Welcome to the class website for Introduction to Mathematical Biology. Mathematical approaches are playing an increasingly important role in understanding biological systems as technological advances are allowing for increasingly more quantitative measurements to be made. This class will focus on mathematical techniques for modeling, analysis, and simulation useful for investigating biological phenomena. Topics covered in the class will include the dynamics of motor proteins, developmental mechanisms responsible for pattern formation, motility of microorganisms, biochemical reaction networks responsible for cell regulation, and basic mechanisms involved in signal propagation in neural tissues. As prerequisites for the course, a familiarity with ordinary and partial differential equations along with a basic knowledge of linear algebra would be helpful. Some background on these mathematical topics will be developed in the course.
Selection of Topics
- Introduction to Molecular Biology
- Molecular Motor Proteins
- Gene Regulatory Networks
- Pattern Formation
- Motility of Microorganisms
- Hodgkin-Huxley Action Potential Model for Neuronal Signaling
- Linearized Stability Analysis
- Stochastic Differential Equations
- Modeling with Discrete Recurrence Equations, Ordinary Differential Equations, Partial Difference Equations.
Grading:
The grade for the class will be based on the homework assignments and projects.
Supplemental Class Notes:
GNU Octave Software and Documentation
Octave Software (Binaries from SourceForge.net)
GNU Octave Links (Tutorials and other Information)
Ubuntu (Linux Operating System) [May be useful to install dual-boot for running Octave]
Matlab Software and Documentation
Class Annoucements:
- The class on Tuesday, May 25th is canceled. For your interest, here is a paper offering some perspectives on the topics discussed in recent lectures [PDF] Δ.
Homework Assignments:
Turn all homeworks into the graders mailbox (TBA) in South Hall 6th Floor by 5pm on the due date. Graded homeworks will be returned in class.
HW1: (Due Tue, April 13) Develop a matlab code to perform bifurcation analysis of the logistic map discussed in lecture. Plot a bifurcation diagram of the logistic map as r is varied. Sample matlab program to help get you started: runLogistic1.m Δ.
HW2: (Problems given in lecture.)
HW3: (Problems given in lecture.)
HW4: (Problems given in lecture.)
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