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Barbeau E.J. Ч Polynomials: a problem book
Barbeau E.J. Ч Polynomials: a problem book



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Ќазвание: Polynomials: a problem book

јвтор: Barbeau E.J.

язык: en

–убрика: ћатематика/јлгебра/”чебники/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1989

 оличество страниц: 461

ƒобавлена в каталог: 12.03.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Abel      126
Absolute value      13 212
Algebraically closed      146
Algorithms, determination of zeros      92Ч94 160Ч167
Algorithms, Euclidean      31Ч33 34 63 100
Algorithms, evaluation of polynomials      49Ч53
Algorithms, factorial powers      55Ч56
Algorithms, Horner's methods      49Ч53 58
Algorithms, long division      58
Algorithms, multiplication      4
Algorithms, synthetic division      58
Algorithms, Taylor expansion      51Ч53
Alternation      214Ч217
Approximation, nonrational by rational      12 362
Approximation, over interval      213Ч219 227 414 420
Approximation, successive      160Ч165 323
Approximation, zeros      159Ч165 362
Argand diagram      13 187Ч188 303Ч305 335Ч338
Arithmetic progression      26 (1.5.7) 201 416
Bernoulli inequality      222 (7.3.9) 358
Bernoulli numbers      413
Bernstein polynomials      217Ч219 356Ч357
Binomial expansion      8 53 67 98 404Ч405
biology      159 177
Bisection, method of      160Ч161
Calculator      50Ч51 53
Cardan      18Ч20 126
Catalan numbers      262
Cauchy Ч Riemann conditions      70Ч71 406
Cauchy's estimate      180
Cayley      20 412
Chaos      413
chebyshev      see Tchebychef
Chromatic polynomials      61Ч63
Coloring      61Ч63 405 411
Combinatorics      7-8 44 61Ч63 396 405 406
complex numbers      13Ч16 401
Complex numbers, square root      16
Complex variable, function of      142Ч146 155 303Ч305 406Ч407
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 96Ч97 402
Congruences, polynomial      95Ч98 99Ч100 116 278Ч279 296Ч297
Continued fraction      168Ч169 236 387 412
Critical point      72
Cube root of unity, imaginary      19 158 248 263 313 315 319Ч320 375
Cubics      17Ч20
Cubics, Cardan's method      18Ч19 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      140Ч141 301Ч302
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 3443Ч345
Cubics, reducible      114 (3.7.7)
Cubics, symmetric functions of zeros      26 (4.8.12) 193Ч194 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 280Ч281 294 410Ч411
De Moivre's theorem      15 101 120 141 249 279 294 296 309
Decreasing      72 364
Degree, several variables      24
Degree, single variable      1 4Ч5
Derivative      64Ч68 197
Derivative, commuting with polynomial      76 (2.5.9)
Derivative, composition of functions      68
Derivative, graphing      72
Derivative, partial      68Ч71
Derivative, zeros      68 74Ч75 194 237 322 343 381 411
Descartes, quartic equation      20 195
Descartes, rule of signs      170Ч171 173 323Ч324 330 331 332
Detached coefficients, method of      4 58
Difference      54 208Ч209 212 227
Difference table      207
Differential equation      77 (2.5.11) 270
Differential equation, Legendre      71 407
Dilatation      247 319 416
Diophantine equations      28Ч30 403 410 412
Diophantine equations, Pell      373 396Ч397 409Ч410
Diophantine equations, problems      231Ч232
Diophantine equations, Pythagorean      28 371
Diophantine equations, solutions      369Ч374
Diophantine equations, sum of cubes      29 400Ч401
Discriminant      196Ч197 316 346Ч347
Divisibility of numbers      30Ч31
Divisibility of numbers, greatest common divisor      31Ч35 100 251Ч252 279
Divisibility of numbers, least common multiple      31 33
Divisibility of polynomials      51Ч52 56Ч59
Divisibility of polynomials, division theorem      59
Divisibility of polynomials, greatest common divisor      63Ч64 197 301 405
Divisibility of polynomials, synthetic division      58
Eigenfunction      219
Eigenvalue      219 332 357
Eisenstein criterion      83Ч84 116 273Ч275
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      31Ч33 100 175 251 301
Euclidean algorithm, length      34 402
Euler, Catalan numbers      262
Euler, homogeneous functions      69Ч70 406
Euler, infinite series      334
Euler, little Fermat theorem      98Ч99
Euler, sums of cubes      29 400
Euler, sums of two squares      239
Euler, totient function $(\phi)$      105 106
Extraneous root      124Ч126
Extrapolation      205Ч210
Faa di Bruno      406
Factor Theorem      57 118 156 206 241 243 245 376
Factorial power      54 77 210 270 354Ч355
Factorization      80 84Ч88 110Ч112 118Ч119 275Ч277 279 284Ч288 405 407Ч408
Fermat, little theorem      98Ч99 106Ч107
Ferrari      21 126
Fibonacci sequence      35 183Ч184 387 402 403 409Ч410
Field      37
Field extension      129Ч131 135Ч136 300Ч301
Field, finite      114 (3.8.19) 294
Fieldintegers mod p      38Ч39 87Ч88 252 277
Finite differences      54 207Ч210 211Ч212 354 405
Four-color conjecture      62
Fourier Ч Budan theorem      170 173Ч175
Fractals      412 413 415
Fuchs, theorem of      398
Fundamental theorem of algebra      126Ч127 138Ч148 179 193
Galois theory      131Ч137 411 419Ч420
Gauss Ч Lucas Theorem      411 415
Gauss, fundamental theorem of algebra      127
Gauss, theorem on symmetric functions      26 60 193
Generating functions      7Ч8 262
Geometric progression      201 (6.4.1) 348 416
Graphical solution      12 396
Graphs (curves)      11 71Ч75 138Ч146 160Ч161 163Ч165 175 178 191 206 214Ч217 236 247 265Ч267 301Ч305 319 322Ч323 329 344. 389Ч392
Greatest common divisor      see Divisibility
Group      33Ч136
Half-plane      149 179 181Ч183
Hamilton, W.R.      240
Harmonic progression      201 (6.4.4) 348 416
Hensel's lemma      99Ч100 167Ч168
Heron's formula      243 393 418
Hilbert positive polynomials      414Ч415
Hilbert tenth problem      403
Homogeneous      see Polynomials of several variables
Homogeneous linear system      121Ч122
Horner's method      49Ч53 55Ч56 94 161Ч162 263Ч264 404
Hyperbola      41 139 140 257
Increasing      72 364
Index of refraction      205Ч206 209
Inequalities, arithmetic-geometric mean      12 26 220Ч222 224 228 229 241 243 292 357Ч358 359 361 374
Inequalities, Bernoulli      222
Inequalities, Cauchy Ч Schwarz Ч Bunjakovsky      11 220 228 358 359
Inequalities, Newton      223Ч224
Inequalities, problems      224Ч226
Inequalities, solutions      358Ч362
Infinite series      200 334
Inflection point      73
Integer zeros      94Ч98 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      205Ч210 414
Irreducible polynomials      39 81Ч84 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      168Ч169
lame      402
Least squares      214
Legendre polynomials      71 407
Linear interpolation      161
Linear polynomial      2 12 188 235 339 386
Linear system of equations      121Ч122
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      67Ч68 75 155 267 268 321 322 381
Netto      84
Newton, approximation of root      162Ч164 166Ч167 169 412
Newton, inequalities      223Ч224
Newton, method of divisors      92Ч93
Nonrational zeros      246 247
Nyquist diagram      182Ч183 328Ч329
Olympiad      xv
Olympiad, International      xv 35 403
Olympiad, USA      xiv 344
Oscillation      177Ч179
p-adic numbers      168 410
parabola      143 (4.5.1) 155 319
Partial derivatives      68Ч71 406Ч407
Partial fractions      108Ч110 117Ч118 281Ч283
Pell's equation      373 (8.11) 396Ч397 409Ч410
permutations      133Ч135
Pirate problem      15 45 248
Polygon      116 C.8.29) 148 262 296
Polynomials of several variables, composition      238
Polynomials of several variables, definitions      24Ч27
Polynomials of several variables, elementary symmetric functions      24 25 193 251 384
Polynomials of several variables, homogeneous      24 25 27 59Ч61 87 117 251
Polynomials of several variables, range      28 400
Polynomials of several variables, symmetric      24 27 43 59Ч61 112 251 260 383Ч384
Polynomials of single variable, anatomy of      1
Polynomials of single variable, commuting      see Composition of polynomials
Polynomials of single variable, evaluation of      2 49Ч53
Polynomials of single variable, even and odd      6 (1.1.19) 245 416Ч417
Polynomials of single variable, operations on      2 4 56Ч59
Polynomials of single variable, real coefficients      16 146Ч147
Polynomials of single variable, uniqueness of representation      5
Positive polynomials      43 (1.9.11 12) 47Ч48 220 224 259Ч260 414
Powers of numbers, evaluation      53 404
Powers of numbers, sums      see Sums of first n powers
Powers of numbers, “аrrу Ч Escott problem      6 394Ч396
Powers of roots, sum of      198Ч200 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 9Ч12
Quadratics, common zero      122Ч123
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 344Ч345 370 372 409
Quadratics, factoring      84Ч85
Quadratics, graph      72 265
Quadratics, graphical solution      12 396
Quadratics, hints      45 46Ч47
Quadratics, interpolation      206
Quadratics, intersecting curves      138Ч140 301
Quadratics, location of zeros      115 181 187
Quadratics, nature of zeros      76 115 139 267 272 295 333
Quadratics, over $Z_p$      39 114 120
Quadratics, over quaternions      240
Quadratics, problems      9Ч12 39Ч42
Quadratics, solutions      246Ч247 252Ч258
Quadratics, square values      13 396Ч398
Quadratics, sum and product of zeros      9Ч10 25 371
Quadratics, sums of powers of zeros      199
Quadratics, winding around origin      143Ч145 303Ч305
Quartics      2 20Ч21 57 195Ч196 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      132Ч136
Quartics, graph      3 236 389Ч392
Quartics, intersecting curves      41 302Ч303
Quartics, problems      0Ч21 49Ч150 201Ч202
Quartics, quasi-reciprocal      23 195 250
Quartics, solutions      250 307Ч308
Quartics, symmetric functions of zeros      195 202
Quartics, zeros in harmonic progression      201 (4.4) 348
Quaternions      239Ч240
Quintics      2 74 77 78 79 128Ч129 266Ч267 270 271
Ramanujan      314
Rational functions      107Ч110
Rational zeros      91Ч94 113 291 409
Real zeros, conditions for      186 (5.4.7) 187 193 225 344
Real zeros, location of      160Ч177 187
Reciprocal polynomials      21Ч23 147 250
Reciprocal substitution      22 23
Reciprocal zeros, polynomial with      180 194
Recursion      16 (1.3.15) 23 35 43 48 89Ч90 100 165 177Ч179 183Ч185 200 388 397 408 409Ч410
Remainder      52 57 64 264
Residue      109 411
Rolle's theorem      74Ч75 148 172Ч173 174Ч175 190 223 325 336 407
Rook polynomial      7Ч8
Roots      see Zeros
Roots of unity      16 101Ч104 114 115 191 295
Routh Ч 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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