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

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Part V ABEL’s mathematics and the rise <strong>of</strong> concepts 385
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RePoSS: Research Publications on Sc
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The Mathematics of NIELS HENRIK ABE
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The Mathematics of NIELS HENRIK ABE
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Contents Contents i List of Tables
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8.3 Refocusing on the equation . .
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V ABEL’s mathematics and the rise
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List of Figures 2.1 NIELS HENRIK AB
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List of Boxes 1 The algebraic reduc
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Summary The present PhD dissertatio
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Preface to the 2004 edition For thi
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in connection with the Abel centenn
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items published in the same year ar
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the Mittag-Leffler archives in Djur
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Chapter 1 Introduction In the after
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1.2. The mathematical topics involv
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1.3. Themes from early nineteenth-c
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1.4. Reflections on methodology 9 l
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1.4. Reflections on methodology 11
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18 Chapter 2. Biography of NIELS HE
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Chapter 3 Historical background The
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3.2. ABEL’s position in mathemati
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3.3. The state of mathematics 43 tr
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3.4. ABEL’s legacy 45 As can be s
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Chapter 4 The position and role of
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4.1. Outline of ABEL’s results an
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4.2. Mathematical change as a histo
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4.2. Mathematical change as a histo
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58 Chapter 5. Towards unsolvable eq
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98 Chapter 6. Algebraic insolubilit
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100 Chapter 6. Algebraic insolubili
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Chapter 7 Particular classes of equ
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7.1. Solubility of Abelian equation
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7.2. Elliptic functions 153 Figure
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7.2. Elliptic functions 155 7.2.1 T
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7.3. The concept of irreducibility
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7.3. The concept of irreducibility
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7.4. Enlarging the class of solvabl
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164 Chapter 8. A grand theory in sp
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Part III Interlude: ABEL and the
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192 Chapter 9. The nineteenth-centu
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194 Chapter 10. Toward rigorization
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208 Chapter 11. CAUCHY’s new foun
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Chapter 12 ABEL’s reading of CAUC
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12.1. ABEL’s critical attitude 22
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12.3. Convergence 229 12.3 Converge
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12.3. Convergence 231 and {εm} was
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12.4. Continuity 233 it followed th
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12.4. Continuity 235 Actually, if t
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12.4. Continuity 237 DIRICHLET intr
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12.5. ABEL’s “exception” 239
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12.6. A curious reaction: Lehrsatz
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12.7. From power series to absolute
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12.7. From power series to absolute
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12.8. Product theorems of infinite
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12.8. Product theorems of infinite
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12.9. ABEL’s proof of the binomia
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12.10. Aspects of ABEL’s binomial
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12.10. Aspects of ABEL’s binomial
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266 Chapter 13. ABEL and OLIVIER on
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Chapter 14 Reception of ABEL’s co
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14.1. Reception of ABEL’s rigoriz
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14.2. Conclusion 281 of basic notio
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Part IV Elliptic functions and the
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286 Chapter 15. Elliptic integrals
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300 Chapter 16. The idea of inverti
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Chapter 17 Steps in the process of
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17.1. Infinite representations 323
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17.2. Elliptic functions as ratios
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17.2. Elliptic functions as ratios
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17.3. Characterization of ABEL’s
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Chapter 18 Tools in ABEL’s resear
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Page 367 and 368: 18.1. Transformation theory 337 Sum
Page 369 and 370: 18.2. Integration in logarithmic te
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
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Page 405 and 406: 19.4. The fate of the Paris memoir
Page 407 and 408: 19.6. Conclusion 377 hyperelliptic
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Page 411 and 412: 20.2. Other ways of introducing ell
Page 413: 20.3. Conclusion 383 All these four
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Page 433 and 434: Appendix A ABEL’s correspondence
Page 435: Table A.1: Correspondence sorted by
Page 438 and 439: 408 Appendix B. ABEL’s manuscript
Page 440 and 441: 410 Appendix B. ABEL’s manuscript
Page 442 and 443: 412 Bibliography Abel, N. H. (1826b
Page 444 and 445: 414 Bibliography Ayoub, R. G. (1980
Page 446 and 447: 416 Bibliography Cauchy, A.-L. (182
Page 448 and 449: 418 Bibliography Dirichlet, G. L. (
Page 450 and 451: 420 Bibliography solvi posse”. in
Page 452 and 453: 422 Bibliography II (1844), pp. 275
Page 454 and 455: 424 Bibliography chen Akademie der
Page 456 and 457: 426 Bibliography Ore, Ø. (Jan. 195
Page 458 and 459: 428 Bibliography Seidel, P. L. (184
Page 461 and 462: Index of names Abbati, Pietro (1768
Page 463: Index of names 433 Lützen, Jesper,
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436 Index convergence tests, 265 co
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RePoSS issues #1 (2008-7) Marco N.
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