Advanced High-School Mathematics

420 Index

negative binomial, 330
distributive laws, 192
divides, 57
division algorithm, 56
dual graph, 143

e
formal definition, 268
edge, 109
elementary symmetric polynomials,
176
elements
of a set, 185
equivalence class, 202
equivalence relation, 201
equivalence relations, 186
Euclid’s Theorem, 3
Euclidean algorithm, 59
Euclidean trick, 58
Eulerφ-function, 63
Euler characteristic, 139
Euler line, 22
Euler’s constant, 269
Euler’s constantγ, 269
Euler’s degree theorem, 112
Euler’s formula, 140
Euler’s method, 314
Euler’s theorem, 87, 112
Euler’s totient function, 63
Euler-Mascheroni constant, 269
Eulerian circuit, 111
Eulerian trail, 111
expectation, 318
explicit law of sines, 34
exponential distribution
mean, 360
variance, 360

external division, 41

failure rate, 360

Fermat conjecture, 55

Fermat number, 78

Fermat’s Little Theorem, 86

Fibonacci difference equation, 106

Fibonacci sequence, 93, 106, 276

generalized, 106

fibre

of a mapping, 198

fundamental theorem of arithmetic,

76

fundamental theorem of calculus,

251

gambler’s ruin, 343

Gamma function, 261

general linear group, 219

generalized Fibonacci sequence, 106

generalized Riemann hypothesis, 226

generating function, 109

geometric

sequence, 93

geometric distribution

generalizations, 330

geometric mean, 147

geometric random variable, 327

distribution, 327

mean, 328

variance, 329

geometric sequence, 93

Gergonne point, 18

golden ratio, 27, 41, 277

golden triangle, 27

graph, 109

bipartite, 136