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).
A brief course in Fourier analysis may be helpful if one is going into crystallography.
It can be really difficult to decide what students NEED versus what students would find USEFUL. Some things are fairly standard - calculus and statistics for instance.
Linear algebra is a sort of grey area. On the one hand, the material is useful (who doesn't like solving systems of linear equations!), but rather I felt that the course could have been taught in two weeks, rather than a whole semester - I wasted my time taking the course.
Programming should almost be a necessity for science majors now. Its become such a ubiquitous method of study and research that it really should be a 1st or 2nd year req. But please don't teach them java...
Lol, just as somebody said it, one of my country's private university is teaching her biotechnology students Java Programming... =P
I'm currently at the pre-university level. My Maths lecturer has told me that life science courses will use very in depth statistics. =) So I urge those following the British GCE A-level, take up Further Mathematics (if your have room for subjects), choosing Statistics units as your option.
Wonderful information! As a biology student moving forward with my undergraduate studies, I found this very useful. I'm finished up with calculus 1 & 2, but had not considered linear algebra. I will do so now.
Anyway, I was already planning on taking a programming course next winter and should probably retake statistics...it has been many years. Phew.
Thanks and keep up the great posts. (I'm an avid reader, but until now I've never been a "commenter.")
I think bio undergrads should take two semesters of statistics, not just one.
My one semester of college stats was similar to RPM's: it covered the basics of hypothesis testing, including the major distributions and tests (normal, t-test, chi-square, ANOVA, regression, etc). However, I think it would have been very useful to add a second semester that spent more time on intermediate level topics. Keith Robinson mentioned designe of experiments and Bayesian stats. To those, I would add things like confidence intervals, power calculations, post-hoc testing, dealing with unbalanced designs, etc.
Some of these things are no doubt covered in 1st semester college stats at some schools. But in my experience, there are so many stat topics that are relevant to a biologist that one semester just isn't enough to cover them all adequately.
And, I should note, I don't even work in an especially stat-heavy area of biology.
This post has completely inspired me.
so far you've got 12 credits of math, 3 of stats and 3 of programming... that's 18credits -- which, in todays universe (universities?) counts as a minor.
it is simply not possible. college degrees should be ca. 120 credits (in the semester system) -- of which 30, or so, are general education credits. and i think the current trend of 10-12 credits of electives may just be too few.
1. save statistics/experimental design for grad school.
2. continue to take 2 semesters of calc
(it is excellent training in a cognitive process and work ethic)
3. take a good course in logic and/or philosophy
(which would double-count for a humanities/gen ed course).
I was encouraged to take a programming class by one of my Chem professors, and so I did - intro to programming 101 or something, and it was AWFUL! It was a Java class, I barely got a C - the guy had to curve a class of twelve of us, and I can't do much besides write some overwhelmingly basic codes, and have no understanding of the underlying rules or theory, so I'm stuck. Maybe it was the teacher, maybe it was me, I dunno - but I'd been thinking of minoring in CP so as to be prepared for bioinformatics etc, and it totally turned me off to any CP classes - I think I'll stick to For Dummies type literature from now on.
Also, my university only requires Bio majors to take Calculus 1, no statistics classes at all. I might take a statistics class now. Thanks
Somehow physicists are able to incorporate a lot of math into undergraduate curricula without skimping on the actual physics. Here is what Cornell tells its potential applicants to the PhD program:
"You are expected to know ordinary and partial differential equations, vector calculus, Fourier analysis, and linear algebra, and familiarity with computing and topics in mathematical physics is highly desirable. "
Biologists need to figure out how to work in much more math into the curriculum. Past generations of biologists-in-training could get by without knowing how to analyze their own microarray data, understand how BLAST works, or evaluate the results of a gene prediction program. But today, in my opinion, an undergrad who skips out on some serious stats and linear algebra is going to be at a disadvantage.
Until undergrad biology curricula modernize and start requiring more math, students thinking of grad school should take a look at courses, books, and papers that deal with some of the most interesting stuff in current biology to get an idea of what math is used, such as this course and this course.
I'm a Microbiology and Immunology major doing a minor in Math. I will have ended up taking four calculus courses, two linear algebra courses, an ODE course, a geometry course, a nonlinear dynamics course, a probability course, and a statistics course. It's a good base in mathematics, although I would have liked to see some logic, number theory, and analysis.
The thing is, the statistics course was purely theoretical. It had probability theory as its prerequisite, and started from first principles, working up to things like likelihood ratio testing and linear regression. We never even covered ANOVA - it's a whole separate course. However, I feel like I learned more about statistics than anyone could have in one of those here's-how-it-works-don't-ask-why introductory courses. Most people who take them probably don't even know, deep down, what a statistic is! I realize that for most publishing intents and purposes, you don't really need to know, but there's something about understanding what's going on at the lowest level that appeals more to the biologist in me than anything else. Being the young idealist that I am, I think that attitude will, in the end, result in sounder science. Don't you?
Wow, something was in the air today; I wrote a similar post on the topic at GNXP dot com (afraid to provide a link lest this comment be banished to pur-queue-tory... ok, that was bad).
Do what Andrew's doing: just double-major in math / applied math. For a BA in Math at most places, you only need 6 classes after calc & linear algebra. It's a puny investment that will pay handsomely as the years go on -- the science region of academia is temporally heterogeneous in what math it selects for. You might as well hedge your bets.
In sum, kill as many math courses as you can, and let God sort 'em all out when you're in grad school and beyond.
also, re: math, if you take the courses suggested above, don't dump what you've learned cuz you think it is going to be useless. i took all the courses that rich mentions, but after i was done i pretty much data dumped because i was focused on learning enzymatic pathways and shit and you didn't need much math for that (some kinetics used super simple diff eqs and what not, but nothing that was real math). of course later on i got real bored of that crap, and now i need to dig up all my linear algebra texts and re-familiarize myself with identity matrices and all that....
Not my game, but I will play anyway ... to reinforce what Mike said about going to Cornell. My best friend in college tailored his math (and other) classes to match the admissions requirements of SIO, because that is where he wanted to go to get his PhD. He had to go well beyond the minimum for a biology major (at a top state R1) to keep them happy.
The key course for him was differential equations, because of his interest in dynamical problems. You may not use it on a daily basis, but it will help you understand those simple growth curves and how they change in coupled ODE system.
I always tell bio majors to look at what their top choices for grad school want them to know. As others mentioned above, the time for taking math is early in your career.