MAT 108 Review

Part 1

Axiomatic Mathematics - Prove using axiom

Mathematical Logic - Truth tables - English sentences and manipulation of those (unless, ...)) - negation, contrapositive, converse

Quantifiers: - For every: universal quantification - Exists: existential quantification

Proof techniques: - Proof by contradiction

principle of mathematical induction - Standard - Generalized - Strong / complete induction

Well-ordering principle

Part 2

Zeckendorf's Theorem

Sets - union - set difference - product - intersection

Relations

'Prove for all numbers, p(x) is divisible by n'

Part 3

TA Ch. 3.1, 3.2, 3.3 - Partitions

Ch. 4.1, 4.2, 4.3 - 1-1, onto, bijections

Ch. 5.1, 5.2, 5.3 - Cardinality

AoP Ch. 5.4

Ch. 6.1, 6.2, 6.3 - Modular arithmetic

relation - Identity, domain, range - Union, intersection - inverse, equivalence - Represent as directed graphs or tables - reflexivity, symmetry, transivity function - examples / constructions - 1-1 / onto / bijections - Functions as relations - Composition / Inverse relation - Relation, codomain - Well-defined or not - Symmetry - Nodes will point to itself - Edges are bidirectional - If I can find a connection, then everything else in it is connected - Equivalence relations are the same as relations