Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 227: Mathematical Biology
Approved: 2009-03-01, Alexander Mogilner

Units/Lecture:

Fall, alternate years; 4 units; lecture/term paper or discussion

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Instructor's notes + reading material (see below)

Prerequisites:

Graduate standing or consent of instructor

Course Description:

Nonlinear ordinary and partial differential equations and stochastic processes of cell and molecular biology. Scaling, qualitative, and numerical analysis of mathematical models. Applications to nerve impulse, chemotaxis, muscle contraction, and morphogenesis.

Suggested Schedule:

Department Syllabus

Lectures Sections Topics/Comments
1-2 How mathematical models in biology are developed, analyzed and used
3-4 Scaling and non-dimensionalization
5-6 Nonlinear ordinary differential equations Stable steady states and "bottlenecks" in biology
7 Nonlinear ordinary differential equations Switches in biology
8-9 Nonlinear ordinary differential equations Limit cycles in biology
10-11 Nonlinear ordinary differential equations Coupled oscillators in biology
12 Nonlinear partial differential equations Diffusion in biology
13-14 Nonlinear partial differential equations Reaction-diffusion phenomena in biology
15 Nonlinear partial differential equations Drift-diffusion phenomena in biology
16-17 Nonlinear partial differential equations Pattern formation in biology
18-19 Nonlinear partial differential equations Wave phenomena in biology
20 Probability estimates in biology Example of choice from cell, molecular, neurobiology or ecology
21 Stochastic processes: direct Monte-Carlo simulations Example of choice from cell, molecular, neurobiology or ecology
22 Stochastic processes: Gillespie algorithm Example of choice from cell, molecular, neurobiology or ecology
23-24 Methods of discrete mathematics in biology Example of choice using Boulean networks, graph theory and topology
25-26 Using software to solve numerically equations of mathematical biology Example of choice from cell, molecular, neurobiology or ecology using Virtual Cell, Matlab tools and other software
27 Review of models from cell, molecular and developmental biology, neuroscience, ecology Examples from current literature of instructor's choice

Additional Notes:

The course is based on 27 lectures.

Suggested reading includes but is not limited to:
  • Edelstein-Keshet, L (1988) Mathematical Models in Biology, Random House, New York, ISBN 0-89871-554-7 ($46)
  • Murray, JD, (1989), Mathematical Biology, Springer-Verlag, New York, ISBN-10: 0387952233 ($75)
  • Nossal, R., and Lecar, H., (1991), Molecular and Cell Biophysics, Addison-Wesley, Redwood City, CA, ISBN-10: 0201195607 ($30)
  • Keener, J., and Sneyd, J., (1998), Mathematical Physiology, Springer-Verlag, New York, ISBN-10: 0387983813 ($70)
  • Fall, C. P., Marland, E., and Wagner, E., Eds (dedicated to the memory of Joel Keizer)(2001), Computational Cell Biology, Springer-Verlag, New York ISBN-10: 0387953698 ($80)
  • Taubes, C. H., Modeling differential equations in biology, Cambridge University Press, ISBN-10: 0521708435 ($50)

Assessment:

There is a final exam, homework, and a research project, and a number of computer exercises. No midterms.