Logic: assertions. logical connectives and properties, propositions, quantifiers
(Sections 2.1 and 2.2)
Sets: notation, representation, characteristic function, operations on sets
(Sections 1.1 and 1.2)
Mathematical structures: sets, operations, and closure (Section 1.6)
Proof methods: direct derivation, contradiction, and induction
(Sections 2.3 and 2.4, Handout A)
Counting: permutations, combinations, pigeonhole principle (Sections 3.1, 3.2,
and 3.3)
Discrete probability: sample space, events, frequency of occurrence, expected
value, basic relationships (Section 3.4, Handout B)
Directed Graphs and Relations: notations, properties, equivalence relations,
paths and abstract closure (Sections 4.2, 4.3, 4.4, and 4.5)
Relations: representation in a computer and basic operations (Sections 4.6, 4.7,
and 4.8)
Functions as Special Relations: properties, some useful functions, asymptotic
classes of functions (Sections 5.1, 5.2, 5.3)
Order Relations: p.o. sets, lattices, boolean algebras (Sections 6.1, 6.2,
6.3, and 6.4)
Trees: definitions, properties, representation, and searching
(Sections 7.1, 7.2, 7.3, and 7.4)
Graphs: definition, paths, circuits, tours, spanning trees (Sections 8.1, 8.2, 8.3, 7.5)
Graphs: coloring, flow, matching, and other problemss (Sections 8.4, 8.5, and 8.6)
If time allows: introduction to finite-state machines (Sections 10.3 and 10.5)