Topics in Mathematical Biology

General Information

Lecture Time: WF 1:00PM - 2:15PM
Classroom: Vincent Hall 311

Instructor: Duane Nykamp
Office: 202 Vincent Hall
E-mail: nykamp@math.umn.edu
Phone: 625-0338
Office hours: MW 2:00PM-3:30PM, or by appointment

See the course description for an overview of topics covered in this course.

Grading will be based on homework assignments and a final project.  Sorry, there will be no tests or final exam.

Homework

Homework will be assigned periodically throughout the course.  I encourage even auditors of the course to attempt the homework as it will help solidify the concepts discussed in lecture.

The homework will include small computing assignments.  It can be done in whatever software you choose. The textbook includes simple Matlab programs that could be useful.

Some of the assignments will be most easily done using phase plane software such as XPP.  XPP is especially nice for its incorporation of AUTO, a bifurcation analysis program.  However, XPP requires either Unix/Linux or an X-Windows client running on top of Microsoft windows. XPP is installed on the math Linux computers and can be run via the command
xppaut
A tutorial for XPP can be found here.

Here is an XPP file demonstrating two coupled integrate-and-fire neurons.

Textbook/References

For parts of the course, we will draw on Spikes, decisions, and actions by Hugh R. Wilson. Note: This textbook is out of print. It can also be downloaded from the author's web page.

Books

• Steven H. Strogatz. Nonlinear Dynamics and Chaos. Perseus Books, Reading, MA, 1984.
  
  This book is a good introduction to the mathematical tools we will use for much of this course.
  
  
• Christof Koch and Idan Segev, editors. Methods in Neuronal Modeling: From Ions to Networks. MIT Press, Cambridge, MA, second edition, 1998.
  
  We'll be discussing selected topics from this book, especially material from chapters 7 and 13.
  
  Chapter 7 is available in interactive form on the web. If you are technically savy, you can set up XPP to open up the example files, or even ftp the source and run it locally.
  
  
• Daniel Johnston and Sameul Wu. Foundations of Cellular Neurophysiology. MIT Press, Cambridge, MA, 1995.
  
  This book provides derivations for elements of the base model used at the beginning of the course.

Research Papers