Course overview
Description
This is a course on the mathematics of probability and statistics. In probability, we describe the distribution of a random phenomenon and then study how the realizations of that phenomenon typically behave. In statistics, we do the reverse; we observe realizations of a random phenomenon with unknown distribution, and then use the data to figure out what the distribution is. We will spend twelve weeks on the first, and then three weeks on the second. Topics include set theory, probability spaces, counting methods, conditional probability, discrete and (absolutely) continuous random variables, transformations of random variables, (pseudo)random number generation, bivariate distributions, concentration inequalities, limit theorems, maximum likelihood estimation, and Bayesian inference with conjugate priors.
Aside from the concrete topics, the course emphasizes four generic intellectual themes:
- Students in this class will improve their mathematical maturity. They will deepen their experience with all of the main ideas and techniques of univariate calculus, they will encounter topics like set theory and combinatorics, which may be new to them, and they will get a taste of rigorous mathematical proof;
- Probability and statistics weasel their way into pretty much everything these days, and students will study a wide variety of famous and obscure applications coming from the natural and social sciences, technology and industry, and even arts and culture;
- Probability and statistics are often counterintuitive, and humans frequently make silly and harmful mistakes in reasoning. Students will use their mathematical knowledge to identify and critique these errors…and hopefully avoid them themselves;
- This is a course about doing the math, but in the modern era, this has a symbiotic relationship with computer simulation. Simulation is used both to verify and probe mathematical results, as well as to substitute for them when a proof remains beyond the frontier. Students will learn the basics of the
Rprogramming language and use it to simulate probabilistic environments and reinforce their mathematical reasoning.
Prerequisites: single-variable calculus.
Meetings
| Meeting | Location | Time | Staff |
|---|---|---|---|
| Lectures | Old Chem 116 | MoWe 3:05 PM - 4:20 PM | John |
| Lab 01 | Perkins LINK 087 (Classroom 3) | Th 1:25 PM - 2:40 PM | Aurora |
| Lab 02 | Perkins LINK 087 (Classroom 3) | Th 3:05 PM - 4:20 PM | Aurora |