MCB111: Mathematics in Biology (Fall 2022)

 Instructors: Dr. Elena Rivas Student drop-off hours: Tues 10:30-12:30/Northwest#430 Thur 10:00-11:45/Northwest#430 Nicolas Gort Freitas Mon 13:00-14:30 Wed 13:00-14:30 Biolabs 1087 Tianzhu Xiong Wed 15:00-16:30 Biolabs 1087 Thrs 17:00-18:00 Lectures: Mon/Wed 10:30-11:45 Biolabs 1080 Section: Fri 10:30-11:45 Biolabs 1080 Homework: Due Friday of following week at 9:00 Canvas: link Piazza: link

Description

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

This is a required course for graduate students in Molecular, Cells and Organisms (MCO) graduate program. The course is also available to interested undergraduates. This is not a formal course in Math, but some background and interest in calculus, algebra and stats are necesary. This is not a formal biology course, but also some interest and basic background in molecular biology is also important.

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%).

Materials

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).