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

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Part II “My favorite subject is algebra” 47
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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
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: 1.4. Reflections on methodology 13
Page 45: 1.4. Reflections on methodology 15
Page 48 and 49: 18 Chapter 2. Biography of NIELS HE
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 80 and 81: 50 Chapter 4. The position and role
Page 87 and 88: Chapter 5 Towards unsolvable equati
Page 89 and 90: 5.1. Algebraic solubility before LA
Page 95 and 96: 5.2. LAGRANGE’s theory of equatio
Page 103 and 104: 5.3. Solubility of cyclotomic equat
Page 111 and 112: 5.4. Belief in algebraic solubility
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Page 115 and 116: 5.5. RUFFINI’s proofs of the inso
Page 121 and 122: 5.6. CAUCHY’ theory of permutatio
Page 123 and 124: 5.6. CAUCHY’ theory of permutatio
Page 125 and 126: 5.7. Some algebraic tools used by G
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Chapter 6 ABEL on the algebraic ins
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6.1. The first break with tradition
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6.3. Classification of algebraic ex
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6.4. ABEL and the theory of permuta
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6.5. Permutations linked to root ex
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6.6. Combination into an impossibil
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6.7. ABEL and RUFFINI 123 The noteb
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6.9. Reception of ABEL’s work on
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6.10. Summary 139 of ABEL’S argum
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142 Chapter 7. Particular classes o
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Chapter 8 A grand theory in spe: al
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8.2. Construction of the irreducibl
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8.3. Refocusing on the equation 171
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8.4. Further ideas on the theory of
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8.4. Further ideas on the theory of
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8.5. General resolution of the prob
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Chapter 9 The nineteenth-century ch
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Chapter 10 Toward rigorization of a
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10.1. EULER’s vision of analysis
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10.2. LAGRANGE’s new focus on rig
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10.3. Early rigorization of theory
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10.4. New types of series 205 Figur
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Chapter 11 CAUCHY’s new foundatio
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11.2. CAUCHY’s concepts of limits
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11.3. Divergent series have no sum
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11.4. Means of testing for converge
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11.5. CAUCHY’s proof of the binom
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11.5. CAUCHY’s proof of the binom
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11.6. Early reception of CAUCHY’s
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222 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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