MCB 111: Mathematics in Biology

W-00  Introduction to coding and probability distributions

              We will learn to sample from any probability distribution as an intro to coding.

W-01   Information Theory.

             What is information content, and why it's good to assume ignorance!

W-02   Probability and Inference.

                Using the data to reverse engineer your system.

W-03 Model comparison - Hypothesis testing.

               Which model is best supported by my data?

W-04 Significance: The Student's t-test and p-values.

             Looking behind a classical statistical test, and how to use null models.

W-05 Maximum likelihood and least-squares.

            A principled derivation of linear regression.

W-06 Probabilistic Models and Inference.

                A Hidden Markov Model to assign ancestry to chromosomal segments.

W-07 Probabilistic Models and Expectation Maximization.

             How to train your model.

W-08 Neural Networks. Learning as Inference.

             Where we will design, train and make inferences with a simple neural network.

W-09 Random Walks in Biology.

             Diffusion: from the microscopic to the macroscopic.

W-10 Molecular Population Dynamics as a Markov Process.

             mRNA birth-and-death (synthesis/degradation and steady state)

W-11 Feedback Control in Biological Interactions.

              Study of several cases of gene regulation by positive and negative feedback loops.

W-12 Gene switches.

            Synthetically designed switches in bacteria and circadian rhythms in flies.

W-13 Pattern formation and Turing Instability.

             Making cool biological patterns by diffusion/reaction as Alan Turing showed as to do.

For more information:

course website: http://www.mcb111.org

course syllabus: http://mcb111.org/downloads/MCB111-syllabus.pdf

 

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Course goals:

To introduce mathematical and computational modeling principles and specific methods that have been successfully applied to biological questions. There is an important emphasis in probabilistic modeling as well as Bayesian inference, and molecular biological questions. All methods will be introduced from first principles, but student with different backgrounds will concentrate on different aspects of it. In any case, the goal is to be practical and to go from modeling to actual implementations, all based on recent literature.

 

I go by this quote by Alan Turing:

“It must be admitted that the biological examples which it has been possible to give in the present [course] are very limited. This can be ascribed quite simply to the fact that biological phenomena are usually very complicated. Taking this in combination with the relatively elementary mathematics used in this [course] one could hardly expect to find that many observed biological phenomena would be covered. [I hope], however, that the imaginary biological systems which have been treated, and the principles which have been discussed, should be of some help in interpreting real biological forms.”

Course format:

Each week is an independent unit, with two lectures to introduce the concepts, one section to discuss practical details to implement the concepts, and one homework for the students to implement the method with some practical application, ordinarily involving coding (using python as default).

Typical enrollees:

Two fold: Students with computational and mathematical interests that want to apply those methods to biological problems, and Students with biological interests who want to see how far can mathematics model biological processes. The course is also oriented to students with a research interest.

When is course typically offered?

fall

What can students expect from you as an instructor?

I like to teach from first principles, but I understand that each person learns differently, and I am happy to follow you in that process. My office door/zoom is always open.

Assignments and grading:

There is one homework per week that will represent the mayority of the grade and the work you will have to perform for the course. The homework is always a practical biological application very closely related to the topics discussed in class for that week. I encourage students to approach the homework as a research project. How far can I go formulating the problem?

Sample reading list:

mcb111.org includes extensive notes for all the class materials, and multiple links to original papers and also relevant books.

Past syllabus:

course syllabus: http://mcb111.org/downloads/MCB111-syllabus.pdf

Absence and late work policies:

Class participation is a requirement. Late work needs to be justified in advance, otherwise 10% of the grade will be taken for each late day.