MCB111: Mathematics in Biology (Fall 2024)
 Description
 Aims and objectives
 Prerequisites and background
 Policies, expectations, grading
 Materials
 Academic integrity
 Accommodations for students with disabilities
Instructors:  Dr. Elena Rivas (She/her/hers) (Northwest #430)  Student hours: Tues 10:0011:30, Wed 12:0013:00, Thu 11:0012:00 
Nick Hilgert (He/his/him)  Student hours: Thur 17:0018:30 BL1033  
Lectures:  Mon/Wed 10:3011:45  Biolabs BL1080 
Section:  Fri 10:3011:45  Biolabs BL1080 
Homework:  Due Friday of following week at 9:00  
Canvas:  link  
Piazza:  link 
Description
This course is meant for those looking to explore mathematical principles relevant to current biological research. The course covers topics on information theory, inference, statistics, probabilistic modeling, ML algorithms, statistical significance, neutral networks and more. All methods are covered from first principles but always using examples relevant to biological problems. Each unit is devoted to one specific topic, and is based in one or more scientific papers selected from the recent life science literature. Each unit includes a set of lectures (available online from mcb111.org), a practical session, and a homework.
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.
Prerequisites and background
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.
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\%).
I expect attendance and completion of homework.
You can work with other students when completing your homework, but you have to present your own materials and code, showing the logic behind the coding statements.
As for using ChatGPT and other generative AI tools to produce your homework, these are the guidelines:

You can look at AI generated materials at any time during the completion of your work, but you cannot present AI generated material as your own.

These materials should be considered as a tool, sometimes useful for you to learn a technique or to see code implementing it. But be aware that these contents (unlike those in published books with authors responsible for them), are not produced with the expectation that they are correct or accurate.

Ultimately, you are responsible for all work that you present as being yours.
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, McGrawHill, 2013.
It is cheap, and it includes most of the mathematical expressions I need on a daytoday 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.