Unknown

(^438) Index
Hensel’s lemma, 99-100, 167-168
Heron’s formula, 243, 393, 418
Hilbert
positive polynomials, 414-415
tenth problem, 403
homogeneous, see polynomials of
several variables
homogeneous linear system, 121-
122
Horner’s method, 49-53, 55-56,
94,161-162,263-264,404
hyperbola, 41, 139, 140, 257
increasing, 72, 364
index of refraction, 205-206, 209
inequalities
arithmetic-geometric mean, 12,
26,220-222,224,228,229,
241, 243, 292, 357-358,
359,361, 374
Bernoulli, 222
Cauchy-Schwarz-Bunjakovsky,
11, 220, 228, 358, 359
Newton, 223-224
problems, 224-226
solutions, 358-362
infinite series, 200, 334
inflection point, 73
integer zeros, 94-98, 113,119,202
(6.4.12), 237, 290, 291
integral domain, 37
F[t], 38, 252
intermediate value theorem, 160
(5.1.1), 243, 375 (8.19),
381 (8.31), 418
interpolation, 205-210, 414
irreducible polynomials, 39, 81-
84, 86, 87, 101, 102, 114
(3.8.19) 147, 148, 226,
240, 294, 306, 404
Lagrange
identity, 11
polynomial, 207,210,211,212,
226 (7.5.1-2), 228 (7.5.10)
229, 230, 354, 355, 363,
369, 386, 406
solution of equations, 419
solution of quadratic, 168-169
Lam& 402
least squares, 214
Legendre polynomials, 71, 407
linear interpolation, 161
linear polynomial, 2, 12, 188 (5.4.23),
235 (8.42), 339, 386
linear system of equations, 121-
122
Lipschitz, 20
locus, 15, 247, 319 (4.9.2), 416
logarithm, 5 (1.1.14), 209, 245
Lucas sequence, 410
Mandelbrot set, 238, 415
matrix, 332 (5.4.11), 414 (E.54)
maximum, 72, 235, 265, 364, 386
minimum, 72, 225 (7.4.12), 235,
265,361,364,381(8.30),
386
Mobius function, 105, 411
modular arithmetic, 34
manic polynomial, 1, 91, 156
multiplicity, 67-68, 75, 155, 267,
268,321, 322, 381
Netto, 84
Newton
approximation of root, 162-
164, 166-167, 169, 412
inequalities, 223-224
method of divisors, 92-93
nonrational zeros, 246, 247
Nyquist diagram, 182-183, 328-
329
Olympiad, xv
International, xv, 35, 403
USA, xiv, 344
oscillation, 177-179
p-adic numbers, 168, 410