"Mathematics is biology's next microscope, only better; Biology is mathematics' next physics, only better." --Joel E. Cohen

"All models are wrong, but some are useful." --George E. P. Box

We will begin with some classical models such as the logistic and predator-prey models for population growth and the SIR model in epidemiology. Most of the class will be spent learning about a relatively new but widely popular trend of discrete modeling. In particular, the field of mathematical biology has been transformed over the past 15 years by researchers using novel tools from discrete mathematics and computational algebra to tackle old and new problems. These ideas have impacted a wide range of topics such as gene regulatory networks, RNA folding, genomics, infectious disease modeling, phylogenetics, and ecology networks and food-webs. In some cases they have even spawned completely new research areas. This is approach is arguably more accessible and appealing to many scientists and engineers, encouraging cross-disciplinary communication and collaborations.

- Course Syllabus
- Matlab files for HW 2, 3, and 4
- If smallpox strikes Portland C.L. Barrett,
S.G. Eubank, J.P. Smith.
*Scientific American*, Vol. 292 (2005), pp. 54-61. - 2-minute video on gene expression
- Discrete Visualizer of Dynamics (DVD) tool for multi-state discrete models of biological networks.
- Sage: free open-source mathematics software. Homepage | Sage Notebook home | Clemson Sage Notebook server
- Sage worksheet:
*lac*operon Boolean network model - Michaelis-Menten kinetics
- The Circada's Love Affair with Prime Numbers, from the
*New Yorker*. - NetLogo, a multi-agent programmable modeling environment.
- RabbitsGrass.nlogo file for Chapter 5 exercises.
- RabbitsGrass-GA.nlogo file for Chapter 5 exercises.
- The CpG Educate suite
- Final project ideas.

Homework 2: pdf | tex. Due Tuesday, January 29nd.

Homework 3: pdf | tex. Due Tuesday, February 5th.

Homework 4: pdf | tex. Due Tuesday, February 12th.

Homework 5: pdf | tex. Due Tuesday, February 19th.

Homework 6: pdf | tex. Due Tuesday, February 26th.

Homework 7: pdf | tex. Due Tuesday, March 5th.

Homework 8: pdf | tex. Due Thursday, March 14th.

1. Introduction to modeling. 4 pages. Updated Jan 22, 2013.

2. Difference equations. 4 pages. Updated Jan 22, 2013.

3. Analyzing nonlinear models . 4 pages. Updated Jan 22, 2013.

4. Models of structured populations. 4 pages. Updated Jan 29, 2013.

5. Nonlinear models of interacting populations. 5 pages. Updated Jan 31, 2013.

6. Infectious disease modeling. 7 pages. Updated Feb 6, 2013.

7. Modeling biochemical reactions. 5 pages. Updated Feb 27, 2013.

1.

A. The

B. A Boolean network model of the

C. Using Gröbner bases to find fixed points. 7 pages. Updated Feb 19, 2013.

D. Bi-stability and a differential equation model of the

E. Boolean models of bistable systems. 6 pages. Updated Mar 5, 2013.

F. Finite dynamical systems and computational algebra preliminaries. 9 pages. Updated Mar 15, 2013.

G. Reverse engineering of polynomial dynamical systems. 7 pages. Updated Apr 1, 2013.