Advanced book on Mathematics Olympiad

Index

AM–GM,seearithmetic mean–geometric
mean inequality
argument by contradiction, 1
arithmetic mean–geometric mean inequality,
39
axiom of choice, 189

basis, 77

Bayes’ formula, 314

Bernoulli scheme, 314

binary operation, 87

associative, 87

commutative, 87

Binet formula, 102

binomial coefficient, 294

quantum, 296

cab-bacidentity, 202

Cantor set, 129

Cantor’s nested intervals theorem, 116

Catalan numbers, 299

Cauchy’s criterion for convergence, 109

Cauchy’s equation, 189

Cauchy–Schwarz inequality, 32, 33

for integrals, 157

Cayley–Hamilton theorem, 83

Cesàro–Stolz theorem, 114

characteristic equation

of a differential equation, 195

of a sequence, 100

Chebyshev polynomial, 58

Chebyshev’s inequality, 158

Chebyshev’s theorem, 59

Chinese Remainder Theorem, 268

congruent, 258

conic, 212

equation of tangent line, 213

continued fraction expansion, 271, 277

coordinates

affine, 206

Cartesian, 206

complex, 209

cylindrical, 175

polar, 175

spherical, 175

coprime, 253

critical point, 134, 170

Crofton’s theorem, 226

cross-product, 202

area, 204

de Moivre’s formula, 235

derivative, 134

partial, 168

determinant, 63

rule of Laplace, 67

Vandermonde, 63

differentiable function

multivariable, 167

directrix, 212

divergence theorem,seeGauss–Ostrogradski

theorem

divisor, 253

dot product, 202