A few years ago Mike Steel wrote a wonderful whimsical short story “My friend and I catch a bus“. It describes a conversation between the narrator (a biologist?) and a friend (a probabilist?) as they take a bus to the movies.
Along the way the narrator learns some statistics: Bayes rule, expectation (of the exponential distribution) and the Poisson distribution. The latter comes up in response to a question about the probability that we are alone in the universe.
The “solution” is as follows: suppose that the probability that life evolves on any given planet is some tiny number p, and that there are a huge number N of planets in the universe. The probability that life evolved on k planets is then approximately
based on the Poisson approximation to the binomial distribution. The question of interest is equivalent to asking for the probability that given that . Assuming that (why? well, why not!?) the answer is
At UC Berkeley, the mathematicians and biologists have decided, proverbially, to catch a bus together. In 2008 then deans Mark Richards of natural sciences and Mark Schlissel of biological sciences took the bold step of forming a committee, which I chaired, charged with investigating the possibility of revamping the math education of biology majors. The goal was not blind reform but rather a plan for training that would prepare students for upper division biology courses with more math and statistics.
The initial vision became reality and the result is a new two semester 1st year math course for biology majors with the title “Methods in Mathematics: Calculus, Statistics and Combinatorics” (course number Math 10). I started working on the course in 2008 and in 2010–2011 spent the year working with graduate students and faculty to develop content (syllabus, notes, exercises, exams). I taught a pilot of the course to 50 students in 2011–2012, which expanded to 150 students in 2012–2013. This year the course is officially listed as satisfying the math requirement for Molecular & Cell Biology and Integrative Biology majors (update 2015: the course is now required for MCB and IB majors).
Next week our semester begins and I’ll be teaching Math 10 to more than 250 incoming students. Math 1, which is the standard 1st year calculus course is an option for students as well (although that may be discontinued in the future). To accommodate the new course requirements Integrative Biology has increased its math requirement from one to two semesters, and hopefully other biology departments will follow suit.
The course covers topics from three different areas:
- calculus: the language of change.
- discrete mathematics: the art of counting.
- probability theory and statistics: the science of data analysis.
The premise of the course is that these topics are essential for describing and understanding biological systems, and for working with biological data. We are not alone in this belief. Recent reports and recommendations from institutions such as the HHMI and AAMC all suggest that undergraduate institutions rethink math education of biology students. In particular, they emphasize the point that there is much more for students to learn than just calculus.
Ideally a course covering the topics in Math 10 would be 2 years long, but this is impossible given the constraints of biology majors, who are already overburdened with course requirements. Instead, Math 10 integrates these topics so that they complement and reinforce each other. For example, integration is used to obtain cumulative distribution functions from probability density functions. Similarly, combinatorial concepts are introduced in the context of their statistical applications. The syllabus for my Fall 2013 class is posted on the Math 10a class website.
In an era where education debates are dominated by technology issues, its easy to forget the basics: biology students are better off learning more math, statistics and computer science, and academics in those fields are better off teaching them.