## Index Index

\(n\)th root of unity, Paragraph

Cancellation law

for groups, Paragraph

Cayley table, Paragraph

Composite integer, Paragraph

Congruence modulo \(n\), Example

Conjugate, complex, Paragraph

De Morgan's laws

for sets, Theorem

DeMoivre's Theorem, Theorem

Division algorithm

for integers, Theorem

Element

identity, Item

inverse, Item

order of, Paragraph

Equivalence class, Paragraph

Equivalence relation, Paragraph

Euclidean algorithm, Paragraph

Function

bijective, Paragraph

composition of, Paragraph

definition of, Paragraph

domain of, Paragraph

identity, Paragraph

injective, Paragraph

invertible, Paragraph

one-to-one, Paragraph

onto, Paragraph

range of, Paragraph

surjective, Paragraph

Fundamental Theorem

of Arithmetic, Theorem

Galois, Évariste, Paragraph

Generator of a cyclic subgroup, Paragraph

Greatest common divisor

of two integers, Paragraph

Group

abelian, Paragraph

circle, Paragraph

commutative, Paragraph

cyclic, Paragraph

definition of, Paragraph

finite, Paragraph

general linear, Example

infinite, Paragraph

nonabelian, Paragraph

noncommutative, Paragraph

of units, Example

order of, Paragraph

quaternion, Example

special linear, Example

Induction

first principle of, Principle

second principle of, Principle

International standard book number, Exercise

Klein, Felix, Paragraph

Lagrange, Joseph-Louis, Paragraph

Lie, Sophus, Paragraph

Linear transformation

definition of, Example

Mapping.

*See*Functionmatching derivatives, Exercise

matching US dates, Exercise

Matrix

similar, Example

Partitions, Paragraph

Permutation

definition of, Example

Prime integer, Paragraph

Primitive \(n\)th root of unity, Paragraph

Quaternions, Example

Rigid motion, Paragraph

Universal Product Code, Exercise

vector space, Exercise