Invitation To The Mathematics Of Fermat Wiles

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Author: Yves Hellegouarch
Publisher: Elsevier
ISBN: 9780080478777
Size: 68.42 MB
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Invitation To The Mathematics Of Fermat Wiles by Yves Hellegouarch

Original Title: Invitation To The Mathematics Of Fermat Wiles

Assuming only modest knowledge of undergraduate level math, Invitation to the Mathematics of Fermat-Wiles presents diverse concepts required to comprehend Wiles' extraordinary proof. Furthermore, it places these concepts in their historical context. This book can be used in introduction to mathematics theories courses and in special topics courses on Fermat's last theorem. It contains themes suitable for development by students as an introduction to personal research as well as numerous exercises and problems. However, the book will also appeal to the inquiring and mathematically informed reader intrigued by the unraveling of this fascinating puzzle. Rigorously presents the concepts required to understand Wiles' proof, assuming only modest undergraduate level math Sets the math in its historical context Contains several themes that could be further developed by student research and numerous exercises and problems Written by Yves Hellegouarch, who himself made an important contribution to the proof of Fermat's last theorem

Arithmetic Tales

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Author: Olivier Bordellès
Publisher: Springer Science & Business Media
ISBN: 1447140966
Size: 49.72 MB
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Arithmetic Tales by Olivier Bordellès

Original Title: Arithmetic Tales

Number theory was once famously labeled the queen of mathematics by Gauss. The multiplicative structure of the integers in particular deals with many fascinating problems some of which are easy to understand but very difficult to solve. In the past, a variety of very different techniques has been applied to further its understanding. Classical methods in analytic theory such as Mertens’ theorem and Chebyshev’s inequalities and the celebrated Prime Number Theorem give estimates for the distribution of prime numbers. Later on, multiplicative structure of integers leads to multiplicative arithmetical functions for which there are many important examples in number theory. Their theory involves the Dirichlet convolution product which arises with the inclusion of several summation techniques and a survey of classical results such as Hall and Tenenbaum’s theorem and the Möbius Inversion Formula. Another topic is the counting integer points close to smooth curves and its relation to the distribution of squarefree numbers, which is rarely covered in existing texts. Final chapters focus on exponential sums and algebraic number fields. A number of exercises at varying levels are also included. Topics in Multiplicative Number Theory introduces offers a comprehensive introduction into these topics with an emphasis on analytic number theory. Since it requires very little technical expertise it will appeal to a wide target group including upper level undergraduates, doctoral and masters level students.

The Fermat Diary

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Author: Charles J. Mozzochi
Publisher: American Mathematical Soc.
ISBN: 9780821826706
Size: 61.61 MB
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The Fermat Diary by Charles J. Mozzochi

Original Title: The Fermat Diary

This book concentrates on the final chapter of the story of perhaps the most famous mathematics problem of our time: Fermat's Last Theorem. The full story begins in 1637, with Pierre de Fermat's enigmatic marginal note in his copy of Diophantus's Arithmetica. It ends with the spectacular solution by Andrew Wiles some 350 years later. The Fermat Diary provides a record in pictures and words of the dramatic time from June 1993 to August 1995, including the period when Wiles completed the last stages of the proof and concluding with the mathematical world's celebration of Wiles' result at Boston University. This diary takes us through the process of discovery as reported by those who worked on the great puzzle: Gerhard Frey who conjectured that Shimura-Taniyama implies Fermat; Ken Ribet who followed a difficult and speculative plan of attack suggested by Jean-Pierre Serre and established the statement by Frey; and Andrew Wiles who announced a proof of enough of the Shimura-Taniyama conjecture to settle Fermat's Last Theorem, only to announce months later that there was a gap in the proof. Finally, we are brought to the historic event on September 19, 1994, when Wiles, with the collaboration of Richard Taylor, dramatically closed the gap. The book follows the much-in-demand Wiles through his travels and lectures, finishing with the Instructional Conference on Number Theory and Arithmetic Geometry at Boston University. There are many important names in the recent history of Fermat's Last Theorem. This book puts faces and personalities to those names. Mozzochi also uncovers the details of certain key pieces of the story. For instance, we learn in Frey's own words the story of his conjecture, about his informal discussion and later lecture at Oberwolfach and his letter containing the actual statement. We learn from Faltings about his crucial role in the weeks before Wiles made his final announcement. An appendix contains the Introduction of Wiles' Annals paper in which he describes the evolution of his solution and gives a broad overview of his methods. Shimura explains his position concerning the evolution of the Shimura-Taniyama conjecture. Mozzochi also conveys the atmosphere of the mathematical community--and the Princeton Mathematics Department in particular--during this important period in mathematics. This eyewitness account and wonderful collection of photographs capture the marvel and unfolding drama of this great mathematical and human story.

Mathematics And Music

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Author: Gerard Assayag
Publisher: Springer Science & Business Media
ISBN: 9783540437277
Size: 56.75 MB
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Mathematics And Music by Gerard Assayag

Original Title: Mathematics And Music

In Western Civilization Mathematics and Music have a long and interesting history in common, with several interactions, traditionally associated with the name of Pythagoras but also with a significant number of other mathematicians, like Leibniz, for instance. Mathematical models can be found for almost all levels of musical activities from composition to sound production by traditional instruments or by digital means. Modern music theory has been incorporating more and more mathematical content during the last decades. This book offers a journey into recent work relating music and mathematics. It contains a large variety of articles, covering the historical aspects, the influence of logic and mathematical thought in composition, perception and understanding of music and the computational aspects of musical sound processing. The authors illustrate the rich and deep interactions that exist between Mathematics and Music.

Invitation Aux Math Matiques De Fermat Wiles

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Author: Yves Hellegouarch
ISBN: 9782100537211
Size: 14.19 MB
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Invitation Aux Math Matiques De Fermat Wiles by Yves Hellegouarch

Original Title: Invitation Aux Math Matiques De Fermat Wiles

Retrace l'aventure intellectuelle qui a conduit à l'élucidation par Wiles d'une des plus belles énigmes mathématiques. S'adresse aux étudiants du second cycle et peut servir d'introduction à diverses théories habituellement enseignées en licence et maîtrise (algèbre commutative, théorie des corps, représentations linéaires des groupes, géométrie algébrique, fonctions d'une variable complexe).--[Memento].

Books In Print

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Books In Print by

Original Title: Books In Print

Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Notes On Fermat S Last Theorem

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Author: A. J. Van Der Poorten
Publisher: Wiley-Interscience
Size: 56.78 MB
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Notes On Fermat S Last Theorem by A. J. Van Der Poorten

Original Title: 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 fourth powers, or any higher power into two like powers, but not leaving behind the marvelous proof he claimed to have had, Fermat prompted three and a half centuries of mathematical inquiry which culminated only 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. The book's most distinctive feature is its easy-to-read, humorous style, complete with examples, anecdotes, and some of the lesser-known mathematics underlying the newly discovered proof. In the author's own words, the book deals with "serious mathematics without being too serious about it." Alf van der Poorten demystifies mathematical research, offers an intuitive approach to the subject-loosely suggesting various definitions and unexplained facts-and invites the reader to fill in the missing links in some of the mathematical claims. Entertaining, controversial, even outrageous, 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. An exciting introduction to modern number theory as reflected by the history of Fermat's Last Theorem This book displays the unique talents of author Alf van der Poorten in mathematical exposition for mathematicians. Here, mathematics' most famous question and the ideas underlying its recent solution are presented in a way that appeals to the imagination and leads the reader through related areas of number theory. The first book to focus on Fermat's Last Theorem since Andrew Wiles presented his celebrated proof, Notes on Fermat's Last Theorem surveys 350 years of mathematical history in an amusing and intriguing collection of tidbits, anecdotes, footnotes, exercises, references, illustrations, and more. Proving that mathematics can make for lively reading as well as intriguing thought, this thoroughly accessible treatment Helps students and professionals develop a background in number theory and provides introductions to the various fields of theory that are touched upon * Offers insight into the exciting world of mathematical research * Covers a number of areas appropriate for classroom use * Assumes only one year of university mathematics background even for the more advanced topics * Explains why Fermat surely did not have the proof to his theorem * Examines the efforts of mathematicians over the centuries to solve the problem * Shows how the pursuit of the theorem contributed to the greater development of mathematics

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