Course Summary

Roughly speaking, probability is the mathematics of determining the likelihood that a certain outcome occurs. Answering this question in a particular context requires us to understand --- with a lot of precision --- precisely what sorts of outcomes could occur, as well as some notion of how those outcomes are (for lack of a better term) doled out. For instance: if we roll a standard six-sided die, then the outcomes that are possible are the numbers $1$, $2$, $3$, $4$, $5$, and $6$; furthermore, each of these outcomes is equally likely. As a result, we can say that there's a 50/50 chance that we roll an odd number (or a one-third chance that we roll a multiple of $3$, etc.). On the other hand, if our die is "unfair" (say if there's additional weight that is situated on one face of the die), then we still have the same suite of possible outcomes, but they don't all occur with equal likelihood. This changes probability calculations from the standard die, despite the fact that much is the same in these two situations.

To aid in our investigation, we will develop a framework and vocabulary for understanding probabilistic questions. This includes some fundamental concepts (e.g., conditional probability, independent events) and theorems (e.g., Bayes's Theorem). In addition to this, we will also need to develop facility in a number of calculations. For example, we must develop the ability to carefully enumerate possibilities (and, believe it or not, counting is really hard), but we must also know how to add up infinite series and compute certain integrals. By the end of the semester, we will have explored many of the common discrete and continuous probability distributions, and we will see how they are related to the so-called normal distribution via the Central Limit Theorem.

Course Instructor

The professor for this class is Andy Schultz. His office is on the fourth floor of the Science Center, room W408. You are highly encouraged to attend office hours, and you never need an appointment to do so. Office hours will be held in (or near) his office at the following times: Mondays from 2-3; Wednesdays from 10:30-11:20; Thursdays from 8:30-9:45; and Fridays from 11:30-1:00. If these office hours don't fit with your schedule, contact the instructor so that he can either adjust when ``official" office hours are held or set up an appointment to help you outside of office hours.

You can contact the instructor at . Though he is always happy to receive emails from you with questions or concerns about the course, he can't guarantee that he'll be able to promptly reply to emails late at night or over the weekend. If you do contact the professor by email, please be sure to follow standard email etiquette. In particular, please make sure you include a greeting and signature and avoid abbreviations. If you're contacting him to ask about a problem, please be sure to specify what the problem asks (as opposed to asking something like ``I can't get problem 2 and need your help").