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