# 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:

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.