Prelim 1 study guide
=================
Everything covered in lecture or homework on or before Monday, March 6 is in
scope. Material that was covered on the homework may receive a heavier
emphasis.
[Here](p1-sample.pdf) are some sample questions from previous semesters
([solutions](p1-sample-sol.pdf)). Prelim 1 did not cover probability in past
semesters, [here](p1-prob-sample.pdf) are some sample questions from prelim 2, some
of which cover probability ([solutions](p1-prob-sample-sol.pdf)).
There is always variation between semesters on the exact topics covered and the
extent to which they are emphasized, so take the sample prelims with a grain of
salt.
Topics include, but are not limited to:
- modeling problems using sets and functions
- writing and reading definitions
- writing and reading proofs, including inductive proofs
- functions, 'jectivity, left and right inverses
- functions that take functions as arguments
- cardinality definitions: $|X| \leq |Y|$, countability
- relations, equivalence relations, equivalence classes, closure, well-defined functions on $A/R$
- basic combinatorics: sum, product, quotient rule; $n \choose k$
- you are not responsible for knowing the definitions of the rational or
real numbers, but they do serve as good examples for other concepts.
- definition of probability space, event, outcome, sample space, etc.
- definition of conditional probability, bayes's rule, law of total probability
- definition of random variables, expectation, variance
- Markov's and Chebychev's inequalities