topics outline:

sets
• set notation (for example A={x|x in Z and x<25})
• element, subset
• operations: union, intersection, complement, subtraction, power set, cartesian-product, cardinality
• inclusion/exclusion principle

logic
• operations: and, or, xor, not, implies, if-and-only-if
• order of operations
• truth tables
• equivalence of logic expressions
• logic laws
• translate from English to propositional logic

relations
• graphical representation
• representations by sets of ordered pairs
• properties: reflexive, symmetric, transitive

functions
• domain, codomain, rule
• injection, surjection, bijection
• Pigeonhole principle
• function inversion
• function composition

counting
• addition rule
• multiplication rule
• permutations
• combinations

probability
• counting outcomes in event and state space
• complement
• disjoint and independent
• addition rule
• multiplication rule