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

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RePoSS (Research Publications on Science Studies) is a series of electronic publications originating in research done at the Centre for Science Studies, University of Aarhus. The publications are available from the Centre homepage (��). ISSN 1903-413X Centre for Science Studies University of Aarhus Ny Munkegade 120, building 1520 DK-8000 Aarhus C DENMARK �� Faculty of Science Department of Science Studies 1
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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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18.1. Transformation theory 333 The
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18.1. Transformation theory 335 Obv
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18.1. Transformation theory 337 Sum
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18.2. Integration in logarithmic te
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18.3. Conclusion 345 Summary. ABEL
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Chapter 19 The Paris memoir N. H. A
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19.1. ABEL’s approach to the Pari
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19.2. The contents of ABEL’s Pari
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19.3. Additional, tentative remarks
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19.3. Additional, tentative remarks
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19.4. The fate of the Paris memoir
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19.6. Conclusion 377 hyperelliptic
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Chapter 20 General approaches to el
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20.2. Other ways of introducing ell
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20.3. Conclusion 383 All these four
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Chapter 21 ABEL’s mathematics and
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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 465 and 466: Index École Normale, 40, 187 Écol
Page 467: Index 437 Lagrange interpolation, 3
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