Index 607Riemann–Roch theorem, 341, 358, 387
Riemannian manifold, 388, 481–482,
483
Riesz representation theorem, 433
Riesz–Fischer theorem, 75
right
coset, 58–60
multiple, 167
vector spaces, 68
ring, 60–64, 68, 96, 107
ring theory, texts, 78
Rogers–Ramanujan identities,546–549,
582
root, 99–100, 219, 277
lattice, 348–351, 359
Roth’s theorem on algebraic numbers,
123, 214–216, 219
ruler and compass constructions, 160,
175
scalar, 64
schemes, 582
Schmidt’s
discrepancy theorem, 463–464, 489
subspace theorem, 214–215, 219
Schmidt’s orthogonalization process, 74,
230
Schreier’s refinement theorem, 123–124
Schur’s lemma, 413, 415, 417, 418
Schwarz’s inequality, 28, 72, 234, 373,
453
self-dual lattice, 334, 335, 340
semi-simple
Lie algebra, 441–442, 444
Lie group, 441–442, 444
semi-stable elliptic curve, 572, 574, 580
semidirect product, 428
semigroup, 76
Serre’s
ε-conjecture, 580
conjecture, 175–176
set, 2–4, 61
set of representatives, 276, 289
shift map, 477, 479, 487
Siegel’s
formula, 335
lemma, 340, 358
modular group, 218–219
theorem on Diophanite equations, 216,
217, 219, 583
sigma algebra, 433, 465
sign of a permutation, 57, 130–131,
227
signed permutation matrix, 242, 246,
252
simple
associative algebra, 69
basis, 349–350
group, 58, 251, 258, 427, 428
Lie algebra, 441–442, 444
Lie group, 77, 251
pole, 48
ring, 63
simply-connected, 53, 437
covering space, 53, 441–442
Lie group, 441–442
simultaneous diagonalization, 239, 429
singular matrix, 227, 228
small
divisor problems, 219–220
oscillations, 257, 429–430
Smith normal form, 169–173, 176
sojourn time, 470
solvable
by radicals, 39, 79
group, 428
Lie algebra, 443–444
spanned by, 66
special, 53
linear group, 202, 229
orthogonal group, 53, 438–439, 442
unitary group, 53, 437–438, 442
spectrometry, 236, 257
spherical trigonometry, 538
sporadic simple group, 251, 258, 351
square, 14
class, 292, 293, 565–566
design, 249, 258, 321
square 2-design, 249, 258, 321
square root of
complex number, 39, 42
positive real numbers, 22–23, 24–25
square-free