Advanced book on Mathematics Olympiad

Index 797

commutator, 84
rank, 77
transpose conjugate, 71
mean value theorem, 139
Minkowski’s inequality, 157
mod,seemodulo
modulo, 258

n-gon, 9

order, 14
total, 14
ordinary differential equation
first-order, 191
higher-order, 195
homogeneous, 195
inhomogeneous, 195
orthological triangles, 204

parabola, 212
paraboloid
elliptic, 220
hyperbolic, 220
Pascal’s triangle, 295
Peano curve, 129
Pell’s equation, 276
permutation, 283
cycle, 283
inversion, 283
signature, 283
transposition, 283
Perron–Frobenius theorem, 84
pigeonhole principle, 11
point group, 93
Poisson scheme, 314
polynomial, 45
monic, 45
prime,seeprime number
prime number, 254
probability, 310
geometric, 318
Pythagorean triple, 274

quadric, 219
equation of tangent plane, 220

Ramsey number, 292

Ramsey theory, 291

rational curve, 216

regular polyhedron, 290

relatively prime,seecoprime

residue, 258

residue class,seeresidue

Riemann sum, 153

ring, 95

Rolle’s theorem, 139

root, 46

roots of unity, 236

ruled surface, 221

Schur number, 294

separation of variables, 191

sequence

Cauchy, 109

convex, 114, 143

first difference, 114

linear recursive, 100

second difference, 114

series, 117

geometric, 117

p-series, 117

ratio test, 118

telescopic, 120

spectral mapping theorem, 79

squeezing principle, 105

Stirling’s formula, 162

Stokes’ theorem, 179

Sturm’s principle, 42

system of linear equations, 73

Taylor series, 159

Tonelli’s theorem, 177

trace, 61

triangle inequality, 36

vector, 201

vector field

curl, 180

divergence, 180

vector space, 77