Example Courses of Study in Mathematical Biology

A) Mathematical Modeling & Dynamical Systems Theory Applied to Biological Systems:

First, please see the “Example Courses of Study in Dynamical Systems” and review the “Applied Emphasis”. Rather than minor in TAM, you will minor in the biological area of interest. Some typical minor fields are:
Neurobiology and Behavior
Ecology and Evolutionary Biology
Micro-Biology
Biochemistry, Molecular & Cell Biology

Modeling and studying biological systems will require an understanding of the mathematical theory, the biology, and the computer methods that enable us to study such complicated systems.

• Year 1 - Fall: Analysis &/or Algebra (Math 433 is strongly recommended here unless you have a strong linear algebra background!), Math 617*, Math 652
• Year 1 - Spring: Biology class, Analysis &/or Algebra, TAM 578
• Year 1 - Summer: Biology Lab/Field Work
• Year 2 - Fall: CS 621, CIS 629, Biology Class
• Year 2 - Spring: CS 624**, CS 622***, Biology Class
• Year 2 - Summer: Biology Lab/Field Work
• Year 3 - Fall: Math 717*, (Math 652)
• Year 3 - Spring: CS 626
• Year 3 - Summer: Research!
  
  CIS 629 – Computational Methods for Nonlinear Systems
  CS 622*** – Numerical Optimization and Nonlinear Algebraic Equations
  CS 626 – Computational Molecular Biology
  * = every two years, ** = even-numbered years, *** = odd-numbered years

  B) Probability and Statistics Applied to Biology

Recently, there has been a tremendous expansion in the use of probability models in mathematics and in a wide variety of applications. This has created a strong demand for researchers trained in probability to develop new methodologies and to work in an interdisciplinary context. Modeling and studying biological systems will require an understanding of the mathematical theory, the biology, and the computer methods that enable us to study such complicated systems.

Some typical minor fields are: Genetics and Development, Ecology and Evolutionary Biology, Molecular & Cell Biology, Statistics and BSCB (Biological Statistics and Computational Biology). The following example is geared towards applications in genetics, evolutionary biology.


• Year 1 - Fall – Stochastic Processes (OR 650 or 523 – more introductory, offered in spring ), Algebra (Math 433 is highly recommended unless you have a strong linear algebra background!), Analysis (Math 413 or 611*) or Measure Theory (Math 621 – this is a great class!), Biology eg. Population Genetics (BioGD 481) or Human Genomics (BioGD 487)
  (If you need undergraduate probability, take Math 471)
• Year 1 - Spring - – Probability (Math 670), Analysis (Math 414) or Applied Functional Analysis (Math 622), Algebra (Math 434 if you haven't done much abstract algebra), Biology eg. BioGD 684 (if you didn't take 481)
• Year 1 - Summer: Start thinking about possible research projects, talk to professors
  
• Year 2 - Fall: Probability (Math 671); Stats (OR 670); Statistical Genomics (BTRY 682) or Biology class (see year 1 fall)
• Year 2 - Spring: Probability (Math 672), Math Stats (Math 472 or 674), BioGD 684 (if you didn't take 481) or BTRY 694 or BTRY 726
• Year 2 - Summer: Start doing some research
  
• Year 3 - Fall: Matrix Computations (CS 621), Special Topics in stochastic processes (Math 777) or applied prob/stats (OR 768) Biology class
• Year 3 - Spring: Special Topics in stochastic processes (Math 778) or applied prob/stats (OR 769)
• Year 3 - Summer: Research!

  Note: Most students take 3-4 courses a semester in their first year, then 2 or 3 a semester until they've fulfilled their requirements. If you're also a TA, do not take more than 3 courses a semester!

  * Only take Math 611 if you want a challenge! Note that either Math 621 or 611 will count towards your requirement, but not both.