A) Mathematical Modeling & Dynamical Systems Theory Applied to Biological Systems:
First, please see the example of courses 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 4330 is strongly recommended here unless you have a strong linear algebra background!), Math 6170*, Math 6520
- Year 1 - Spring: Biology class, Analysis &/or Algebra, TAM 5780
- Year 1 - Summer: Biology Lab/Field Work
- Year 2 - Fall: CS 6210, CIS 6229, Biology Class
- Year 2 - Spring: CS 6240**, CS 6220***, Biology Class
- Year 2 - Summer: Biology Lab/Field Work
- Year 3 - Fall: Math 7170*, (Math 6520)
- Year 3 - Spring: CS 6510
- Year 3 - Summer: Research!
- CIS 6290 – Computational Methods for Nonlinear Systems
- CS 6220*** – Numerical Optimization and Nonlinear Algebraic Equations
- CS 6570– 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 6500 or 5510– more introductory, offered in spring ), Algebra (Math 4330 is highly recommended unless you have a strong linear algebra background!), Analysis (Math 4130 or 6110*) or Measure Theory (Math 6210 – this is a great class!), Biology eg. Population Genetics (BioGD 4810) or Human Genomics (BioGD 4870)
- (If you need undergraduate probability, take Math 4710)
- Year 1 - Spring - – Probability (Math 6720), Analysis (Math 4140) or Applied Functional Analysis (Math 6220), Algebra (Math 4340 if you haven't done much abstract algebra), Biology eg. BioGD 684 (if you didn't take 4810)
- Year 1 - Summer: Start thinking about possible research projects, talk to professors
- Year 2 - Fall: Probability (Math 6710); Stats (OR 6700); Statistical Genomics (BTRY 6820) or Biology class (see year 1 fall)
- Year 2 - Spring: Probability (Math 6720), Math Stats (Math 4720 or 6740), BioGD 684 (if you didn't take 4810) or BTRY 6940
- Year 2 - Summer: Start doing some research
- Year 3 - Fall: Matrix Computations (CS 6210), Special Topics in stochastic processes (Math 7770) or applied prob/stats (OR 7590) Biology class
- Year 3 - Spring: Special Topics in stochastic processes (Math 7780) or applied prob/stats (OR 7591)
- 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 6110 if you want a challenge! Note that either Math 6210 or 6110 will count towards your requirement, but not both.