Math 1380: Mathematical Biology

Winter Semester 2012 (2124), Dr. Rubin

General Class Information

• Class Meetings: TuTh 4:00-5:15 PM, 525 Thackeray Hall
• Text: Mathematical Models in Biology by Elizabeth S. Allman and John A. Rhodes (ISBN-10 0-521-52586-1). Matlab files mentioned in the book can be accessed using the Resources tab toward the bottom of the Cambridge University Press website for the book.
• Office Hours: M 1-2 PM, F 10:30-11:30 AM and by appointment
• Grader: Baoluo Wang, MAC hours M 9-11 AM, W 9-11 AM, F 9-10 AM
• FINAL EXAM: Saturday, April 28th, 4:00-5:15 PM, 525 Thackeray

Full Syllabus

Agenda/Homework Problems

Below are the schedule of sections from Allman and Rhodes and other topics to be covered, along with links to the handout for the week and homework solutions.

• Weeks 1-2: Th 1/5 - Th 1/12 = start Chapter 1 - Dynamic Modeling with Difference Equations: The Malthusian Model (1.1); Nonlinear Models (1.2). Lab 1, started in class on 1/10, due in class on 1/12. Solutions to Lab 1. Relating to example number 6 on the cobwebbing handout, here is the Rulkov map paper. As done in class, we have the recurrence relation handout and the cobwebbing handout.
• Weeks 3-4: Tu 1/17 - Tu 1/24 = Analyzing Nonlinear Models (1.3); Variations on the Logistic Model (1.4) as well as outside material on sensitivity analysis, chaos, and least squares fitting. We will meet in GSCC 126 on Tuesday 1/24 for Lab 2, which is due on Thursday 1/26. Also, Project 1 will be due on Thursday 1/26 as well! Lab 2 solutions. Weeks 3-4 homework solution.
• Weeks 4-5: Th 1/26 - Tu 1/31 = Linear Models of Structured Populations (2.1-2.3). Weeks 4-5 homework solution. Papers relating to 1-D dynamics, period 3 orbits, and Sharkovsky's theorem: Li and Yorke, 1975: note the misleading title! Du, 2007: a short paper with a proof of Sharkovsky that I like. Blaya and Lopez, 2006: the introduction gives some history and an interesting example with "invisible" chaos - it has the right orbits to fit the definition of chaos but the chaos only occurs on a set of measure zero (i.e., undetectably!). Ingram and Mahavier, 2004: interesting and possibly accessible but long - you might glance at the pictures to see some interesting things 1-d maps can generate, related to chaos.
• Weeks 5-6: Th 2/2 - Tu 2/7 = Nonlinear Models of Interactions (3.1-3.3). Weeks 5-6 homework solution. Lab 3 will take place in class on Tuesday, Feb. 7th and is due in class on Thursday, Feb. 9th. Project 2 is due on Thursday, Feb. 16th. Reynolds et al., 2006 is a paper with ordinary differential equation models related to the topic of Project 2.
• Weeks 6-7: Th 2/9 - Tu 2/14 = Modeling Molecular Evolution (4.1-4.3). Ancestral mare paper by Achilli et al.
• Weeks 7-9: Th 2/16 - Th 3/8 = Matrix Models of Base Substitution (4.4), Phylogenetic Distances (4.5) -- Solutions to homework from 4.4 and 4.5. Also, we will discuss absorbing Markov chains, which are the Lab 4 topic, with a Tuesday, Feb. 28th due date. Lab 4 solutions. Our MIDTERM EXAM will take place in class on Thursday, March 1st. There is no class on March 6th and March 8th due to Spring Break.
• Weeks 10-11: Tu 3/13 - Th 3/22 = Conservation Equations; Convection, Attraction, and Diffusion. We will meet in GSCC 126 to work on Lab 5 on Tuesday, March 20th. The lab is due in class on Thursday, March 22nd. Be sure to refer to notes on diffusion and standard deviation to help complete the lab. Also, Project 3 is due in class on Thursday, March 29th. Solutions to Weeks 10-11 homework.
• Week 12: Tu 3/27 - Th 3/29 = More on Convection, Attraction, and Diffusion; Chemotaxis; Steady State Solutions. Lauffenberger et al., 1981 paper on bacterial population dynamics with steady state solutions discussed in class. Week 12 homework solutions.
• Week 13: Tu 4/3 - Th 4/5 = Traveling Waves, Dimensional Analysis. Week 13 homework solutions.
• Weeks 14-15: Tu 4/10 - Th 4/19 = Dimensional Analysis, Morphogenesis. Homework problem listing from Chapter 11 of EK book (see handout for which ones are actually assigned). Relevant pages from EK Chapter 11 for homework. EK conditions for diffusive instability for homework and final. Lauffenberger and Kennedy, 1983 paper for homework assignment.

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