Index
a priori estimate, 185
active transformation, 54
Archimedean principle, 133
Arzel´ a-Ascoli diagonalisation trick, 139
asymptotic notation, xii
Balog-Szemer´ edi-Gowers lemma, 230
barrier, 107
Bayes’ formula, 236
Bayesian probability, 236
Bernoulli numbers, 96
Bolzano-Weierstrass theorem, 160
Burgers’ equation, 185
busy beaver function, 27
Cantor’s theorem, 21, 32
Cartan-Killing form, 211
Cayley graph, 57
cell decomposition, 121
characteristic subgroup, 67
Christoffel symbols, 205
cogeodesic flow, 205
continuity method, 232
coordinate system, 222
decomposition into varieties, 163
difference equation, 186
differentiating the equation, 185
direct product, 66
Duhamel’s formula, 182
elemengary convergence, 154
energy, 197
equipartition of energy, 203
Erd˝ os distance problem, 110
Euclid’s theorem, 19
Euler equations of incompressible fluids,
213
Euler-Arnold equation, 209
Euler-Maclaurin formula, 98
explicit formula, 102
extension problem, 124
Faulhaber formula, 90
finitely generated group, 57
friendship paradox, 229
Furstenberg correspondence principle,
137
Furstenberg recurrence theorem, 143,
164
G-space, 51
odel incompleteness theorem, 25
odel sentence, 24
odel’s universe, 34
Grandi’s series, 91
Gromov’s theorem, 69, 140
growth function, 105
harmonic function, 70
Heine-Borel theorem, 161
hereditary property, 68
homogeneous space, 51
impredicativity of truth, 24
indicator function, xii
interesting number paradox, 31
invariant subspace problem, 104
255
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