 
Summary: Chapter 1 lecture notes
Math 431, Spring 2010
Instructor: David F. Anderson
Tentative Course Outline:
I. Basic combinatorics: how to count.
(a) No real probability yet. Just setting stage for how to calculate simple probabilities
later.
(b) Turns off a lot of students. Admittedly rather boring, but important.
(c) One Week.
II. Axioms of probability: building blocks of subject.
(a) Basic question: what does it mean when we say something has a certain proba
bility?
(b) Build up from basic axioms and prove basic (fundamental and useful) theorems.
(c) One week.
III. Conditional probability and independence: what does partial information get you (much
more than that)
(a) Hard. Maybe hardest of the whole semester conceptually.
(b) Two weeks.
IV. Everything else: Random variables, expectations, limit theorems,...
(a) Functions of outcomes of experiments. Very important. This is what people
