MCB111: Mathematics in Biology (Spring 2018)

Instructors: Dr. Elena Rivas office hours: Fri 10-11, Thurs 14-16, Biolabs 1009A
  Pu Zheng office hours: Wed 17-18, Biolabs 2062
Lectures: Mon/Wed 10-11:30 Biolabs 2062
Section: Fri 14-15:30 Biolabs 1058
Homework: Due Monday after posted 10:00  


This course is meant for biologists who want to learn mathematical principles relevant to current biological research. About half of the course covers topics on information theory, inference, statistics, and probabilistic modeling. The second half of the course covers dynamical systems in biology, including random walks, feedback control, and molecular population dynamics.

Each week-long unit is devoted to one specific topic, and is based in one or more scientific papers selected from the recent literature. Each unit includes a set of lectures (available online), a practical session, and a homework. The practical session follows a flipped-class model in which students work in the classroom implementing the methods described in the lecture.

Aims and objectives

I will show you how to be critical with your data; and how to run the right control experiments. This course covers some of the mathematical tools to do that. I will use plain language as much as possible without losing mathematical rigor. I want to get across to you that you should not use statistical tests for which you do not understand the assumptions (and they all have them!), nor treat math as a black box. And if your calculus fails you and cannot find an analytic expression, then you can solve a problem numerically.

I also would like to show you that doing simple scripting is easy, and that in doing so, you can stop making assumptions about how simple models work, and instead see how they work. The course has an important emphasis on computational work. Computer literacy is fundamental for experimental biologists. You are expected to know some basics of one computer language of choice (Matlab, Python, Perl, or others), but you are not expected to be an expert on any one of them. By the end of the course, hopefully you will be confident launching into your own computational approaches to data collection, data analysis, and model testing.

There. Let’s get started!

Prerequisites and background

If you are a Molecular, Cells and Organisms (MCO) graduate student taking the course, you will be instructed to take a minicourse in mathematics in early January, followed by a qualifying exam. Otherwise, you would need a taste for mathematics applied to biology, and an interests (and hopefully a bit of previous experience) in coding.

We expect to have most students coding in Matlab, because it seems to be the default language that biologist feel they must learn (not sure why), but if you know python or want to use this course as an excuse to learn python, you are encouraged to do so. That is what I plan to do, although my default scripting tool is perl.

Policies, expectations, grading

There will be one homework per week, and one final exam (open book). Grade will be based on homework (60%), final exam (30%), and participation (10%).


The following materials are for reference. You are not expected to get them all, not even one of them. The class notes should contain all materials covered in this course; and specific reading materials will be proposed with each topic. The books will for you on reserve in the Cabot library so you can look at them. One of the books (MacKay’s–one of the most insightful books ever, but not super easy to read) is free online.

For the first half of the course, I will use materials from these books:

``Data Analysis. A Bayesian Tutorial’’, D. S. Sivia J. Skilling, Oxford University Press, 2005.

``Introduction to Probability”, J. K. Blitzstein and J. Hwang, CRC Press, 2014.

``Information Theory, Inference, and Learning Algorithms’’, D. J. C. MacKay, Cambridge University Press, 2003. (A pdf of Mackay’s book is available online here).

``The Cartoon Guide to Statistics’’, L. Gonick and W. Smith, Harper Perennial, 1993.

``Statistical Distributions’’, 3rd edition, M Evans, N. Hastings, and B. Peacock, Wiley Interscience, 2000.

``Probability Theory. The Logic of Science’’, E. T. Jaynes, Cambridge University Press, 2003.

For the second half of the course, I will use materials mostly from these books:

``Physical Models of Living Systems’’, P. Nelson, W. H. Freeman and Company, 2015.

``Random Walks in Biology’’, H. C. Berg, Princeton University Press, 1993.

These days any mathematical results can be found online. Still, if you want an old fashion approach, I have always found this Schaum manual very useful,

``Mathematical handbook of formulas and tables’’, 4th edition, M. R. Spiegel and S. Lipschutz and J. Liu, McGraw-Hill, 2013.

It is cheap, and it includes most of the mathematical expressions I need on a day-to-day basis for integrals, series, special functions, etc. And you can also find the pdf of the whole book online (here).

Academic integrity

You must do each week’s project individually, on your own, rather than working collaboratively in groups. Your writing and your code must be your original work.

Meanwhile, you are free to talk with each other, and to consult any resource, and to study code from other sources.

Accommodations for students with disabilities

Students needing accommodations because of a disability should present their Faculty Letter from the Accessible Education Office (AEO) and speak with an instructor by the end of the second week of the term for us to be able to respond in a timely manner.