# Index Index

¶\(\Delta^k\)-constant, Paragraph

additive principle, Section Subsection

ancestor, Paragraph

antecedent, Subsection

argument, Chapter

arithmetic sequence, Section

biconditional, Item

bijection, Paragraph

binomial coefficients, Subsection

binomial identity, Paragraph

bit string, Subsection

breadth first search, Paragraph

Brooks' Theorem, Theorem

Canadians, Paragraphs

Cartesian product, Paragraph Subsection

cases, Subsection

characteristic equation, Paragraph

characteristic roots, Subsection Subsection

child, Paragraph

chromatic index, Paragraph

clique, Paragraph

closed formula, Section

for a function, Paragraph

codomain, Paragraph

coloring, Paragraph

combination, Paragraph

complement, Paragraph

composition, Exercise

conclusion, Subsection Chapter

conditional, Item

congruence, Subsection

conjunction, Item

connectives, Paragraph

and, Item

if and only if, Item

implies, Item

not, Item

or, Item

consequent, Subsection

contradiction, Subsection

contrapositive, Item

proof by, Subsection

converse, Item

convex, Paragraph

counterexample, Subsection

cube, Investigate!

cycle, Item

De Morgan's laws, Subsection

deduction rule, Paragraph

degree, Item

degree sum formula, Lemma

depth first search, Paragraph

derangement, Paragraph

descendant, Paragraph

difference, of sets, Paragraph

Diophantine equation, Paragraph

direct proof, Subsection

disjoint, Paragraph

disjuction

equivalent implication, Subsection

disjunction, Item

divides, Paragraph

divisibility relation, Subsection

Division algorithm, Subsection

Doctor Who, Paragraph

dodecahedron, Subsection

domain, Paragraph

double induction, Exercise

double negation, Subsection

edges, Paragraph

empty set, Item

Euler circuit, Item

Euler path, Item

Euler's formula, Section

existential quantifier, Subsection

faces, Paragraph

factorial, Paragraph

finite differences, Section

forest, Section

Four Color Theorem, Theorem

free variable, Paragraph

function, Paragraph

gcd, Paragraph

geometric sequence, Section

girth, Paragraph

Goldbach conjecture, Paragraph

graph, Item

greatest commond divisor, Paragraph

Hall's Marriage Theorem, Theorem

Hamilton path, Paragraph

handshake lemma, Lemma

Hanoi, Investigate!

hypothesis, Subsection

icosahedron, Subsection

if and only if, Item

if…, then…, Item

implication, Item

equivalent disjuction, Subsection

inclusive or, Paragraph

induced subgraph, Section

induction, Paragraph Subsection

strong, Subsection

induction>

double, Exercise

inductive hypothesis, Item

injection, Paragraph

isomorphism, Section

isomorphism class, Paragraph

iteration, Paragraph

lattice path, Paragraph

law of logic, Example

logical equivalence, Subsection

logically valid,

*see*law of logicmagic chocolate bunnies, Exercise

matching, Paragraph

matching condition, Section

mod, Paragraph

modular arithmetic, Subsection

modulo \(n\), Subsection

*modus ponens*, Paragraph

monochromatic, Paragraphs

multiplicative principle, Section Subsection

natural numbers, Item

necessary condition, Subsection

negation, Item

neighbors, Paragraph

NP-complete, Paragraph

parent, Paragraph

partial sums, Paragraph

Pascal's triangle, Subsection

path, Item

perfect graph, Paragraph

permutation, Section

Petersen graph, Exercise

PIE, Paragraph

pigeonhole principle, Example

Platonic solid, Investigate!

polyhedron, Paragraph

polynomial fitting, Section

powers of 2, Section

predicate, Paragraph

premises, Chapter

principle of inclusion/exclusion, Paragraph

product notation, Paragraphs

proof by cases, Subsection

proof by contradiction, Subsection

proof by contrapositive, Subsection

proposition, Paragraph

Ramsey theory, Paragraphs

range, Paragraph

rationals, Item

reals, Item

recurrence relation, Section

recursive definition, Section

recursively defined functions, Subsection

reference, self,

*see*self referenceroot, Paragraph

search

breadth first, Paragraph

depth first, Paragraph

self reference,

*see*reference, selfsequence, Paragraph

set, Paragraph

set difference, Paragraph

sibling, Paragraph

Sigma notation, Paragraphs

square numbers, Section

stars and bars, Section

statement, Paragraph

strong induction, Subsection

induced, Section

subset, Paragraph

sufficient condition, Subsection

summation notation, Paragraphs

surjection, Paragraph

tautology, Paragraph

telescoping, Paragraph

tetrahedron, Subsection

Tower of Hanoi, Paragraph

truth table, Subsection

truth value, Paragraph

universal quantifier, Subsection