Math 463 provides an introduction to the use of continuous differential equations in the biological and biomedical sciences. In this course, mathematical models are developed, analyzed and numerically simulated in order to investigate mechanisms underlying specific ecological, cellular and molecular processes. The goals of this course are (1) Critical understanding of the use of a variety of dynamical systems methods in biology and (2) Exposure to computational techniques that are required to study ordinary differential equations that arise in mathematical biology. By the end of this course students are able to derive, interpret, solve, understand, discuss, and critique ordinary differential equation models of biological systems.
Here is what a few former students had to say about their experience:
“Math 463 was a phenomenal, interesting course, and I appreciated how theoretical concepts were always connected back to real-world examples. Your teaching style was very engaging and devising my own models during the final project helped me fully understand how to use mathematical modeling to advance the fields of biophysics and cancer research.” Anna Argento Fall 2018
“I took math 463 as one of my first graduate classes at Michigan. This course increased my confidence in my ability to master aspects of mathematical biology, largely because of Dr.Jackson’s teaching. I reccomend this class to anyone with interest in Computational/mathematical interest in biology as you will surely gain a solid base of knowledge in the field.” Johanna Buschhaus Fall 2018
“I really enjoyed taking your class last year! Being able to use what we learned from you to explore areas of science and math that we were passionate about and interested in made the course one of my favorites that I’ve taken at the university.” Jamieson Hunter Fall 2018
“Your course last semester has been one of my favorite courses that I have taken at the University of Michigan and I attribute a lot of that passion, as well as my success in the class, to your teaching. I really enjoyed learning from you.” Lindsy Ades Fall 2017
Math 563 – Advanced Mathematical Methods of the Biological Sciences
This course focuses on the derivation, analysis, and simulation of partial differential equations (PDEs) that model specific phenomena in molecular, cellular, and population biology. A goal of this course is to understand how the underlying spatial variability in natural systems influences motion and behavior. Mathematical topics covered include derivation of relevant PDEs from first principles; reduction of PDEs to ODEs under steady state, quasi-steady state, and traveling wave assumptions; analytical and numerical solution techniques for PDEs and concepts of spatial stability and instability. These concepts will be introduced within the setting of classical and current problems in the biological and the biomedical sciences such as cell motion, transport of biological substances, tumor growth, invasion, epidemiology and biological pattern formation. Above all, this course aims to enhance the interdisciplinary training of advanced undergraduate and graduate students from mathematics and other disciplines by introducing fundamental properties of partial differential equations in the context of interesting biological phenomena.