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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.
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In the second part of the course, we will make use of Jupyter notebooks and the R programming language. We plan to start using Jupyter around the 5th week of class. There are (at least) three ways to run Jupyter R notebooks. Here is a brief guide.
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In the first part of the course, a good tool for typesetting mathematical homeworks is LaTeX. A good tutorial to learn LaTeX is here.
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In the second part of the course, we will make use of R. A few good tutorials and resources:
- R Tutorial from W3C
- R cheatsheet with loops, if statements,
lapply, etc. - R for Data Science
- Jupyter and R Documentation
This course follows MATH 227A and 227B in establishing mathematical and computational tools for 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.
Special dates
- There will be no lecture Friday, April 25th (week 4).
- There will be no lecture Monday, May 5th (week 6).
- Instead we will have
- [You picked:] out-of-class recorded lectures. These will be released throughout the quarter.
A bonus class Tue, Jun 10, 1:30-3:30pm (our exam slot)
There is no required textbook for the course. However, the following textbooks are recommended for further reading.
- Wan, F. Stochastic Models in the Life Sciences
- Ross, S. Introduction to Probability Models. Academic press.
- James, Tibshirani, R, An Introduction to Statistical Learning free online.
- Huber and Holmes, Modern Statistics for Modern Biology free online.
- Goodfellow, I., Bengio, Y., & Courville, A. Deep learning. free online.
A rough correspondence between topics and textbooks is given below.
| Topic | Textbooks |
|---|---|
| Probability basics | Goodfellow3, Ross1,2 |
| Discrete Markov chains | Wan2, Ross4 |
| First-passage a.k.a. first-hitting | Wan3, Ross4 |
| Poisson processes | Wan5, Ross5.3 |
| Continuous-time Markov chain | Ross6 |
| Heterogeneity | Wan9 |
| Variance-bias tradeoff (aka bias-variance tradeoff) | James2.2, James5.1, Huber12.6 |
| k-nearest-neighbors | James4, Huber5.6, Huber12.6 |
| Logistic regression | James4.3 |
| LASSO | James6, Huber12, Goodfellow7 |
| Bootstrap | James5 |
| Cross-validation | James5 |
| MCMC | Goodfellow17 |