Math 227C: Stochastic modeling and statistical modeling for the life sciences

We will update this live in class!

• The repository will be updated throughout the course, including with lecture notes. A convenient way to rapidly synchronize a copy onto your computer is using git, available openly online.
• In the second part of the course, we will make use of Jupyter notebooks and the R programming language. The easiest way to install Jupyter and R on your machine is through Anaconda, available openly online, by first installing Anaconda and then installing R. We plan to start using Jupyter around the 5th week of class.
• In the first part of the course, a good tool for typesetting mathematical homeworks is LaTeX. A good tutorial to learn LaTeX is here.

Premise

This course follows MATH 227A and 227B in establishing mathematical and computational tools that are useful in modeling the dynamics of biological systems. This course, MATH 227C, is in two parts: the first covers stochastic processes, where randomness plays a role in the system behavior; the second covers statistical modeling, where models, including their attributes such as parameters, are learned from data in the presence of noise or inherent randomness in the model.

Lecture notes

• In-class hand notes

• In-class Jupyter notebooks

Problem sets

1. Discrete probability. Fair dice.

2. Discrete-state Markov chains, base pairs

3. Discrete-state Markov chains, MFPTs and a biologist in the rain

4. Poisson rates, my advisor is always late, viral DNA

5. Receptors, continuous-time Markov chains, and MFPTs

6. Parametric noise in an ODE

7. Fitting linear and nonlinear regression to a power law

8. Variance-bias tradeoff of k-Nearest-Neighbors classification

9. Gut microbiome and the elastic net

10. Bootstrap and the Standard Error of the Mean, bootstrap on linear regression

11. MCMC and chemical kinetics