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

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Part III Interlude: ABEL and the ‘new rigor’ 189
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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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Page 168 and 169: 138 Chapter 6. Algebraic insolubili
Page 171 and 172: Chapter 7 Particular classes of equ
Page 173 and 174: 7.1. Solubility of Abelian equation
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
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Page 194 and 195: 164 Chapter 8. A grand theory in sp
Page 221 and 222: Chapter 9 The nineteenth-century ch
Page 223 and 224: Chapter 10 Toward rigorization of a
Page 225 and 226: 10.1. EULER’s vision of analysis
Page 227 and 228: 10.2. LAGRANGE’s new focus on rig
Page 229 and 230: 10.3. Early rigorization of theory
Page 235 and 236: 10.4. New types of series 205 Figur
Page 237 and 238: Chapter 11 CAUCHY’s new foundatio
Page 239 and 240: 11.2. CAUCHY’s concepts of limits
Page 241 and 242: 11.3. Divergent series have no sum
Page 243 and 244: 11.4. Means of testing for converge
Page 245 and 246: 11.5. CAUCHY’s proof of the binom
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Page 252 and 253: 222 Chapter 12. ABEL’s reading of
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238 Chapter 12. ABEL’s reading of
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Chapter 13 ABEL and OLIVIER on conv
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13.1. OLIVIER’s theorem 267 imati
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13.2. ABEL’s counter example 269
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13.3. ABEL’s general refutation 2
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13.4. More characterizations and te
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13.4. More characterizations and te
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278 Chapter 14. Reception of ABEL
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Chapter 15 Elliptic integrals and f
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15.1. Elliptic transcendentals befo
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15.2. The lemniscate 289 in which t
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15.2. The lemniscate 291 Figure 15.
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15.3. LEGENDRE’s theory of ellipt
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15.3. LEGENDRE’s theory of ellipt
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15.5. Chronology of ABEL’s work o
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Chapter 16 The idea of inverting el
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16.2. Inversion in the Recherches 3
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16.3. The division problem 313 16.3
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16.3. The division problem 315 Base
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16.3. The division problem 317 and
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16.4. Perspectives on inversion 319
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322 Chapter 17. Steps in the proces
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332 Chapter 18. Tools in ABEL’s r
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348 Chapter 19. The Paris memoir 19
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350 Chapter 19. The Paris memoir An
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354 Chapter 19. The Paris memoir wh
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356 Chapter 19. The Paris memoir AB
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358 Chapter 19. The Paris memoir Th
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360 Chapter 19. The Paris memoir th
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364 Chapter 19. The Paris memoir se
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366 Chapter 19. The Paris memoir In
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368 Chapter 19. The Paris memoir 2.
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370 Chapter 19. The Paris memoir wh
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374 Chapter 19. The Paris memoir Fi
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378 Chapter 19. The Paris memoir As
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380 Chapter 20. General approaches
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382 Chapter 20. General approaches
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Part V ABEL’s mathematics and the
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388 Chapter 21. ABEL’s mathematic
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Appendix A ABEL’s correspondence
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Table A.1: Correspondence sorted by
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408 Appendix B. ABEL’s manuscript
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410 Appendix B. ABEL’s manuscript
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412 Bibliography Abel, N. H. (1826b
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414 Bibliography Ayoub, R. G. (1980
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416 Bibliography Cauchy, A.-L. (182
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418 Bibliography Dirichlet, G. L. (
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420 Bibliography solvi posse”. in
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422 Bibliography II (1844), pp. 275
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424 Bibliography chen Akademie der
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426 Bibliography Ore, Ø. (Jan. 195
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428 Bibliography Seidel, P. L. (184
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Index of names Abbati, Pietro (1768
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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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RePoSS #11: The Mathematics of Niels Henrik Abel: Continuation ...

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