Notes on Fermat's last theorem:
Around 1637, the French jurist Pierre de Fermat scribbled in the margin of his copy of the book Arithmetica what came to be known as Fermat's Last Theorem, the most famous question in mathematical history. Stating that it is impossible to split a cube into two cubes, or a fourth power into two...
Gespeichert in:
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1996
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| Schriftenreihe: | Canadian Mathematical Society series of monographs and advanced texts
[13] |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Around 1637, the French jurist Pierre de Fermat scribbled in the margin of his copy of the book Arithmetica what came to be known as Fermat's Last Theorem, the most famous question in mathematical history. Stating that it is impossible to split a cube into two cubes, or a fourth power into two fourth powers, or any higher power into two like powers, but not leaving behind the marvelous proof claimed to have had, Fermat prompted three and a half centuries of mathematical inquiry which culminated recently with the proof of the theorem by Andrew Wiles This book offers the first serious treatment of Fermat's Last Theorem since Wiles's proof. It is based on a series of lectures given by the author to celebrate Wiles's achievement, with each chapter explaining a separate area of number theory as it pertains to Fermat's Last Theorem. Together, they provide a concise history of the theorem as well as a brief discussion of Wiles's proof and its implications. Requiring little more than one year of university mathematics and some interest in formulas, this overview provides many useful tips and cites numerous references for those who desire more mathematical detail This book not only tells us why, in all likelihood, Fermat did not have the proof for his last theorem, it also takes us through historical attempts to crack the theorem, the prizes that were offered along the way, and the consequent motivation for the development of other areas of mathematics. Notes on Fermat's Last Theorem is invaluable for students of mathematics, and of real interest to those in the physical sciences, engineering, and computer sciences - indeed for anyone who craves a glimpse at this fascinating piece of mathematical history |
| Beschreibung: | XV, 222 S. Ill., graph. Darst. |
| ISBN: | 0471062618 |
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| 490 | 1 | |a Canadian Mathematical Society series of monographs and advanced texts |v [13] | |
| 520 | 3 | |a Around 1637, the French jurist Pierre de Fermat scribbled in the margin of his copy of the book Arithmetica what came to be known as Fermat's Last Theorem, the most famous question in mathematical history. Stating that it is impossible to split a cube into two cubes, or a fourth power into two fourth powers, or any higher power into two like powers, but not leaving behind the marvelous proof claimed to have had, Fermat prompted three and a half centuries of mathematical inquiry which culminated recently with the proof of the theorem by Andrew Wiles | |
| 520 | |a This book offers the first serious treatment of Fermat's Last Theorem since Wiles's proof. It is based on a series of lectures given by the author to celebrate Wiles's achievement, with each chapter explaining a separate area of number theory as it pertains to Fermat's Last Theorem. Together, they provide a concise history of the theorem as well as a brief discussion of Wiles's proof and its implications. Requiring little more than one year of university mathematics and some interest in formulas, this overview provides many useful tips and cites numerous references for those who desire more mathematical detail | ||
| 520 | |a This book not only tells us why, in all likelihood, Fermat did not have the proof for his last theorem, it also takes us through historical attempts to crack the theorem, the prizes that were offered along the way, and the consequent motivation for the development of other areas of mathematics. Notes on Fermat's Last Theorem is invaluable for students of mathematics, and of real interest to those in the physical sciences, engineering, and computer sciences - indeed for anyone who craves a glimpse at this fascinating piece of mathematical history | ||
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Datensatz im Suchindex
| _version_ | 1804125317489491968 |
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| adam_text | Contents
I. Quasi historical introduction 1
The cases n = 2 and n = 4. The Parisian Academy in the 1840 s.
Notes: Some details. Descent. Algebraic numbers and integers.
II. Remarks on unique factorization 11
A digression.
Notes: Continued fractions. Plagiarism.
HI. Elementary methods 19
Sophie Germain, Abel s formulas, Mirimanoff Wieferich,...
Notes: Fermat s Theorem. Bernoulli numbers. Euler Maclaurin.
Pseudoprimes. Fermat numbers. Mersenne primes. Cranks.
IV. Rummer s arguments 31
Proof of the FLT for regular primes.
Notes: Some remarks for undergraduates on elementary algebra.
Equivalence relations.
V. Why do we believe Wiles? More quasi history 41
Rantings. Work on the FLT this century.
Notes: Euler s conjecture. The growing of the gap .
VI. Diophantus and Fermat 51
What the study of diophantine equations is really all about.
Notes: The chord and tangent method. Examples.
VII. A child s introduction to elliptic functions 65
For a precocious child.
Notes: Discriminants.
VIII. Local and global 75
Some remarks on p adic numbers.
Notes: The Riemann ^ function. Much more on p adic numbers.
IX. Curves 89
Particularly, about elliptic curves.
Notes: Minimal model. Semisimplicity of the Frey curve.
Birational equivalence.
X. Modular forms 103
Some formulas and assertions.
Notes: More formulas. The discriminant function.
xv
XI. The Modularity Conjecture 113
An attempt at an explanation.
Notes: What s in a name?
XII. The functional equation 123
Poisson summation; ^ functions.
Notes: Details. Hecke operators.
xm. Zeta functions and L series 135
Introduction to the Birch Swinnerton Dyer Conjectures.
Notes: Hasse s Theorem.
XIV. The ABC Conjecture 143
Darmon and Granville s Generalized Fermat Equation
Notes: Hawkins primes. The Generalized Fermat Conjecture.
XV. Heights 151
Remarks on the Mordell Weil Theorem.
Notes: Lehmer s Question. Elliptic curves of high rank.
XVI. Class number of imaginary quadratic number fields 161
The proof of Goldfeld Gross Zagier.
Notes: Composition of quadratic forms. Tate Shafarevitch group.
Jacobian. Heegner points.
XVII. Wiles proof 177
Not the commutative algebra, of course.
Notes: Some details.
Appendices
A. Remarks on Fermat s Last Theorem 187
For those who only want to pretend to have read the rQst of this book.
B. The Devil and Simon Flagg , by Arthur Forges 201
The devil fails where Wiles will succeed.
C. Math Riots Prove Fun Incalculable , by Eric Torn 207
Is the FLT truly as important as sport?
Index 211
|
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| dewey-sort | 3512 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010831424 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:59:38Z |
| institution | BVB |
| isbn | 0471062618 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007239006 |
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| physical | XV, 222 S. Ill., graph. Darst. |
| publishDate | 1996 |
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| publisher | Wiley |
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| series | Canadian Mathematical Society series of monographs and advanced texts |
| series2 | Canadian Mathematical Society series of monographs and advanced texts |
| spelling | Van der Poorten, Alf J. 1942-2010 Verfasser (DE-588)135854075 aut Notes on Fermat's last theorem Alf van der Poorten New York [u.a.] Wiley 1996 XV, 222 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Canadian Mathematical Society series of monographs and advanced texts [13] Around 1637, the French jurist Pierre de Fermat scribbled in the margin of his copy of the book Arithmetica what came to be known as Fermat's Last Theorem, the most famous question in mathematical history. Stating that it is impossible to split a cube into two cubes, or a fourth power into two fourth powers, or any higher power into two like powers, but not leaving behind the marvelous proof claimed to have had, Fermat prompted three and a half centuries of mathematical inquiry which culminated recently with the proof of the theorem by Andrew Wiles This book offers the first serious treatment of Fermat's Last Theorem since Wiles's proof. It is based on a series of lectures given by the author to celebrate Wiles's achievement, with each chapter explaining a separate area of number theory as it pertains to Fermat's Last Theorem. Together, they provide a concise history of the theorem as well as a brief discussion of Wiles's proof and its implications. Requiring little more than one year of university mathematics and some interest in formulas, this overview provides many useful tips and cites numerous references for those who desire more mathematical detail This book not only tells us why, in all likelihood, Fermat did not have the proof for his last theorem, it also takes us through historical attempts to crack the theorem, the prizes that were offered along the way, and the consequent motivation for the development of other areas of mathematics. Notes on Fermat's Last Theorem is invaluable for students of mathematics, and of real interest to those in the physical sciences, engineering, and computer sciences - indeed for anyone who craves a glimpse at this fascinating piece of mathematical history Theorema van Fermat gtt Fermat's last theorem Fermatsche Vermutung (DE-588)4154012-8 gnd rswk-swf Fermatsche Vermutung (DE-588)4154012-8 s DE-604 Canadian Mathematical Society series of monographs and advanced texts [13] (DE-604)BV012067942 13 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007239006&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Van der Poorten, Alf J. 1942-2010 Notes on Fermat's last theorem Canadian Mathematical Society series of monographs and advanced texts Theorema van Fermat gtt Fermat's last theorem Fermatsche Vermutung (DE-588)4154012-8 gnd |
| subject_GND | (DE-588)4154012-8 |
| title | Notes on Fermat's last theorem |
| title_auth | Notes on Fermat's last theorem |
| title_exact_search | Notes on Fermat's last theorem |
| title_full | Notes on Fermat's last theorem Alf van der Poorten |
| title_fullStr | Notes on Fermat's last theorem Alf van der Poorten |
| title_full_unstemmed | Notes on Fermat's last theorem Alf van der Poorten |
| title_short | Notes on Fermat's last theorem |
| title_sort | notes on fermat s last theorem |
| topic | Theorema van Fermat gtt Fermat's last theorem Fermatsche Vermutung (DE-588)4154012-8 gnd |
| topic_facet | Theorema van Fermat Fermat's last theorem Fermatsche Vermutung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007239006&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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