RePoSS #11: The Mathematics of Niels Henrik Abel: Continuation ...

More documents

Recommendations

Info

Index École Normale, 40, 187 École Polytechnique, 3, 31, 40, 207, 218 a priori properties of roots, 58 Abel’s Vienna review, xix Abel’s exception, 395 Abel’s manuscripts, xix Abelian equations, 49, 51, 52, 141, 142, 145, 149, 150, 152, 163, 165, 171, 172, 176, 178, 180, 186, 314, 316, 334, 392 Abelian groups, 149 Abelian Theorem, 15, 358, 361, 376 absolutely convergent series, 215 Académie des Sciences, 6, 35, 40, 42, 64, 347, 348, 375, 376 Akademie der Wissenschaften, 136 Algebra Fundamental Theorem of, 5, 10, 58, 80, 82, 95 algebraic expression, 61 algebraically solvable equations, 392 amplitude, 309 anachronism, 10 Analytical Society, 42 Annales de mathématiques pures et appliquées, 29, 205, 348, 372 anomaly, 11 arithmetic-geometric mean, 296, 297 arithmetical foundation of calculus, 9 arithmetical concept of equality, 9 Astronomische Nachrichten, 24, 331–333, 337, 338 basic curves, 8 basic functions, 381 Berlin Academy, 32 Berlin Academy, 65 binomial formula, 221 binomial theorem, 221 binomial formula, 238 binomial series, 227, 241, 254, 255, 259, 260, 263 435 binomial theorem, 221, 224, 227, 233, 238, 241, 251, 254, 260, 261, 263 British Association, 129 Bulletin, 123, 126 Bulletin des sciences mathématiques, astronomiques, physiques et chimiques, 98, 123 Cauchy criterion, 395 Cauchy’s Theorem, 251, 395, 396, 399 Cauchy-ism, 7 Cauchy-Riemann-equations, 307 Cauchy-Ruffini theorem, 100, 101, 108, 110, 112, 119–121, 128, 135, 137 chains of roots, 145, 146 chains of roots, 142, 143 change, 11 Christiania cathedral school, 4 circle, 287 circle of permutations, 93 circular substitution, 94 Collegium academicum, 339 coming to know objects, 8 commutativity of rational dependencies, 147 complex of roots, 75 complexum, 75 composite permutations, 85 computational mathematical style, 52 concept definition, 8 concept based mathematics, xiii, xiv, xvii, 8, 9, 13, 15, 55, 124, 141, 187, 192, 286, 387–395, 398–400 concept stretching, 7, 12, 400 conceptual mathematical style, 52 conjugate roots, 76 constructibility, 74 constructions, 74 convergence d’Alembert, 200, 201 Gauss, 200 Olivier, 265 convergence of Fourier series, 399
Page 1 and 2:
RePoSS: Research Publications on Sc
Page 3 and 4:
The Mathematics of NIELS HENRIK ABE
Page 5 and 6:
The Mathematics of NIELS HENRIK ABE
Page 7 and 8:
Contents Contents i List of Tables
Page 9 and 10:
8.3 Refocusing on the equation . .
Page 11:
V ABEL’s mathematics and the rise
Page 15 and 16:
List of Figures 2.1 NIELS HENRIK AB
Page 17:
List of Boxes 1 The algebraic reduc
Page 21 and 22:
Summary The present PhD dissertatio
Page 23 and 24:
Preface to the 2004 edition For thi
Page 25:
in connection with the Abel centenn
Page 28 and 29:
items published in the same year ar
Page 30 and 31:
the Mittag-Leffler archives in Djur
Page 33 and 34:
Chapter 1 Introduction In the after
Page 35 and 36:
1.2. The mathematical topics involv
Page 37 and 38:
1.3. Themes from early nineteenth-c
Page 39 and 40:
1.4. Reflections on methodology 9 l
Page 41 and 42:
1.4. Reflections on methodology 11
Page 43 and 44:
Page 45:
Page 48 and 49:
18 Chapter 2. Biography of NIELS HE
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 69 and 70:
Chapter 3 Historical background The
Page 71 and 72:
3.2. ABEL’s position in mathemati
Page 73 and 74:
3.3. The state of mathematics 43 tr
Page 75:
3.4. ABEL’s legacy 45 As can be s
Page 79 and 80:
Chapter 4 The position and role of
Page 81 and 82:
4.1. Outline of ABEL’s results an
Page 83 and 84:
4.2. Mathematical change as a histo
Page 85:
4.2. Mathematical change as a histo
Page 88 and 89:
58 Chapter 5. Towards unsolvable eq
Page 90 and 91:
Page 92 and 93:
Page 94 and 95:
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
98 Chapter 6. Algebraic insolubilit
Page 130 and 131:
100 Chapter 6. Algebraic insolubili
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
Page 154 and 155:
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
Page 171 and 172:
Chapter 7 Particular classes of equ
Page 173 and 174:
7.1. Solubility of Abelian equation
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
7.2. Elliptic functions 153 Figure
Page 185 and 186:
7.2. Elliptic functions 155 7.2.1 T
Page 187 and 188:
7.3. The concept of irreducibility
Page 189 and 190:
7.3. The concept of irreducibility
Page 191:
7.4. Enlarging the class of solvabl
Page 194 and 195:
164 Chapter 8. A grand theory in sp
Page 196 and 197:
Page 198 and 199:
Page 200 and 201:
Page 202 and 203:
Page 204 and 205:
Page 206 and 207:
Page 208 and 209:
Page 210 and 211:
Page 212 and 213:
Page 214 and 215:
Page 216 and 217:
Page 219:
Part III Interlude: ABEL and the
Page 222 and 223:
192 Chapter 9. The nineteenth-centu
Page 224 and 225:
194 Chapter 10. Toward rigorization
Page 226 and 227:
Page 228 and 229:
Page 230 and 231:
Page 232 and 233:
Page 234 and 235:
Page 236 and 237:
Page 238 and 239:
208 Chapter 11. CAUCHY’s new foun
Page 240 and 241:
Page 242 and 243:
Page 244 and 245:
Page 246 and 247:
Page 248 and 249:
Page 251 and 252:
Chapter 12 ABEL’s reading of CAUC
Page 253 and 254:
12.1. ABEL’s critical attitude 22
Page 255 and 256:
Page 257 and 258:
Page 259 and 260:
12.3. Convergence 229 12.3 Converge
Page 261 and 262:
12.3. Convergence 231 and {εm} was
Page 263 and 264:
12.4. Continuity 233 it followed th
Page 265 and 266:
12.4. Continuity 235 Actually, if t
Page 267 and 268:
12.4. Continuity 237 DIRICHLET intr
Page 269 and 270:
12.5. ABEL’s “exception” 239
Page 271 and 272:
12.6. A curious reaction: Lehrsatz
Page 273 and 274:
Page 275 and 276:
Page 277 and 278:
12.7. From power series to absolute
Page 279 and 280:
12.7. From power series to absolute
Page 281 and 282:
12.8. Product theorems of infinite
Page 283 and 284:
12.8. Product theorems of infinite
Page 285 and 286:
12.9. ABEL’s proof of the binomia
Page 287 and 288:
Page 289 and 290:
Page 291 and 292:
12.10. Aspects of ABEL’s binomial
Page 293:
12.10. Aspects of ABEL’s binomial
Page 296 and 297:
266 Chapter 13. ABEL and OLIVIER on
Page 298 and 299:
Page 300 and 301:
Page 302 and 303:
Page 304 and 305:
Page 307 and 308:
Chapter 14 Reception of ABEL’s co
Page 309 and 310:
14.1. Reception of ABEL’s rigoriz
Page 311 and 312:
14.2. Conclusion 281 of basic notio
Page 313:
Part IV Elliptic functions and the
Page 316 and 317:
286 Chapter 15. Elliptic integrals
Page 318 and 319:
Page 320 and 321:
Page 322 and 323:
Page 324 and 325:
Page 326 and 327:
Page 328 and 329:
Page 330 and 331:
300 Chapter 16. The idea of inverti
Page 332 and 333:
Page 334 and 335:
Page 336 and 337:
Page 338 and 339:
Page 340 and 341:
Page 342 and 343:
Page 344 and 345:
Page 346 and 347:
Page 348 and 349:
Page 351 and 352:
Chapter 17 Steps in the process of
Page 353 and 354:
17.1. Infinite representations 323
Page 355 and 356:
17.2. Elliptic functions as ratios
Page 357 and 358:
17.2. Elliptic functions as ratios
Page 359 and 360:
17.3. Characterization of ABEL’s
Page 361 and 362:
Chapter 18 Tools in ABEL’s resear
Page 363 and 364:
18.1. Transformation theory 333 The
Page 365 and 366:
18.1. Transformation theory 335 Obv
Page 367 and 368:
18.1. Transformation theory 337 Sum
Page 369 and 370:
18.2. Integration in logarithmic te
Page 371 and 372:
Page 373 and 374:
Page 375 and 376:
18.3. Conclusion 345 Summary. ABEL
Page 377 and 378:
Chapter 19 The Paris memoir N. H. A
Page 379 and 380:
19.1. ABEL’s approach to the Pari
Page 381 and 382:
19.2. The contents of ABEL’s Pari
Page 383 and 384:
Page 385 and 386:
Page 387 and 388:
Page 389 and 390:
Page 391 and 392:
Page 393 and 394:
Page 395 and 396:
Page 397 and 398:
Page 399 and 400:
Page 401 and 402:
19.3. Additional, tentative remarks
Page 403 and 404:
19.3. Additional, tentative remarks
Page 405 and 406:
19.4. The fate of the Paris memoir
Page 407 and 408:
19.6. Conclusion 377 hyperelliptic
Page 409 and 410:
Chapter 20 General approaches to el
Page 411 and 412:
20.2. Other ways of introducing ell
Page 413: 20.3. Conclusion 383 All these four
Page 417 and 418: Chapter 21 ABEL’s mathematics and
Page 419 and 420: 21.1. From formulae to concepts 389
Page 421 and 422: 21.1. From formulae to concepts 391
Page 423 and 424: 21.2. Concepts and classes enter ma
Page 425 and 426: 21.3. The role of counter examples
Page 431: 21.4. Conclusion 401 It is beyond t
Page 434 and 435: 404 Appendix A. ABEL’s correspond
Page 437 and 438: Appendix B ABEL’s manuscripts Man
Page 439 and 440: 1. Précis d’une théorie des fon
Page 441 and 442: Bibliography Abel (MS:351:A). “M
Page 443 and 444: Bibliography 413 in: Journal für d
Page 445 and 446: Bibliography 415 — (1990). “Geo
Page 447 and 448: Bibliography 417 — (1830). “Mé
Page 449 and 450: Bibliography 419 — (1768). “Ins
Page 451 and 452: Bibliography 421 Grattan-Guinness,
Page 453 and 454: Bibliography 423 Jahnke, H. N. (198
Page 455 and 456: Bibliography 425 Legendre, A. M. (1
Page 457 and 458: Bibliography 427 Rosen, M. (1981).
Page 459: Bibliography 429 Toti Rigatelli, L.
Page 462 and 463: 432 Index of names Frobenius, Georg
Page 466 and 467: 436 Index convergence tests, 265 co
Page 469 and 470: RePoSS issues #1 (2008-7) Marco N.
show all

RePoSS #11: The Mathematics of Niels Henrik Abel: Continuation ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?