MA 225-003

Foundations of Advanced Mathematics

Mathematics

Material on Test 3 (Monday, November 22)

Secs. 3.1 - 3.2. Product of two sets; checking whether relations are reflexive, symmetric, transitive; finding equivalence classes for equivalence relations; proving that a relation is an equivalence relation.

Sec. 4.1. Domain, codomain, and range of a function; checking that a function is well-defined (problem 8); special functions (canonical map, identity, inclusion, projection).

Sec. 4.2. Constructing the composition of two functions; proofs involving composition.

Sec. 4.3. One-to-one and onto functions; inverse of a function; proofs involving composition, one-to-one and onto functions, and inverses.

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