Winter 2025
MATH - BIOINF- STAT 547: Mathematics of Data
Instructor: Prof. INDIKA Rajapakse (indikar@umich.edu)
Graduate Student Instructor (GSI): MARC Andrew Choi (machoi@umich.edu)
Location: 2140 SKB (School of Kinesiology Building)
Class Time: Tuesday and Thursday, 2:30 PM - 4:00 PM
Office Hours:
INDIKA Rajapakse - Wednesday and Friday, 3:00 PM - 5:00 PM: https://meet.google.com/dnm-zipr-tsb or in person after class
MARC Choi - Wednesday 2:00-3:00 PM (Zoom) and Thursday 1:00-2:00 PM (East Hall Lower Atrium)
Links
Topics and Timeline (Topics and Timeline subject to change without notice. Please check regularly)
Piazza (Please sign in and add yourself to the course if you have not already)
References of Interest
MATLAB: 1) MATLAB Tutorial 2) Basic Functions Reference
Digital Library: An unofficial digital library I maintain that contains books and papers on topics related to my research and teaching
Great book with codes: Cleve Moler . Numerical computing with MATLAB. Society for Industrial and Applied Mathematics, (2004)
Dr. Gilbert Strang's Book
Dr. Lars Eldén's Book
Great Blogs! I visit these from time to time, and they have many great articles
Amazing TED Talk: The mathematician who cracked Wall Street | Jim Simons
PROBLEM OF THE DAY (POD)
PROBLEM SETS
This section includes assignments, solutions, and helpful resources.
Problem Set 1: Due Thursday, January 30
NOTES, SLIDES, AND PAPERS
Date: 01-09-2025
Introduction: Slides
Date: 01-14-2025
"You can always recognize truth by its beauty and simplicity"―Richard P. Feynman
Papers
Lieberman-Aiden, Erez, ..., Groudine Mark, ..., Lander Eric. "Comprehensive mapping of long-range interactions reveals folding principles of the human genome." Science 326.5950 (2009): 289-293.
Turk, Matthew, and Alex Pentland. "Eigenfaces for recognition." Journal of cognitive neuroscience 3.1 (1991): 71-86. (Classic! just browse)
Martin CD, Porter MA. The extraordinary SVD. The American Mathematical Monthly. 2012 Dec 1;119(10):838-51. (Excellent Review!)
Date: 01-16-2025
"If you don’t believe in yourself why is anyone else going to believe in you?" ― Tom Brady
Eckhart-Young Theorem and Low Rank Approximations
Poincare Diagram: Stability diagram classifying Poincaré maps as stable or unstable according to their features
Image Compression with Low-Rank SVD: Example
My talk yesterday (1/15/2025)
Date: 01-21-2025
Quote of the Day
"Young man, in mathematics you don't understand things. You just get used to them" ― John von Neumann
Guest Lecture: Dr. Cleve Moler
MathWorks Co-Founder and Chief Mathematician Cleve B. Moler
Direct link to YouTube: https://www.youtube.com/watch?v=R9UoFyqJca8
Date: 1-23-2025
Quote of the Day
"Everything is practice" ― Pele
Optimal Hard Threshold (OHT)
Low Rank Approximations
Additional Reading
Gavish, Matan, and David L. Donoho. "The optimal hard threshold for singular values is 4/sqrt(3)." IEEE Transactions on Information Theory 60.8 (2014): 5040-5053. (Amazing Paper!)
Excellent book chapter (Please read pages 31 - 32)
Donoho, David, Matan Gavish, and Elad Romanov. "ScreeNOT: Exact MSE-optimal singular value thresholding in correlated noise." The Annals of Statistics 51, no. 1 (2023): 122-148.
Udell, Madeleine, and Alex Townsend. "Why are big data matrices approximately low rank?." SIAM Journal on Mathematics of Data Science 1.1 (2019): 144-160.
Thibeault, Vincent, Antoine Allard, and Patrick Desrosiers. "The low-rank hypothesis of complex systems." Nature Physics 20, no. 2 (2024): 294-302.
Date: 1-28-2025
Quote of the Day
"Nature has a great simplicity and therefore a great beauty" ― Richard Feynman
Poincare Diagram: Stability diagram classifying Poincaré maps as stable or unstable according to their features
Dynamic Mode Decomposition (DMD)
Book
Kutz, J. Nathan, et al. Dynamic mode decomposition: data-driven modeling of complex systems. Society for Industrial and Applied Mathematics, 2016.
Chapter 1: Dynamic Mode Decomposition: An Introduction
http://dmdbook.com/
Additional Reading
Schmid, Peter J. "Dynamic mode decomposition of numerical and experimental data." Journal of fluid mechanics 656 (2010): 5-28.
Schmid, Peter J. "Dynamic mode decomposition and its variants." Annual Review of Fluid Mechanics 54 (2022): 225-254.
Tu, Jonathan H. "Dynamic mode decomposition: Theory and applications." PhD diss., Princeton University, 2013.
Date: 1-30-2025
Quote of the Day
"Be constantly on the lookout for hype"―David Heckerman
Guest Lecture: Causal discovery from data (Dr. David Heckerman from Amazon)
Please visit and like these GitHub:
GENERAL READING
I will add to this list throughout the semester
Rajapakse, Indika. "Conversation with Dr. Steve Smale and Dr. Lee Hartwell." NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 68, no. 9.
Aksoy SG, Hagberg A, Joslyn CA, Kay B, Purvine E, Young SJ. Models and Methods for Sparse (Hyper) Network Science in Business, Industry, and Government. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY.;69(2).
Vaswani, Ashish, et al. "Attention is all you need." Advances in neural information processing systems 30 (2017).
Kolda T. Mathematics: The Tao of Data Science. (2020).
Turing, Alan Mathison. "The chemical basis of morphogenesis." Bulletin of mathematical biology 52.1-2 (1990): 153-197.