MAT1801: Methods of Applied Mathematics II

Reference text and notes

The primary reference text is Foundations of Data Science, by Blum, Hopcroft, and Kannan. Other supplemental references will be added here as they come up. You may also find some of Jelani Nelson's lecture notes helpful for sketching algorithms. For percolation theory, I based my lecture off a combination of Jeffrey Steif's lecture notes, and a simpler argument made in an AMS feature column by David Austin. The AMS column is not rigorous at all, but provides I think nicer intuition than Steif's lecture notes, which are rigorous, but made use of much more sophisticated tools from probability. For wavelets, I also used the 2000 PhD thesis of David Malone.

For the persistent homology lectures, I used a combination of http://www.dam.brown.edu/people/mmcguirl/homologyBootcamp.pdf and Computation Topology: An Introduction by Edelsbrunner and Harer.

For epidemic modelling, here are some references that I'm taking as inspiration/following for my notes:

• https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6002090/pdf/main.pdf
• https://mysite.science.uottawa.ca/rsmith43/MAT4996/earn.pdf
• https://arxiv.org/pdf/1111.4875.pdf

I am also making available my pre-lecture notes (which may differ from what I actually write up on the board in lecture).

• 0 Introduction.pdf
• 1 High dimensional space.pdf
• 1.5 Gaussian.pdf
• 2 SVD.pdf
• 2.5 PCA.pdf
• 3 Markov chains.pdf
• 3.5 Markov chain convergence _ pagerank.pdf
• 4. overview.pdf (PDF slides)
• 4.5 Streams and Sketches.pdf
• 5 more sketching.pdf
• 5.5 Matrix sketches.pdf
• 6. Random graph theory.pdf
• 6.5 Random graph theory continued.pdf
• 7 percolation theory.pdf
• 7.5a wavelets.pdf
• 8 Wavelets (2).pdf
• 8.5 Wavelets and VC-dim.pdf
• 9 VC-dimension.pdf
• 9.5 deep learning.pdf
• 10 Persistent homology (pre-lecture).pdf
• 10 persistent homology lecture.pdf
• 11 persistent homology 2 (pre-lecture).pdf
• 12 Epidemic modelling.pdf

Homework

All homework should be submitted on Quercus by the due date, ideally as a PDF, though any standard format that I can easily read is fine.

• Assignment 1
• Assignment 2
• Assignment 3
• Assignment 4 - project proposal
• Assignment 5
• Assignment 6
• Assignment 7
• Assignment 8
• Assignment 9
• Assignment 10

 

• Final report - due April 10

Term Test

Date: Thursday March 26 in class.
Update: canceled, and weight shifted, as detailed in the class syllabus vote, due to COVID-19

The term test will resemble the theory problems on the homework.