The Last Theorem

The Last Theorem Pdf

The Last Theorem

Author: ,

Publisher: Del Rey

ISBN: 0345509684

Genre: Fiction

Page: 320

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Book Summary: Two of science fiction’s most renowned writers join forces for a storytelling sensation. The historic collaboration between Frederik Pohl and his fellow founding father of the genre, Arthur C. Clarke, is both a momentous literary event and a fittingly grand farewell from the late, great visionary author of 2001: A Space Odyssey. The Last Theorem is a story of one man’s mathematical obsession, and a celebration of the human spirit and the scientific method. It is also a gripping intellectual thriller in which humanity, facing extermination from all-but-omnipotent aliens, the Grand Galactics, must overcome differences of politics and religion and come together . . . or perish. In 1637, the French mathematician Pierre de Fermat scrawled a note in the margin of a book about an enigmatic theorem: “I have discovered a truly marvelous proof of this proposition which this margin is too narrow to contain.” He also neglected to record his proof elsewhere. Thus began a search for the Holy Grail of mathematics–a search that didn’t end until 1994, when Andrew Wiles published a 150-page proof. But the proof was burdensome, overlong, and utilized mathematical techniques undreamed of in Fermat’s time, and so it left many critics unsatisfied–including young Ranjit Subramanian, a Sri Lankan with a special gift for mathematics and a passion for the famous “Last Theorem.” When Ranjit writes a three-page proof of the theorem that relies exclusively on knowledge available to Fermat, his achievement is hailed as a work of genius, bringing him fame and fortune. But it also brings him to the attention of the National Security Agency and a shadowy United Nations outfit called Pax per Fidem, or Peace Through Transparency, whose secretive workings belie its name. Suddenly Ranjit–together with his wife, Myra de Soyza, an expert in artificial intelligence, and their burgeoning family–finds himself swept up in world-shaking events, his genius for abstract mathematical thought put to uses that are both concrete and potentially deadly. Meanwhile, unbeknownst to anyone on Earth, an alien fleet is approaching the planet at a significant percentage of the speed of light. Their mission: to exterminate the dangerous species of primates known as homo sapiens.


Fermat’s Last Theorem

Fermat’s Last Theorem Pdf

Fermat’s Last Theorem

Author: Simon Singh

Publisher: HarperCollins UK

ISBN: 0007381999

Genre: Science

Page: 368

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Book Summary: ‘I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.’


Modular Forms and Fermat’s Last Theorem

Modular Forms and Fermat’s Last Theorem Pdf

Modular Forms and Fermat’s Last Theorem

Author: Gary Cornell,Joseph H. Silverman,Glenn Stevens

Publisher: Springer Science & Business Media

ISBN: 1461219744

Genre: Mathematics

Page: 582

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Book Summary: This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource.


13 Lectures on Fermat's Last Theorem

13 Lectures on Fermat's Last Theorem Pdf

13 Lectures on Fermat's Last Theorem

Author: Paulo Ribenboim

Publisher: Springer Science & Business Media

ISBN: 1468493426

Genre: Mathematics

Page: 302

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Book Summary: Fermat's problem, also ealled Fermat's last theorem, has attraeted the attention of mathematieians far more than three eenturies. Many clever methods have been devised to attaek the problem, and many beautiful theories have been ereated with the aim of proving the theorem. Yet, despite all the attempts, the question remains unanswered. The topie is presented in the form of leetures, where I survey the main lines of work on the problem. In the first two leetures, there is a very brief deseription of the early history, as well as a seleetion of a few of the more representative reeent results. In the leetures whieh follow, I examine in sue eession the main theories eonneeted with the problem. The last two lee tu res are about analogues to Fermat's theorem. Some of these leetures were aetually given, in a shorter version, at the Institut Henri Poineare, in Paris, as well as at Queen's University, in 1977. I endeavoured to produee a text, readable by mathematieians in general, and not only by speeialists in number theory. However, due to a limitation in size, I am aware that eertain points will appear sketehy. Another book on Fermat's theorem, now in preparation, will eontain a eonsiderable amount of the teehnieal developments omitted here. It will serve those who wish to learn these matters in depth and, I hope, it will clarify and eomplement the present volume.


The Simpsons and Their Mathematical Secrets

The Simpsons and Their Mathematical Secrets Pdf

The Simpsons and Their Mathematical Secrets

Author: Simon Singh

Publisher: Bloomsbury Publishing USA

ISBN: 1620402793

Genre: Mathematics

Page: 288

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Book Summary: The brainy book by the bestselling author of Fermat's Enigma-a must for anyone interested in numbers and mathematics, as well as for the millions of Simpsons fans worldwide. “Simon Singh's excellent book blows the lid off a decades-long conspiracy to secretly educate cartoon viewers.” ?David X. Cohen, writer for The Simpsons and Futurama You may have watched hundreds of episodes of The Simpsons (and its sister show Futurama) without ever realizing that cleverly embedded in many plots are subtle references to mathematics, ranging from well-known equations to cutting-edge theorems and conjectures. That they exist, Simon Singh reveals, underscores the brilliance of the shows' writers, many of whom have advanced degrees in mathematics in addition to their unparalleled sense of humor. While recounting memorable episodes such as “Bart the Genius” and “Homer3,” Singh weaves in mathematical stories that explore everything from p to Mersenne primes, Euler's equation to the unsolved riddle of P v. NP; from perfect numbers to narcissistic numbers, infinity to even bigger infinities, and much more. Along the way, Singh meets members of The Simpsons' brilliant writing team-among them David X. Cohen, Al Jean, Jeff Westbrook, and Mike Reiss-whose love of arcane mathematics becomes clear as they reveal the stories behind the episodes. With wit and clarity, displaying a true fan's zeal, and replete with images from the shows, photographs of the writers, and diagrams and proofs, The Simpsons and Their Mathematical Secrets offers an entirely new insight into the most successful show in television history.


Fermat’s Last Theorem for Amateurs

Fermat’s Last Theorem for Amateurs Pdf

Fermat’s Last Theorem for Amateurs

Author: Paulo Ribenboim

Publisher: Springer Science & Business Media

ISBN: 0387216928

Genre: Mathematics

Page: 407

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Book Summary: In 1995, Andrew Wiles completed a proof of Fermat's Last Theorem. Although this was certainly a great mathematical feat, one shouldn't dismiss earlier attempts made by mathematicians and clever amateurs to solve the problem. In this book, aimed at amateurs curious about the history of the subject, the author restricts his attention exclusively to elementary methods that have produced rich results.


Number Theory Related to Fermat’s Last Theorem

Number Theory Related to Fermat’s Last Theorem Pdf

Number Theory Related to Fermat’s Last Theorem

Author: Koblitz

Publisher: Springer Science & Business Media

ISBN: 1489966994

Genre: Juvenile Nonfiction

Page: 366

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Book Summary:


The Code Book: The Secrets Behind Codebreaking

The Code Book: The Secrets Behind Codebreaking Pdf

The Code Book: The Secrets Behind Codebreaking

Author: Simon Singh

Publisher: Delacorte Books for Young Readers

ISBN: 0375890122

Genre: Young Adult Nonfiction

Page: 272

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Book Summary: "As gripping as a good thriller." --The Washington Post Unpack the science of secrecy and discover the methods behind cryptography--the encoding and decoding of information--in this clear and easy-to-understand young adult adaptation of the national bestseller that's perfect for this age of WikiLeaks, the Sony hack, and other events that reveal the extent to which our technology is never quite as secure as we want to believe. Coders and codebreakers alike will be fascinated by history's most mesmerizing stories of intrigue and cunning--from Julius Caesar and his Caeser cipher to the Allies' use of the Enigma machine to decode German messages during World War II. Accessible, compelling, and timely, The Code Book is sure to make readers see the past--and the future--in a whole new way. "Singh's power of explaining complex ideas is as dazzling as ever." --The Guardian


Fermat's Last Theorem: The Proof

Fermat's Last Theorem: The Proof Pdf

Fermat's Last Theorem: The Proof

Author: Takeshi Saito

Publisher: American Mathematical Soc.

ISBN: 0821898493

Genre: Mathematics

Page: 234

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Book Summary: This is the second volume of the book on the proof of Fermat's Last Theorem by Wiles and Taylor (the first volume is published in the same series; see MMONO/243). Here the detail of the proof announced in the first volume is fully exposed. The book also includes basic materials and constructions in number theory and arithmetic geometry that are used in the proof. In the first volume the modularity lifting theorem on Galois representations has been reduced to properties of the deformation rings and the Hecke modules. The Hecke modules and the Selmer groups used to study deformation rings are constructed, and the required properties are established to complete the proof. The reader can learn basics on the integral models of modular curves and their reductions modulo that lay the foundation of the construction of the Galois representations associated with modular forms. More background materials, including Galois cohomology, curves over integer rings, the Néron models of their Jacobians, etc., are also explained in the text and in the appendices.


Ramanujan’s Notebooks

Ramanujan’s Notebooks Pdf

Ramanujan’s Notebooks

Author: Bruce C. Berndt

Publisher: Springer Science & Business Media

ISBN: 1461210887

Genre: Mathematics

Page: 357

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Book Summary: Srinivasa Ramanujan is, arguably, the greatest mathematician that India has produced. His story is quite unusual: although he had no formal education inmathematics, he taught himself, and managed to produce many important new results. With the support of the English number theorist G. H. Hardy, Ramanujan received a scholarship to go to England and study mathematics. He died very young, at the age of 32, leaving behind three notebooks containing almost 3000 theorems, virtually all without proof. G. H. Hardy and others strongly urged that notebooks be edited and published, and the result is this series of books. This volume dealswith Chapters 1-9 of Book II; each theorem is either proved, or a reference to a proof is given.


The Girl Who Played with Fire

The Girl Who Played with Fire Pdf

The Girl Who Played with Fire

Author: Stieg Larsson

Publisher: Penguin Canada

ISBN: 014317729X

Genre: Fiction

Page: 576

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Book Summary: The electrifying follow-up to the phenomenal best seller The Girl with the Dragon Tattoo. The fierce heart of this novel is Lisbeth Salander: the troubled, wise-beyond-her-years genius hacker who teamed up with crusading journalist Mikael Blomkvist in The Girl with the Dragon Tattoo. This time, Lisbeth is implicated in a murder: her fingerprints found on the weapon used to kill two journalists the night before their explosive story about sex trafficking in Sweden was set to be published. Now, while Blomkvist—alone in his belief in her innocence—plunges into his own investigation of the slayings, Lisbeth is drawn into a hunt in which she is the prey, and which compels her to revisit her dark past in an effort to settle with it once and for all.


The Heritage of Thales

The Heritage of Thales Pdf

The Heritage of Thales

Author: W.S. Anglin,J. Lambek

Publisher: Springer Science & Business Media

ISBN: 1461208033

Genre: Science

Page: 331

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Book Summary: The authors' novel approach to some interesting mathematical concepts - not normally taught in other courses - places them in a historical and philosophical setting. Although primarily intended for mathematics undergraduates, the book will also appeal to students in the sciences, humanities and education with a strong interest in this subject. The first part proceeds from about 1800 BC to 1800 AD, discussing, for example, the Renaissance method for solving cubic and quartic equations and providing rigorous elementary proof that certain geometrical problems posed by the ancient Greeks cannot be solved by ruler and compass alone. The second part presents some fundamental topics of interest from the past two centuries, including proof of G del's incompleteness theorem, together with a discussion of its implications.


Fermat's Enigma

Fermat's Enigma Pdf

Fermat's Enigma

Author: Simon Singh

Publisher: Anchor

ISBN: 0525435328

Genre: Mathematics

Page: 336

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Book Summary: xn + yn = zn, where n represents 3, 4, 5, ...no solution "I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain." With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations. What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years. In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it. Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.


Euclid's Window

Euclid's Window Pdf

Euclid's Window

Author: Leonard Mlodinow

Publisher: Simon and Schuster

ISBN: 9781439135372

Genre: Science

Page: 320

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Book Summary: Through Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space -- in the living room or in some other galaxy -- have been the hidden engine of the highest achievements in science and technology. Based on Mlodinow's extensive historical research; his studies alongside colleagues such as Richard Feynman and Kip Thorne; and interviews with leading physicists and mathematicians such as Murray Gell-Mann, Edward Witten, and Brian Greene, Euclid's Window is an extraordinary blend of rigorous, authoritative investigation and accessible, good-humored storytelling that makes a stunningly original argument asserting the primacy of geometry. For those who have looked through Euclid's Window, no space, no thing, and no time will ever be quite the same.


Algebraic Number Theory and Fermat's Last Theorem

Algebraic Number Theory and Fermat's Last Theorem Pdf

Algebraic Number Theory and Fermat's Last Theorem

Author: Ian Stewart,David Tall

Publisher: CRC Press

ISBN: 1498738400

Genre: Mathematics

Page: 322

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Book Summary: Updated to reflect current research, Algebraic Number Theory and Fermat’s Last Theorem, Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics—the quest for a proof of Fermat’s Last Theorem. The authors use this celebrated theorem to motivate a general study of the theory of algebraic numbers from a relatively concrete point of view. Students will see how Wiles’s proof of Fermat’s Last Theorem opened many new areas for future work. New to the Fourth Edition Provides up-to-date information on unique prime factorization for real quadratic number fields, especially Harper’s proof that Z(√14) is Euclidean Presents an important new result: Mihăilescu’s proof of the Catalan conjecture of 1844 Revises and expands one chapter into two, covering classical ideas about modular functions and highlighting the new ideas of Frey, Wiles, and others that led to the long-sought proof of Fermat’s Last Theorem Improves and updates the index, figures, bibliography, further reading list, and historical remarks Written by preeminent mathematicians Ian Stewart and David Tall, this text continues to teach students how to extend properties of natural numbers to more general number structures, including algebraic number fields and their rings of algebraic integers. It also explains how basic notions from the theory of algebraic numbers can be used to solve problems in number theory.


Arthur C. Clarke

Arthur C. Clarke Pdf

Arthur C. Clarke

Author: Gary Westfahl

Publisher: University of Illinois Press

ISBN: 0252050630

Genre: Literary Criticism

Page: 224

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Book Summary: Already renowned for his science fiction and scientific nonfiction, Arthur C. Clarke became the world's most famous science fiction writer after the success of 2001: A Space Odyssey. He then produced novels like Rendezvous with Rama and The Fountains of Paradise that many regard as his finest works. Gary Westfahl closely examines Clarke's remarkable career, ranging from his forgotten juvenilia to the passages he completed for a final novel, The Last Theorem. As Westfahl explains, Clarke's science fiction offered original perspectives on subjects like new inventions, space travel, humanity's destiny, alien encounters, the undersea world, and religion. While not inclined to mysticism, Clarke necessarily employed mystical language to describe the fantastic achievements of advanced aliens and future humans. Westfahl also contradicts the common perception that Clarke's characters were bland and underdeveloped, arguing that these reticent, solitary individuals, who avoid conventional relationships, represent his most significant prediction of the future, as they embody the increasingly common lifestyle of people in the twenty-first century.


The Collected Kagan

The Collected Kagan Pdf

The Collected Kagan

Author: Janet Kagan

Publisher: Baen Books

ISBN: 162579536X

Genre: Fiction

Page: 155

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Book Summary: A collection of classic science fiction stories ranging from alien anthropology to solving tricky theorems, by Hugo-winner Janet Kagan. Janet Kagan was a unique voice in the business, bringing her witty sense of humor and refreshing outlook to stories that tackled political intrigue, murder mysteries, and ecological puzzles. Her stories are thought-provoking, often funny, and always entertaining. “Janet Kagan explores the interfaces of culture, language, intelligence, and what it means to be human.”—Sharon Lee and Steve Miller, coauthors of the best-selling Liaden Universe® series “An absolute delight.”—Mike Resnick At the publisher's request, this title is sold without DRM (Digital Rights Management).


Sophie Germain

Sophie Germain Pdf

Sophie Germain

Author: Dora Musielak

Publisher: Springer Nature

ISBN: 303038375X

Genre: Mathematics

Page: 254

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Book Summary: This biography of the mathematician, Sophie Germain, paints a rich portrait of a brilliant and complex woman, the mathematics she developed, her associations with Gauss, Legendre, and other leading researchers, and the tumultuous times in which she lived. Sophie Germain stood right between Gauss and Legendre, and both publicly recognized her scientific efforts. Unlike her female predecessors and contemporaries, Sophie Germain was an impressive mathematician and made lasting contributions to both number theory and the theories of plate vibrations and elasticity. She was able to walk with ease across the bridge between the fields of pure mathematics and engineering physics. Though isolated and snubbed by her peers, Sophie Germain was the first woman to win the prize of mathematics from the French Academy of Sciences. She is the only woman who contributed to the proof of Fermat’s Last Theorem. In this unique biography, Dora Musielak has done the impossible―she has chronicled Sophie Germain’s brilliance through her life and work in mathematics, in a way that is simultaneously informative, comprehensive, and accurate.


Prime Numbers

Prime Numbers Pdf

Prime Numbers

Author: Richard Crandall,Carl B. Pomerance

Publisher: Springer Science & Business Media

ISBN: 1468493167

Genre: Mathematics

Page: 547

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Book Summary: Bridges the gap between theoretical and computational aspects of prime numbers Exercise sections are a goldmine of interesting examples, pointers to the literature and potential research projects Authors are well-known and highly-regarded in the field


New Waves in Philosophical Logic

New Waves in Philosophical Logic Pdf

New Waves in Philosophical Logic

Author: G. Restall,G. Russell

Publisher: Springer

ISBN: 1137003723

Genre: Mathematics

Page: 244

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Book Summary: Philosophical logic has been, and continues to be, a driving force behind much progress and development in philosophy more broadly. This collection by up-and-coming philosophical logicians deals with a broad range of topics, including, for example, proof-theory, probability, context-sensitivity, dialetheism and dynamic semantics.