Index
Abel, 126
absolute value, 13, 212
algebraically closed, 146
algorithms
determination of zeros, 92-
94, 160-167
Euclidean, 31-33,34,63, 100
evaluation of polynomials, 49-
53
factorial powers, 55-56
Horner’s methods, 49-53, 58
long division, 58
multiplication, 4
synthetic division, 58
Taylor expansion, 51-53
alternation, 214-217
approximation
nonrational by rational, 12,
362,412
over interval, 213-219,227 (7.5.8-
9), 414 (E.58) 420
successive, 160-165,323 (5.1.9)
zeros, 159-165, 362
Argand diagram, 13,187-188,303-
305,335-338
arithmetic progression, 26 (1.5.7),
201 (6.4.1) 416Bernoulli
inequality, 222 (7.3.9), 358
numbers, 413
Bernstein polynomials, 217-219,
356-357
binomial expansion 8, 53 (E.17),
67 (2.3.12) 98, 404-405
bisection, method of, 160-161calculator, 50-51, 53
Cardan, 18-20, 126
Catalan numbers, 262
Cauchy-Riemann conditions, 70-
71, 406
Cauchy’s estimate, 180
Cayley, 20, 412 (E.42)
chaos, 413
Chebyshev, see Tchebychef
chromatic polynomials, 61-63
coloring, 61-63, 405, 411 (E.37)
combinatorics, 7-8,44 (1.9.15), 61-
63, 396, 405, 406 (E.22)
complex numbers, 13-16, 401
square root, 16
complex variable, function of, 142-
146, 155, 303-305, 406-
407,411
composition of polynomials, 2, 43
(1.9.8, 13) 259
commuting,5 (l.l.ll), 6 (1.1.20),
17, 23 (E.7), 42 (1.9.2),
76 (2.5.9), 232 (8.19), 245,
258,269, 375, 399
degree, 5, 245
derivatives, 68, 406
several variables, 238, 415
congruences
linear, 34, 35, 96-97, 402
polynomial, 95-98,99-100, 116
(3.8.30) 278-279, 296-
297
continued fraction, 168-169, 236
biology, 159, 177 (E.49) (8.44), 387, 412