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| Ïîèñê ïî óêàçàòåëÿì |
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| Barbeau E.J. — Polynomials: a problem book |
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| Ïðåäìåòíûé óêàçàòåëü |
Abel 126
Absolute value 13 212
Algebraically closed 146
Algorithms, determination of zeros 92—94 160—167
Algorithms, Euclidean 31—33 34 63 100
Algorithms, evaluation of polynomials 49—53
Algorithms, factorial powers 55—56
Algorithms, Horner's methods 49—53 58
Algorithms, long division 58
Algorithms, multiplication 4
Algorithms, synthetic division 58
Algorithms, Taylor expansion 51—53
Alternation 214—217
Approximation, nonrational by rational 12 362
Approximation, over interval 213—219 227 414 420
Approximation, successive 160—165 323
Approximation, zeros 159—165 362
Argand diagram 13 187—188 303—305 335—338
Arithmetic progression 26 (1.5.7) 201 416
Bernoulli inequality 222 (7.3.9) 358
Bernoulli numbers 413
Bernstein polynomials 217—219 356—357
Binomial expansion 8 53 67 98 404—405
biology 159 177
Bisection, method of 160—161
Calculator 50—51 53
Cardan 18—20 126
Catalan numbers 262
Cauchy — Riemann conditions 70—71 406
Cauchy's estimate 180
Cayley 20 412
Chaos 413
chebyshev see Tchebychef
Chromatic polynomials 61—63
Coloring 61—63 405 411
Combinatorics 7-8 44 61—63 396 405 406
complex numbers 13—16 401
Complex numbers, square root 16
Complex variable, function of 142—146 155 303—305 406—407
Composition of polynomials 2 43 13) 259
Composition of polynomials, commuting 5 A.1.11) 6 17 23 42 76 232 245 258 269 375 399
Composition of polynomials, degree 5 245
Composition of polynomials, derivatives 68 406
Composition of polynomials, several variables 238 415
Congruences, linear 34 35 96—97 402
Congruences, polynomial 95—98 99—100 116 278—279 296—297
Continued fraction 168—169 236 387 412
Critical point 72
Cube root of unity, imaginary 19 158 248 263 313 315 319—320 375
Cubics 17—20
Cubics, Cardan's method 18—19 249
Cubics, Cayley's observation 20 249
Cubics, discriminant 19 195 196 197 242 316 347 379 389
Cubics, graph 73 265
Cubics, inflection point 73 334
Cubics, intersecting curves 140—141 301—302
Cubics, irreducible 114 (3.8.17)
Cubics, local extrema 235
Cubics, location of zeros 155 (4.9.3 5) 181 188 334 338
Cubics, nature of zeros 19 (1.9.1) 155(4.9.5) 187 195 233 3443—345
Cubics, reducible 114 (3.7.7)
Cubics, symmetric functions of zeros 26 (4.8.12) 193—194 312
Cubics, triple zero 77 (2.5.13) 271
Cubics, Vieta's method 20
Cubics, winding around origin 145 305
Cubics, zeros in progression 201 232
Cubics, zeros of derivative 187 (5.4.19) 412
Cubics, zeros, surds 42 (1.9.4) 156 258
Cyclotomic polynomials 103 105 106 120 280—281 294 410—411
De Moivre's theorem 15 101 120 141 249 279 294 296 309
Decreasing 72 364
Degree, several variables 24
Degree, single variable 1 4—5
Derivative 64—68 197
Derivative, commuting with polynomial 76 (2.5.9)
Derivative, composition of functions 68
Derivative, graphing 72
Derivative, partial 68—71
Derivative, zeros 68 74—75 194 237 322 343 381 411
Descartes, quartic equation 20 195
Descartes, rule of signs 170—171 173 323—324 330 331 332
Detached coefficients, method of 4 58
Difference 54 208—209 212 227
Difference table 207
Differential equation 77 (2.5.11) 270
Differential equation, Legendre 71 407
Dilatation 247 319 416
Diophantine equations 28—30 403 410 412
Diophantine equations, Pell 373 396—397 409—410
Diophantine equations, problems 231—232
Diophantine equations, Pythagorean 28 371
Diophantine equations, solutions 369—374
Diophantine equations, sum of cubes 29 400—401
Discriminant 196—197 316 346—347
Divisibility of numbers 30—31
Divisibility of numbers, greatest common divisor 31—35 100 251—252 279
Divisibility of numbers, least common multiple 31 33
Divisibility of polynomials 51—52 56—59
Divisibility of polynomials, division theorem 59
Divisibility of polynomials, greatest common divisor 63—64 197 301 405
Divisibility of polynomials, synthetic division 58
Eigenfunction 219
Eigenvalue 219 332 357
Eisenstein criterion 83—84 116 273—275
Elementary symmetric function 24 25 27 193
Ellipse, diameters of 11 42 257
Ellipse, Steiner 412
Entire function 406
Entire set of polynomials 399
Equilateral triangle 155 318 319
Error, propagation of 212
Euclidean algorithm, greatest common divisor 31—33 100 175 251 301
Euclidean algorithm, length 34 402
Euler, Catalan numbers 262
Euler, homogeneous functions 69—70 406
Euler, infinite series 334
Euler, little Fermat theorem 98—99
Euler, sums of cubes 29 400
Euler, sums of two squares 239
Euler, totient function  105 106
Extraneous root 124—126
Extrapolation 205—210
Faa di Bruno 406
Factor Theorem 57 118 156 206 241 243 245 376
Factorial power 54 77 210 270 354—355
Factorization 80 84—88 110—112 118—119 275—277 279 284—288 405 407—408
Fermat, little theorem 98—99 106—107
Ferrari 21 126
Fibonacci sequence 35 183—184 387 402 403 409—410
Field 37
Field extension 129—131 135—136 300—301
Field, finite 114 (3.8.19) 294
Fieldintegers mod p 38—39 87—88 252 277
Finite differences 54 207—210 211—212 354 405
Four-color conjecture 62
Fourier — Budan theorem 170 173—175
Fractals 412 413 415
Fuchs, theorem of 398
Fundamental theorem of algebra 126—127 138—148 179 193
Galois theory 131—137 411 419—420
Gauss — Lucas Theorem 411 415
Gauss, fundamental theorem of algebra 127
Gauss, theorem on symmetric functions 26 60 193
Generating functions 7—8 262
Geometric progression 201 (6.4.1) 348 416
Graphical solution 12 396
Graphs (curves) 11 71—75 138—146 160—161 163—165 175 178 191 206 214—217 236 247 265—267 301—305 319 322—323 329 344. 389—392
Greatest common divisor see Divisibility
Group 33—136
Half-plane 149 179 181—183
| Hamilton, W.R. 240
Harmonic progression 201 (6.4.4) 348 416
Hensel's lemma 99—100 167—168
Heron's formula 243 393 418
Hilbert positive polynomials 414—415
Hilbert 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
Inequalities, Bernoulli 222
Inequalities, Cauchy — Schwarz — Bunjakovsky 11 220 228 358 359
Inequalities, Newton 223—224
Inequalities, problems 224—226
Inequalities, solutions 358—362
Infinite series 200 334
Inflection point 73
Integer zeros 94—98 113 119 202 237 290 291
Integral domain 37
Integral domain, F[t] 38 252
Intermediate Value Theorem 160 (5.1.1) 243 375 381 418
Interpolation 205—210 414
Irreducible polynomials 39 81—84 86 87 101 102 114 147 148 226 240 294 306 404
Lagrange identity 11
Lagrange polynomial 207 210 211 212 226 228 229 230 354 355 363 369 386 406
Lagrange, solution of equations 419
Lagrange, solution of quadratic 168—169
lame 402
Least squares 214
Legendre polynomials 71 407
Linear interpolation 161
Linear polynomial 2 12 188 235 339 386
Linear system of equations 121—122
Lipschitz 20
Locus 15 247 319 416
Logarithm 5 (1.1.14) 209 245
Lucas sequence 410
Mandelbrot set 238 415
Matrix 332 (5.4.11) 414
Maximum 72 235 265 364 386
Minimum 72 225 235 265 361 364 381(8.30) 386
Modular arithmetic 34
Moebius function 105 411
Monic 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
Newton, inequalities 223—224
Newton, method of divisors 92—93
Nonrational zeros 246 247
Nyquist diagram 182—183 328—329
Olympiad xv
Olympiad, International xv 35 403
Olympiad, USA xiv 344
Oscillation 177—179
p-adic numbers 168 410
parabola 143 (4.5.1) 155 319
Partial derivatives 68—71 406—407
Partial fractions 108—110 117—118 281—283
Pell's equation 373 (8.11) 396—397 409—410
permutations 133—135
Pirate problem 15 45 248
Polygon 116 C.8.29) 148 262 296
Polynomials of several variables, composition 238
Polynomials of several variables, definitions 24—27
Polynomials of several variables, elementary symmetric functions 24 25 193 251 384
Polynomials of several variables, homogeneous 24 25 27 59—61 87 117 251
Polynomials of several variables, range 28 400
Polynomials of several variables, symmetric 24 27 43 59—61 112 251 260 383—384
Polynomials of single variable, anatomy of 1
Polynomials of single variable, commuting see Composition of polynomials
Polynomials of single variable, evaluation of 2 49—53
Polynomials of single variable, even and odd 6 (1.1.19) 245 416—417
Polynomials of single variable, operations on 2 4 56—59
Polynomials of single variable, real coefficients 16 146—147
Polynomials of single variable, uniqueness of representation 5
Positive polynomials 43 (1.9.11 12) 47—48 220 224 259—260 414
Powers of numbers, evaluation 53 404
Powers of numbers, sums see Sums of first n powers
Powers of numbers, Òàrró — Escott problem 6 394—396
Powers of roots, sum of 198—200 347
PRIMES 31
Primes, decomposition 33 252
Primes, values of polynomials 35
Primitive root of unity 102 117 280
Principal part 411
Putnam Competition xiv 365 400
Quadratic residue 103
Quadratics 2 6 9—12
Quadratics, common zero 122—123
Quadratics, completion of square 9 72 334
Quadratics, complex coefficients 16 140
Quadratics, continued fraction 169
Quadratics, discriminant 9 (3.8.7 11) 139 147 196 248 250 253 254 257 286 290 341 344—345 370 372 409
Quadratics, factoring 84—85
Quadratics, graph 72 265
Quadratics, graphical solution 12 396
Quadratics, hints 45 46—47
Quadratics, interpolation 206
Quadratics, intersecting curves 138—140 301
Quadratics, location of zeros 115 181 187
Quadratics, nature of zeros 76 115 139 267 272 295 333
Quadratics, over  39 114 120
Quadratics, over quaternions 240
Quadratics, problems 9—12 39—42
Quadratics, solutions 246—247 252—258
Quadratics, square values 13 396—398
Quadratics, sum and product of zeros 9—10 25 371
Quadratics, sums of powers of zeros 199
Quadratics, winding around origin 143—145 303—305
Quartics 2 20—21 57 195—196 307
Quartics, biological species 160
Quartics, composition of quadratics 43 259
Quartics, Descartes' method 20 195 250
Quartics, Ferrari's method 21 250
Quartics, Galois theory 132—136
Quartics, graph 3 236 389—392
Quartics, intersecting curves 41 302—303
Quartics, problems 0—21 49—150 201—202
Quartics, quasi-reciprocal 23 195 250
Quartics, solutions 250 307—308
Quartics, symmetric functions of zeros 195 202
Quartics, zeros in harmonic progression 201 (4.4) 348
Quaternions 239—240
Quintics 2 74 77 78 79 128—129 266—267 270 271
Ramanujan 314
Rational functions 107—110
Rational zeros 91—94 113 291 409
Real zeros, conditions for 186 (5.4.7) 187 193 225 344
Real zeros, location of 160—177 187
Reciprocal polynomials 21—23 147 250
Reciprocal substitution 22 23
Reciprocal zeros, polynomial with 180 194
Recursion 16 (1.3.15) 23 35 43 48 89—90 100 165 177—179 183—185 200 388 397 408 409—410
Remainder 52 57 64 264
Residue 109 411
Rolle's theorem 74—75 148 172—173 174—175 190 223 325 336 407
Rook polynomial 7—8
Roots see Zeros
Roots of unity 16 101—104 114 115 191 295
Routh — Hurwitz criteria 182
Ruffini 126
Ruler and compasses constructions 411
Ruler and compasses constructions, angle trisection 130 137
Ruler and compasses constructions, complex operations 15 247
Ruler and compasses constructions, duplication of cube 137
Ruler and compasses constructions, quadratic equation 12 396
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