Mathematical Modeling and Numerical Methods
Math 350, Fall 2009

Coursework and Handouts

1. Sep 01-03: Introduction, Matlab and some Statistics
   • Course Syllabus
   • Some common stats definitions
   • Homework Set 1
   • Introduction to Matlab
   • Summary of Matlab Commands
2. Sep 08-10: Finish up stats and Matlab (See notes above)
   • Notes on the stats we've been doing (Added Sep 8)
   • Homework due on Friday, Sep 11: Homework set 1 from last week (see link above). This counts as Quiz 1.
3. 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.
4. Sep 22-24: Linear Algebra, continued.
   • Finish up projections and Matlab coding for projections. HW: Finish Quiz 2.
   • Continue with Linear Algbra.
5. Sep 29-Oct 1: Exam passed out this week. Due on Monday, Oct 5th at 4PM.
   • 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).
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.
   • Linear Models handout
   • The M-file for the best line (orthog. projections), save as Line2.m
   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.
   • M-file for the associative learning, Hebb's Rule (this is the code from the notes, pages 9 and 10)
8. Oct 20-22: The Widrow-Hoff learning rule. Applications to time-series analysis. Gradient descent for minimization.
   • Second part of the old linear algebra handout (forgot to post it)
   • Continuation of the notes ("Linear Models")
   • Appendix A (Derivatives and gradient descent)
   • Homework set due next Thursday, Oct 29. This is a summary of the previous homework assigments, and brings us up to date.
9. Oct 27-29
   • M-file: ExampleWriteUp.m
   • How to turn in your write ups (download the previous M-file)
   • A function that will plot contours (implot.m). Also available from Matlab's website.
   • A script file showing how to plot contours and a trajectory of gradient descent (sampleImplot.m)
   • (NOTE: THe homework due today has a new due date: Tuesday, Nov 3)
10. Nov 3-5
    • "Chapter 6" notes on the best basis (forgot to post it earlier).
    • Function to produce a lagged matrix (lag.m)
    • Widrow-Hoff (wid_hoff1.m, p. 16)
    • Script file that implements the Example on p. 19 in detail. (scriptP19.m) (Updated Nov 5)
    • Exam 2 Review Notes
    • Review SOLUTIONS
    • Computer Lab, Thursday
    • Sunspot data (text file, sunspots.dat)
    • Movie data for the last question in the lab.
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.
    • Radial Basis Function Notes
    • Matlab file vander1.m
    • Lab Instructions (PDF)
    • Matlab file LabNov18.m
13. Dec 1-3: Lab materials for this week:
    • Lab Questions
    • Matlab file: edm.m
    • Matlab file: rbf1.m
    • Matlab file: edmInterp1.m
    • Matlab file: edmInterp2.m
    • Matlab file: rbfError2d.m
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:
    • Data for Matlab: IrisData.mat
    • M-File: IrisClass1.m This script file explores the relationship between the classification error and the width of the Gaussians (in the transfer function).
    • M-File: IrisClass2.m Example of how to analyze a classifier by building a confusion matrix.

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.