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 are some sample questions from previous semesters (solutions). Prelim 1 did not cover probability in past semesters, here are some sample questions from prelim 2, some of which cover probability (solutions).
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