Embedded Files
Instructor: Prof. INDIKA Rajapakse (indikar@umich.edu)
Graduate Student Instructor (GSI): RAM Prakash (nuvi@umich.edu)
Location: UMMA Auditorium (Room: UMMA061)
Class Time: Tuesday and Thursday, 2:30 PM - 4:00 PM
Office Hours: INDIKA R and RAM P- Tuesdays 4:00 PM - 5:00 PM 4088 EH and Thursdays 4:00 PM - 5:00 PM 2866 EH
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)
Challenge Problem! This is from the book by Smale and Hirsch, Differential Equations, Dynamical Systems, and Linear Algebra. If you would like more challenging problems, please see the following paper.
Smale, Steve. "Mathematical problems for the next century." The mathematical intelligencer 20.2 (1998): 7-15.
James Simons: My Guiding Principles
References of Interest
Claude Shannon: His famous paper and his thesis
MATLAB: 1) MATLAB Tutorial 2) Basic Functions Reference
Digital Library and TwinCell Blueprint: 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), Solutions to Exercises
Gilbert Strang's Book: Linear Algebra and Learning from Data
Tom Cover and Joy Thomas's Book: Elements of information theory
Christopher Bishop and Hugh Bishop's Book: Deep Learning : Foundations and Concepts and Web Site
PROBLEM OF THE DAY
PROBLEM OF THE DAY
POD 2 01-20-2026: Emergence
POD 3 01-27-2026: Learning and Memory
POD 4 02-03-2026: PC1 and Fiedler Vector
POD 5 02-10-2026: SVD
POD 6 02-12-2026: David Heckerman
PROBLEM SETS
PROBLEM SETS
This section includes assignments, solutions, and helpful resources.
Problem Set 1: Due Thursday, January 29, 2026
Overleaf version and Data (Math 547 Introductions.csv)
Solutions:
Problem Set 2: Due Thursday, February 19, 2026
NOTES, SLIDES, AND PAPERS
NOTES, SLIDES, AND PAPERS
Date: 01-08-2026
Date: 01-08-2026
Date: 01-15-2024
Date: 01-15-2024
Quote of the Day
"The only way to do great work is to love what you do" ― Steve Jobs
The Extraordinary SVD: During the lecture, Dr. Cleve Moler will join the class virtually
Date: 01-20-2024
Date: 01-20-2024
Quote of the Day
"One never notices what has been done; one can only see what remains to be done" ― Marie Curie
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)
Date: 01-22-2024
Date: 01-22-2024
Quote of the Day
"If you want to be the best, you have to do things that other people aren’t willing to do ― Michael Phelps
Papers
Brin, Sergey, and Lawrence Page. "The anatomy of a large-scale hypertextual web search engine." (1998).
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.
PatentsUS6285999B1
US6285999B1 Method for node ranking in a linked database. Lawrence Page: 1998-01-09
115-008219-US-PS1 Network approach to navigating the human genome. Indika Rajapakse: submitted November 2020.
Date: 01-27-2026
Date: 01-27-2026
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
Inverse and Pseudoinverse of a Matrix: This comes up all the time when you are dealing with real data
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
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: 01-29-2025
Date: 01-29-2025
Quote of the Day
"If you don’t believe in yourself why is anyone else going to believe in you?" ― Tom Brady
Problem Set 1: Discussion and Grading
SVD, PCA and DMD again...
Papers
I would like to share this paper in case you haven’t seen it. Even if it’s not your area, it’s inspiring to see how AI models can achieve beautiful results.
Avsec et. al. Advancing regulatory variant effect prediction with AlphaGenome. Nature 649, 1206–1218 (2026)
Joshua Pickard, Cooper Stansbury, Amit Surana, Anthony Bloch, and Indika Rajapakse. "Biomarker Selection for Adaptive Systems." Proceedings of the National Academy of Sciences, (2025)
Date: 2-03-2026
Quote of the Day
"I think one of the things about creativity is not to be afraid of saying the wrong thing " ― Sydney Brenner
Fiedler Number and Fiedler Vector
Edify Image: Please check this website for applications of diffusion models
Papers: I am sharing these references for completeness; you do not need to read them. I personally think it is helpful to know where these methods were originally introduced.
Von Luxburg, Ulrike. "A tutorial on spectral clustering." Statistics and computing 17.4 (2007): 395-416. (Excellent Review!)
Belkin, Mikhail, and Partha Niyogi. "Laplacian eigenmaps and spectral techniques for embedding and clustering." Advances in neural information processing systems. 2002.
Ng, Andrew Y., Michael I. Jordan, and Yair Weiss. "On spectral clustering: Analysis and an algorithm." Advances in neural information processing systems 2 (2002): 849-856.
Coifman, Ronald R., and Matthew J. Hirn. "Diffusion maps for changing data." Applied and computational harmonic analysis 36, no. 1 (2014): 79-107.
Eliasof, Moshe, Eldad Haber, and Eran Treister. "Graph neural reaction diffusion models." SIAM Journal on Scientific Computing 46, no. 4 (2024): C399-C420.
Date: 02-05-2026
Date: 02-05-2026
Quote of the Day
"Everything is practice" ― Pele
Problem Set 2 discussion
A continuation of Tuesday ....
Date: 02-10-2026
Greg Harden ( – September 12, 2024) : Stay Sane in an Insane World: How to Control the Controllables and Thrive
I will review spectral clustering and DMD, then introduce DMD with control and preview data-driven ideas on controllability and observability.
Network Controllability: Slides Courtesy of Yang Liu
Linear Control Theory (Book Chapter from: Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control)
Papers
Liu, Yang-Yu, Jean-Jacques Slotine, and Albert-László Barabási. "Controllability of complex networks." Nature 473.7346 (2011)
Date: 02-12-2026
Date: 02-12-2026
Quote of the Day
"Enthusiasm is common. Endurance is rare " ― Angela Duckworth
PS2 and continuation of Tuesday ......
Centrality: Centrality helps identify key nodes in a network and understand their influence, aiding decisions and predictions
Synthetic Data and Data Collections (If you are aware of useful resources for time series data, please include them here: DATA 2026)
Date: 02-17-2026
Date: 02-17-2026
Quote of the Day
"Be constantly on the lookout for hype"―David Heckerman
Guest Lecture: Causal discovery from data (Dr. David Heckerman from Amazon)
Heckerthoughts: Chapter 4 provides a step-by-step method for constructing a graphical model from data
Date: 02-19-2026
Date: 02-19-2026
Quote of the Day
"Order and simplification are the first steps toward the mastery of a subject" ― Thomas Mann
Papers
Ronquist S, Patterson G, Muir LA, Lindsly S, Chen H, Brown M, Wicha MS, Bloch A, Brockett R, Rajapakse I. "Algorithm for cellular reprogramming." Proceedings of the National Academy of Sciences. 2017 Nov 7;114(45):11832-7. Data-guided Control (DGC) Supporting Information and Slides from Scott Ronquist
GENERAL READING
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.
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