Topics in Mathematical Modeling
There is no required textbook for this course. Class notes
will be provided.
Syllabus for the course
- Tuesday, Jan 18
Thursday, Jan 20: Meet in the Mathematics Computer Lab
Friday, Jan 21:
Homework 1 was changed to: p. 15-16, 3(a), 4(a), 6, 7. DUE:
- Handout: Sections 0.2, 0.3 from T. Sauer's ``Numerical Analysis''.
(Available on CLEo for a short time)
- Homework for Friday: Exercise 3(a), 4(a), 5(c), 6. (Changed- See
Today, we will finish talking about floating point numbers, and
then on Tuesday we'll pick up with some Matlab.
Use these instructions to move the window options (maximize, minimize,
close) back over to the right side of the window.
- Tuesday, Jan 25: More discussion on Matlab, and the
Case Study on Learning. The
Matlab code is banditE.m and the
script file is banditScript.m. Be
sure to right-click the mouse and choose "Save Link As..." to download
the Matlab code.
Homework 2: Exercises 1-5, pg 2 of the Case Study Handout.
- Thursday, Jan 27: Worked through the epsilon-greedy algorithm,
worked in the computer lab a bit. Homework
- Friday, Jan 28: Finish the Case Study.
Homework 4: is here. Here is the Matlab code discussed:
- Tuesday, Feb 1: Finished the n-armed bandit model, and began the
linear algebra review- The four subspaces. No homework assigned.
- Thursday, Feb 3: Introduction to linear models, and linear neural
nets. Handout is here.
- Friday, Feb 4: Continuing with linear models.
Homework 5 Handout is here.
- Tuesday, Feb 8. Today we started linear neural networks,
and discussed unsupervised learning. Here is a copy of the updated notes that
were passed out in class. Other links:
- Thursday, Feb 10. Our focus is on training the linear network. Here
are the Matlab files:
- Friday, Feb 11: We will meet in the computer lab and try to get
further on understanding the Matlab code. Homework 6 will not
be due until Tuesday, Feb 15. Summary
page with some homework notes.
- Tuesday, Feb 15: Finish up the linear neural networks with a look
at gradient descent and an application: Novelty Detection.
- Thursday, Feb 17: Finish up linear networks, start Appendix A-
The derivative and the gradient.
- Friday, Feb 18: Continue with Appendix A.
- Tuesday, Feb 22: Finish Appendix A, work in the lab for a bit.
- Thursday, Feb 24 - Review for Exam 1 (See links below)
- Friday, Feb 25: Exam 1
- Tuesday, Mar 01: Handout
with more linear algebra (Projections, the SVD, and the Pseudo-Inverse.
- Thursday, Mar 03: Continue with the handout. Homework Assigned today:
p.6, 3, 6, and 7. (Try them all, but only turn in solutions for the three).
- Friday, Mar 04: Continue with the handout. Homework: Compute the SVD
for a ``simple'' matrix by hand (1(a), p. 14).
- Tuesday, March 29: Homework is due. Start working through the notes:
that were passed out last Thursday.
Files: edm.m and InterpExamp1.m.
Homework: p. 175, 1, 2, 3 and p. 178, 1 (not due yet, but work through
- Thursday, March 30: Continue with the RBFs. Here is some Matlab
code for the homework:
- Matlab File: rbf1.m, needed for the transfer functions
- Matlab File: RBFSample0.m, the first example
- Matlab File: RBFSample1.m, the second
- Friday, April 1:
- Write the solution to Exercise 1 (the determinant of the Vandermonde
- Write a Matlab script for classifying the Iris data. Here are the code
- Use the same data as before (X is 150 x 4, Y is 150 x 3).
- Use 10 points from the data (randomly selected) for the "centers".
- Use a Gaussian transfer function with a width of 3.
- For training, use 80 points chosen at random from the data.
- For testing, use all the data and construct the Confusion matrix
(See HW 7, for example).
- Tuesday, April 5: Script: RBFwidths.m
Today, we'll be discussing the role of the Gaussian, Matlab structures.
- Thursday, April 7: Continue with Matlab structures and (time
permitting) Orthogonal Least Squares.
Homework 12: (due Fri)
- Exercise 2 on page 186.
- Compute the RBF by hand
(First problem on today's handout
weight vector corrected)
- Friday, April 8: No homework announced. We talked about
Matlab's "Orthogonal Least Squares" training algorithm.
- Tuesday, April 19: Review for Exam 2 (See below for materials)
- Thursday, April 21: Exam 2 (in class portion)
- Friday, April 22: No class. Work on the Take Home Exam.
- Tuesday, May 10: Discuss the final exam (take home)
- Wednesday, May 11: Reading Day (Math Picnic!)
- Take home exam due on Tuesday, May 17, 6PM.
Exam 1 Links
Exam 2 Links
- Review questions
- Review solutions
- Homework Solutions
- Exam 2 (Take home portion):
NOTE: You do not have to use the template files- You might try to
code the solutions yourself before looking at my suggestions!
Final Exam Links