
(Chapter 5, linked at the top and below):
- Wednesday, Oct 26: Continue with the linear algebra notes.
Add to HW: Page 7: 2, 3 and Page 9: 3, 4.
- Friday, Oct 28: Continue with the linear algebra notes.
Add to HW: Page 9: 3, 4. Also the Matlab stuff below:
- Week 10
- Monday, Oct 31: Projections
- Wednesday, Nov 2: The SVD
- Friday, Nov 4: The SVD
- Week 11
- Monday, Nov 7: Review for Exam
- Wednesday, Nov 9: Exam II
- Friday, Nov 11: Started "The Best Basis", went to p. 6
- Week 12
- Monday, Nov 14: The Best Basis
- Files for the ``eigenfaces'' homework (due Friday):
- Wednesday, Nov 16: Linear Nets
- Friday, Nov 18th: Linear Nets
- Week 13
- Monday, Nov 28: Finish Linear Nets. Homework is below, and is due
on Friday (upload the published scripts to CLEO).
- Homework Problems (due Friday)
- Matlab file: BreastData.m
- Wednesday, Nov 30: Neural Networks (Text handed out on Monday)
- Friday, Dec 2: Finish up the linear network training
(Iris data and Breast Cancer data). In class, we'll continue
discussing the (nonlinear) feedforward neural networks.
- Week 14
- Exam 1 Links
- Exam 2 Links
- Exam 2 Take Home Links
- Final Exam Links
Matlab Handouts and Links