Mathematical Modeling
Math 350, Spring 2021

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.

Beginning Material

Daily Links

Weeks 1 to 11 are here...
Week 12: Apr 12-Apr 16: k-Nearest Neigbor Classifiers and Working with Data.
- Mon, Apr 12
  - (PDF) K-Nearest Neighbors Chapter
  - (Video) Introduction, some coding
  - (Video) Data scaling, the classifier
  - (Video) Accuracy (Split the data, k-fold CV)
  - (Video) The Confusion Matrix
  - Homework: Problem 1 in Chapter 10. A larger group project will be written up shortly, due in one week. You may work in groups of up to 3 people.
- Wed, Apr 14: k-NN Regression.
- Fri, Apr 16: Linear Neural Networks.
  - (PDF) Chapter 11: Linear Neural Networks
  - Video 1 of 3
  - Video 2 of 3
  - Video 3 of 3
  - Video Demonstration: TGF
    - Files for the demonstration (Matlab and Python)
  - Video Demonstration: Adaptive Signals Processing
    - Files for the demonstration (Matlab and Python)
  - Homework: Be sure you're working on the k-Nearest neighbor labs. I'll assign new projects for the linear neural nets on Monday. Until then, try running the examples.
Week 13: Apr 19-Apr 23
- Mon, Apr 19: Live session to chat. All the code folders from last week have been updated to include examples and Python code. Links from today:
  - Latex file for the HW write up (if you want to use Latex)
  - Model comparison table from discussion today (to be added to later)
- Wed, Apr 21: Radial Basis Functions (Day 1- Overview)
  - (PDF) Chapter 12 Notes
  - Video 1 of 3
  - Video 2 of 3
  - Video 3 or 3
  - Homework: Carefully read over the notes. You might consider what the coding will look like (homework assigned on Friday).
- Fri, Apr 23: Radial Basis Functions (Day 2: Applications and Code)
Week 14: Apr 26-Apr 30
- Mon, Apr 26: RBF OLS
  - (PDF) Updated RBF Notes
  - (Video 1) Starting on p. 137 of the notes...
  - (Video 2) Going up to the OLS algorithm (I ended up splitting this video for technical reasons- sorry about all the links!)
  - (Video 3) The OLS algorithm.
  - (Video 4) Conclusion to OLS
  - (Video 5A- Matlab HW) Looking at the homework folders
  - (Video 5B- Python HW) Looking at the homework folders
  - Homework: p. 139, #1 and p. 141, #1-2. Add these to the homework due on Friday.
- Wed, Apr 28: Feed Forward Neural Nets: Today, I'm linking you to some very nicely done introductions to neural networks. Please watch the videos and afterwards read through the notes. On Friday, we're going to go through training, and then hopefully build a net from scratch.
  - (Youtube, not mine) Introduction to neural networks
  - (Youtube, not mine) Part two of the introduction
  - I had a video worked up, but just read over the PDF notes below after you've watched the other videos (they do a nice job).
  - (Video, very short) Nice animation from Matlab to show a neural network training
  - (PDF) The Neural Network Chapter (Part 1)
  - Homework: Look over 1-6 on page 148. We'll be using the result of exercise 5. To understand the phenomena of saturation, look at problem 3.
- Fri, Apr 30: Neural Nets- Backpropagation and building from scratch
  - (PDF) Full chapter on Neural Nets
  - (Video) Backpropagation of Error
  - (Video) Backprop part 2
  - (Video) Gradient Descent
  - (Video) Backprop is Gradient Descent
  - (Video - Matlab) Discussion of the code - Matlab
  - (Video - Python) Discussion of the code - Python
  - Folder with Code and Examples
  - Homework: Fill in the worksheet and look over the neural nets we built from scratch. Try running them in either Octave or Python.
Week 15: May 3 - May 7
- Mon May 3: Autoencoders
- Wed May 5: Deep Learning
- Fri May 7: Spring Break Day
Week 16: May 10 (one day- we'll discuss the final- See the links below).

Exam Links

Exam 1 Links:

Exam 2 Links:

The exam format will be the same as last time, so you might check over the first link from the first exam, "What should I expect from an Exam on Canvas?". The addition is that you may use Matlab/Octave and/or Python, as appropriate.

Topics and Review Questions
Review solutions (There were some typos- Sorry about that!)
TestFile.zip: The exam and scripts/data will be provided in a zip file. If you're not sure if you can open a zip file, try downloading and extracting this file (it just contains 4 Octave script files that are also on the class website).

Final Exam Links

Matlab/Octave Notes

Octave is a free version of Matlab. Some things about it may differ from Matlab, but for the things we'll do in class, it shouldn't be a problem.
Octave online, so you don't have to install it
Example installation of Octave with Ubuntu
Example installation of Octave with Windows 10
"Cheat Sheet" for Matlab - Python - R. Useful to compare!
Numpy for Matlab users

Mathematical Modeling Math 350, Spring 2021