From Mathematics to Generic Programming

Index

* (operator), mathematical convention for, 115

+ (plus sign), mathematical convention for, 115

α. See Aliquot sum

ϕ. See Euler totient function

σ (sum of divisors) formula, 31

A

Abelian group, 86, 108, 153

Abstract algebra

birth of, 85, 140–145

Euclidean domains, 150–151, 153

fields, 151–153

groups, 85–88, 92–95, 108, 152

ideals, 226–228

modules, 151, 154

monoids, 89, 108–109, 152, 154

and programming, 2, 141, 249

principal ideals, 227–228

rings, 142–145, 153

semigroups, 90–91, 108–109, 152

semirings, 145–149, 153

vector spaces, 152, 154

Abstraction

Aristotle, 177, 180, 196

in mathematics, 84, 85–109

and programming, 2, 5, 249

Academy (Plato’s), 41–44, 178

Addition

associativity of, 9, 156, 174

commutativity of, 155–156, 174–175

definition, ...