1. Course Information:
Description:
Introductory survey of applied mathematics with emphasis on modeling of physical and biological problems in terms of differential equations. Formulation, solution, and interpretation of the results.
System of interest: Complex Systems (or this webpage by Sante Fe), which includes most systems in real life
Math Used: Algebra, Calculus, Linear Algebra, Differential Equations (+dynamical systems), and Probability
Modeling Philosophy: There are fundamentally two kinds.
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- "Mechanistic" modeling (gives the phenomena a mechanistic cause), e.g. Newton's Classical Mechanics
- Data-driven modeling (uses data to represent the phenomena mathematically), e.g. Kepler's law
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We will be focusing on the first type.
General Information:
Instructor: Ying-Jen Yang
Email: yangyj@uw.edu
Lectures: T Th 2:30-3:50 at OTB 014 (the original scheduled GLD 322 is having a heating issue)
Lectures will be streamed and recorded on Zoom as well https://washington.zoom.us/j/94782254732
Office Hours: WF 2-3 pm (go to Zoom tab)
TA: Saba Heravi
TA's Office Hours: Th 6-8 pm (go to Zoom tab)
2. Course Material:
Textbook and References:
- Lecture note will be provided.
- (Suggested) Topics in Mathematical Modeling, by K.K. Tung, Princeton University Press
Ebook available at UW library:
Click on the Online access>
Then click on JSTOR ebooks purchased
Here you will be on publisher's webpage, and you will see downloadable .pdf for each and every chapter of the text book.
Many exercises are directly from the book or modified from there.
- (Suggested) Nonlinear Dynamics and Chaos, by Steven H. Strogatz, 2nd ed.
Ebook available at UW library: Click on Online Access
Many exercises are directly from the book or modified from there.
- (Optional) Mathematical Biology I: An Introduction, by J. D. Murray, 3rd ed.
- (Optional) More paper to come
Outline (Tentative):
Week 1 (1/03-1/07): Introduction of mathematical modeling and Kepler's law as an example
Week 2 (1/10-1/14): Formulating ODE and Numerical Method for ODE
Week 3 (1/17-1/21): Concepts of Invariant, Stability Analysis, and Bifurcation
Week 4 (1/24-1/28): 1-D Bifurcation
Week 5 (1/31-2/04): 2-D Systems and Interactions
Week 6 (2/07-2/11): Multi-Stability and Coexistence
Week 7 (2/14-2/18): Oscillation
Week 8 (2/21-2/25): Special Types of Dynamics: Reversible, Conservative, Dissipative,...etc
Week 9 (2/28-3/04): Intro to Stochastic Processes and Markov Chain
Week 10 (3/7-3/11): Stochastic Thermodynamics of Markov chains
From week 7-10, some lectures may have quest speakers, or become a work-in-class day for students to work on their projects.
3. Assignments and Grade
Join Piazza by this link to ask questions about homework and term project.
Homework:
General: Homework is assigned weekly. Homework will be posted on Friday and due at 9 pm on the Friday next week. You must submit your scanned or typed-up homework PDF file to Gradescope. Remember to label your work with corresponding questions. No late homework is allowed. If for some reasons that you need extension, please email the instructor.
Format: Submitted files must be portrait, letter-size, and easy-to-read. LaTeXing (or use LyX) is highly encouraged. You must present all your work to justify how you got those answers. If you didn't show your work, you will get a 0.
Discussion: You are encouraged to talk to your classmate, discuss questions on Piazza and check answers with each other. However, your work should base on your own words. If you didn't show any work or were caught copying people's work (it's fairly obvious from a grader point of view), you will receive a 0 on that particular assignment.
Proposal and Term Paper
One of the main learning goal of this course is to have a first taste on how to do a theoretical/mathematical research. You will form a group of 2-4 people and study one topic that interests all of the group members. The group would submit
- a proposal on the topic of your final project is due by the end of Week 8
(about 2-5 pages long including some preliminary work; font size 11~12, 1.5 to double spaced text) - a term paper is due by the end of Week 10
(about 10 pages if not including figures and about 15 pages including figures; font size 11~12, 1.5 to double spaced text)
The project can be original or a review from journal papers or book sections. A potential project topic list will be provided but you can (and are encouraged) also come up with your own topic (talk to the instructor either way). A guide on how to write a term paper will also be provided soon. Many of the term papers would turn out to be a critical and careful review of some part of journal papers and/or book sections+some extensions/work of your own. Of course, synthesize the several papers you review on the same topic and present them in one single coherent story. Reproduce and discuss the papers' the assumptions, simplifications, analysis, and their discussion,...etc, how they did it and how to improve.
Grade:
- Six weekly assigned homework for the 2/3 of the quarter
- a term paper proposal with a group (2-4 people)
- a term paper with the same group
Details percentage: (tentative) 65% homework; 10% proposal; 25% term paper.