Embedded Files
Instructor: Prof. INDIKA Rajapakse (indikar@umich.edu)
Teaching Assistant: RAM Prakash (nuvi@umich.edu)
Location: 2260 Undergraduate Science Building
Class Time: Tuesday and Thursday, 8:30 AM - 10:00 AM
Office Hours:
Indika R - Tuesday and Thursday , 4:00 PM - 5:00 PM: https://meet.google.com/dnm-zipr-tsb or in person after class
Ram P - Wednesday 3:00 - 4:00 PM Zoom and Friday 3:00 PM - 4:00 PM in person Room 3370, NCRC B520
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) and Course Feedback Form
Challenge Problem! This is from the book by Smale and Hirsch, Differential Equations, Dynamical Systems, and Linear Algebra. If you solve this problem, you are done for the semester. You can easily publish your answer and become famous! If you would like more challenging problems, please see the following paper. Steve Smale: Mathematical problems for the next century.
Simplicity, Rigor, and Magic! and James Simons: My Guiding Principles
References of Interest
Claude Shannon: His famous paper and his thesis
MATLAB: 1) MATLAB Tutorial 2) Basic Functions Reference
Great book with codes: Cleve Moler. Numerical computing with MATLAB. Society for Industrial and Applied Mathematics, (2004), Solutions to Exercises
Digital Library and TwinCell Blueprint: An unofficial digital library I maintain that contains books and papers on topics related to my research and teaching
Jon Kleinberg's Book: Networks, Crowds, and Markets and Albert-László Barabási's Book: Network Science
PROBLEM OF THE DAY
PROBLEM OF THE DAY
POD2 (09-08-2026): Adjacency Matrix and Graph Laplacian
POD3 (09-24-2026): PC1 and Fiedler Vector
PROBLEM SETS
PROBLEM SETS
This section includes assignments, solutions, and helpful resources.
Problem Set 1
Problem Set 2
FINAL Project: Due December 17, 2025 (no extensions!)
NOTES, SLIDES, AND PAPERS
NOTES, SLIDES, AND PAPERS
Date: 09-01-2026
Date: 09-01-2026
Quote of the Day
"Optimism is the faith that leads to achievement. Nothing can be done without hope and confidence" ― Helen Keller
Introduction: Slides
Papers
Turing, Alan Mathison. "The chemical basis of morphogenesis." Philosophical Transactions of the Royal Society B: Biological Sciences, 370(1666), p.20140218. (Classic!)
Rajapakse I. "Conversation with Dr. Steve Smale and Dr. Lee Hartwell." NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 68 (9).
Date: 09-03-2026
Date: 09-03-2026
Quote of the Day
"Ideas only realize their power when people understand them" ― Small Worlds: The Dynamics of Networks between Order and Randomness (Book)
Notes
Networks: (1) Random, (2) Small-world, (3) Scale-free, (4) Ramanujan
Papers
Small World: Watts, Duncan J., and Steven H. Strogatz. "Collective dynamics of ‘small-world’networks." Nature 393.6684 (1998): 440-442.
Scale-free: Barabási, Albert-László, and Réka Albert. "Emergence of scaling in random networks." Science 286, no. 5439 (1999): 509-512.
Small World: Milgram, Stanley. "The small world problem." Psychology today 2, no. 1 (1967): 60-67.
Date: 09-08-2026
Date: 09-08-2026
Quote of the Day
"Nature has a great simplicity and therefore a great beauty" ― Richard Feynman
Notes
Singular Value Decomposition (SVD)! This lecture is in memory of Cleve Moler.
Date: 09-10-2026
Quote of the Day
"Greatness comes from character, and character isn't formed out of smart people. It is formed out of people who have suffered" ― Jensen Huang
Today, we have an in-person visitor from NVIDIA, Dr. Angus Forbes, who will present network visualization methods and NVIDIA tools for digital biology.
Date: 09-15-2026
Date: 09-15-2026
Quote of the Day
"The only way to do great work is to love what you do" ― Steve Jobs
The Extraordinary SVD again: This lecture is in memory of Cleve Moler. During the lecture, we will watch a recording of Cleve.
Singular Value Decomposition (SVD)
Additional Materials from Cleve Moler
Date: 09-17-2026
Date: 09-17-2026
Quote of the Day
"Science and everyday life cannot and should not be separated" ― Rosalind Franklin
SVD again...
Papers
Sweeney P, Chen C, Rajapakse I, Cone R. "Network Dynamics of Hypothalamic Feeding Neurons." Proceedings of the National Academy of Sciences, 118.14 (2021).
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.
Date: 09-22-2026
Date: 09-22-2026
Quote of the Day
"I don't care that they stole my idea . . I care that they don't have any of their own" ― Nikola Tesla
Why Low Rank? Biological Motivations
SVD again... (I would really recommend reading pages 7–22 from time to time!)
Papers
Stankovski, Tomislav, Tiago Pereira, Peter VE McClintock, and Aneta Stefanovska. "Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences." Philosophical transactions. Series A, Mathematical, physical, and engineering sciences 377, no. 2160 (2019): 20190039.
Date: 09-24-2026
Date: 09-24-2026
Quote of the Day
"You never lose a dream, it just incubates as a hobby" ― Larry Page
Papers
Brin, Sergey, and Lawrence Page. "The anatomy of a large-scale hypertextual web search engine." (1998).
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: 2020.
Date: 09-29-2026
Date: 09-29-2026
Quote of the Day
"Innovation distinguishes between a leader and a follower" ― Steve Jobs
Notes
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
Please get familiar with these two papers. They will give you some idea of Network Controllability
Liu, Yang-Yu, Jean-Jacques Slotine, and Albert-László Barabási. "Controllability of complex networks." Nature 473.7346 (2011): 167-173. Slides: Courtesy of Yang Liu
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). Network Controllability and Applications: Slides from Scott Ronquist
GENERAL READING
GENERAL READING
I will add to this list throughout the semester
Strogatz SH. "Exploring complex networks." Nature. 2001 Mar;410(6825):268-76.
Hartwell, Leland H., et al. "From molecular to modular cell biology." Nature 402.6761 (1999): C47-C52.
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