Math 350, Fall 2014
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
- Tue, Sep 2
- Reading from "A First Course in Chaotic Dynamical Systems",
Chapters 2-5. See the "Resources" tab in CLEo.
- Homework: See Week 1 HW below.
- Thu, Sep 4: Discrete Systems, continued.
- Homework for Week 1. Due: 4, 5
from Tuesday, and 1, 4 from Thursday. These are due on Tuesday, Sep
- Week 2
- Mon, Sep 8
- Tue, Sep 9
- Thu, Sep 11: Finish the reading for the n-armed bandit.
Be sure you can run the previous scripts. Finish up Exercises 1-5
assigned last time (Due on Monday).
- Mon, Sep 15
- Tue, Sep 16: Genetic Algorithms.
- Thu, Sep 18: Finish Genetic Algorithms. Start
Optimization if time.
- Monday, Sep 22 (Today we finished GA's).
- Homework: Solve the Knapsack problem. Here is the fitness
function, called testfunction2.m:
testfunction2.m (Fitness function
for the Knapsack problem).
SOLUTION to Knapsack problem
- Tuesday, Sep 23: Start Optimization.
- Thursday, Sep 25: Finished the previous notes.
HOMEWORK DUE ON MONDAY: The knapsack problem, in Matlab.
HOMEWORK NOT DUE YET: Work on implementing Bisection and Newton in
EXAM NOTE: Exam 1 is scheduled for next week- By unanimous
proclamation, we moved it to THURSDAY, OCT 2.
- Monday, Sep 29: Finish up the optimization.
Optimization notes, updated to include
Solutions to Optimization Exercises
Matlab file: bisect.m
Matlab file: MultiNewton.m
Matlab file: Ex4.m (Solution to Exercise
- Tuesday, Sep 30: Review/Catch up day.
Exam 1 Review Sheet
Exam 1 Review Solutions
- Thursday, Oct 2: EXAM 1.
- Mon, Oct 6
Data Clustering (Updated Oct 8). Homework: 1, 2, 3, 4, 6. Turn in next
Monday: 2, 6.
- Tue, Oct 7: K-Means Clustering
- Matlab Function: edm.m (This is the
function that computes the Euclidean Distance Matrix between all the
data and the cluster centers).
- Matlab Function:
kmeansUpdate.m (This performs one step of the K-means algorithm).
- Matlab script:
ClusterExample01.m (Gives an example of how to use the k-means
- Matlab script:
ClusterExample02.m (Same as previous script, except shows the
- HOMEWORK: Download the m-files, try to publish
- Thu, Oct 9: Neural Gas
- Matlab Function: paramUpdate.m
- Matlab Function: initng.m
- Matlab Function:
- Matlab Data:
- Matlab Data: obstacle1.mat
- For fun: Video showing
"Growing Neural Gas"
- Training Examples on Concentric Circles:
- TestNG1: Good parameter
- TestNG2: Bad in two respects-
The value of lambda is too big, as is the learning rate. This
shoves all the centers towards the center of mass. Secondly,
the age cutoff is too old- We're retaining "bad" edges.
- TestNG3: Similar to TestNG2.
Cut off age is still too old.
- TestNG4: The cut off age
is too "young"- We're not retaining connections long enough,
and they're being deleted too early.
- The learning rate is too small.
Notice that the centers are really not moving at all from where
they were initialized.
- Thu, Oct 16: Download HW6scriptA.m and tell me what each of
the lines of code does. Additionally, comment on what you see. Does
k-means depend on the initial centers? (Also, be sure to continue
workingg on the Neural Gas script from last week), the project on
the obstacle course. Some extra scripts (Added Mon, Oct 20):
- Mon, Oct 20: Finish Neural Gas, start Linear Networks
Addition to Course Notes: Linear
- Tue, Oct 21: Some stats and linear regression.
Addition to Course Notes (Chapter 3):
Statistics and Linear Regression
Homework Assigned Week 8 (some Neural Gas,
some about Line of Best Fit). Due on Monday, Oct 27. You can upload
the Matlab files to CLEO- Make an "Oct27" file folder, please!
- Thu, Oct 23: Worked on Linear Neural Networks up through
defining the Widrow-Hoff learning algorithm. No new homework
Week 9 Solutions
- Mon, Oct 27
Homework: Go through the 10.4.1: Derivation of Widrow-Hoff (5
- Tue, Oct 28
Today we finished the linear neural nets and the discussion on
Homework and Matlab files:
- Summary of Homework, Week 9
- Data and Matlab files for the iris data classification example.
- Matlab M-file: BreastData.m.
This is a *script file* containing the data from the homework, so once
you download it, you can open it in Matlab's editor and look at it.
- Thu, Oct 30: Finished the discussion of the covariance and stats,
started looking at the linear algebra notes. Nothing new for the HW
(See Week 9 homework from Tuesday).
Breast Cancer Classifier 1
Breast Cancer Classifier 2
- Mon, Nov 03: Went through some linear algebra review.
using updated notes here. Homework:
#1, 4, 5 on pg. 55.
- Tue, Nov 04: More linear algebra. Looked at projections
and subspaces, high and low dimensional representations.
- Thu, Nov 06: Finished up the linear algebra.
Week 10 HW Summary
Week 10 HW Solutions
- Mon, Nov 10: Eigenvalues.
- Tue, Nov 11: Review/Catch up.
- Thu, Nov 13: Exam 2.
- Mon, Nov 17: Finished the Spectral Theorem and the SVD. No extra
HW assigned (Take home exam due tonight).
- Tue, Nov 18: Finished the SVD, started Karhunen-Loeve Expansions.
- Thu, Nov 20: Begin the "Best Basis" notes. Here are the new set of notes (NOTE: These
are now outdated notes, but have been kept here in case you want to
refer to them. The new notes are given below in Week 13.)
HW: The numbered items on pg. 71-72, 73.
- Mon, Dec 1
HOMEWORK due on THURSDAY: Exercise 2, p. 65 of the SVD notes and
Exercises 1-3 in the "Best Basis" notes. You should run the "author"
example before Thursday as well.
- SOLUTIONS to the HW
- Tues, Dec 2: Continue with Monday's topics.
- Thur, Dec 4: Finish the best basis, start Radial Basis Functions.
- Mon, Dec 8: Radial Basis Functions
- Tue, Dec 9: Orthogonal Least Squares outline
- Thu, Dec 11: Last Day of Class- Finish discussion of
Eigenfaces, Finish up RBFs, discuss the final exam.
- Exam 1 (Thu, Oct 2)
- Exam 2 (Thu, Nov 13)