Keith Robison, at Omics! Omics!, asks and answers the question, “What math courses should a biologist take in college?” His answer: a good statistics course is a must (one where you learn about experimental design and Bayesian statistics), and a survey course that covers topics like graph theory and matrix math would provide a nice introduction to important topics (that course probably doesn’t exist at most colleges). He also advocates taking a programming class and turning math education into something more stimulating rather than rote drilling (easier said than done).
This being a blog, I, obviously, have an opinion. While I can’t say what math courses are best for all biologists, I can suggest which ones are very helpful for a quantitative biologist/geneticist, if not essential. I’ll do so by first describing my math education, and then saying what I would have changed. When I arrived at college, I found that I had completed the math requirement for my biology major by taking two semesters of calculus in high school – my college required either take semester of calculus or one semester of calculus plus a semester of statistics for the major. As an incoming freshman being told that I didn’t have to take any more math, I was ecstatic. My academic advisor at the time was a faculty member in the religious studies department, and he didn’t know any better to suggest I take any more math classes (one of the detriments of a liberal arts education, I guess).
What I should have done was take linear algebra during my freshman year, but I didn’t realize that until a couple of years later. I wanted to be a geneticist (at that point I didn’t even know what population genetics was, let alone that I would be interested in it), and I thought math wouldn’t be all that important. I did end up taking two math courses later on in my undergrad career — one in introductory statistics and one in dynamic modeling — but, by the time I realized that I should have taken linear algebra, it was too late. It had been a few years since my calculus class, and I knew it would be damn near impossible for me to jump right back into a real math class.
I was exposed to eigenvectors and eigenvalues for the first time in the dynamic modeling course. The professor assumed we understood those concepts, so I had to visit with the TA to have him explain them to me. I wasn’t required to understand how eigenvectors and eigenvalues are calculated, only how to interpret them in terms of transition matrices and how to get Matlab to calculate them for me. It was at that point that I realized how valuable a course in linear algebra would have been. Since then, I have encountered various aspects of matrix math and continually lament not enrolling in at least one more semester of math upon arriving at college.
I agree with Keith that a statistics course is essential for any undergrad biology major. My undergrad statistics course was taught through a biostats department, and I had a better experience than Keith did in his stats course with business majors. The course covered all the basics of hypothesis testing, including the major distributions and tests (normal, t-test, chi-square, ANOVA, regression, etc). This course was, in my opinion, the ideal introductory statistics course. For someone interested in quantitative genetics, I would also recommend a course in probability theory. As a grad student, I took a course in which we started with first principles and derived all the major distributions. While this course wasn’t as practical as my undergrad statistics course, it was extremely useful for developing an understanding of how the statistical tests work and where they come from.
With all that said, here is the mathematical coursework I would recommend for anyone interested in quantitative genetics. I generally agree with Keith, although my list draws upon courses that I have seen offered at universities.
- Three to four semesters of the university’s calculus sequence — calculus 1 & 2, plus linear algebra and maybe differential equations.
- An introductory statistics course and possibly a course on probability theory. Ideally, the intro statistics course would also teach students how to use R, rather than use MiniTab.
- At least one programming course. Yes, I realize that this isn’t math per se, but Keith included it in his post, so I’m including it in mine. Ideally, the student would take two courses. The first course would teach programming in C, C++, Java, Python, or an equivalent language. The second course would teach scripting such as PERL for various applications (this type of course is already offered under the guise of a bioinformatics course at some universities).