Uncle Petros And Goldbach S Conjecture

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Uncle Petros and Goldbach's Conjecture

Uncle Petros and Goldbach's Conjecture Pdf/ePub eBook Author:
Editor: Faber & Faber
ISBN: 057129569X
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Uncle Petros and Goldbach's Conjecture by Summary

Uncle Petros is a family joke. An ageing recluse, he lives alone in a suburb of Athens, playing chess and tending to his garden. If you didn't know better, you'd surely think he was one of life's failures. But his young nephew suspects otherwise. For Uncle Petros, he discovers, was once a celebrated mathematician, brilliant and foolhardy enough to stake everything on solving a problem that had defied all attempts at proof for nearly three centuries - Goldbach's Conjecture. His quest brings him into contact with some of the century's greatest mathematicians, including the Indian prodigy Ramanujan and the young Alan Turing. But his struggle is lonely and single-minded, and by the end it has apparently destroyed his life. Until that is a final encounter with his nephew opens up to Petros, once more, the deep mysterious beauty of mathematics. Uncle Petros and Goldbach's Conjecture is an inspiring novel of intellectual adventure, proud genius, the exhilaration of pure mathematics - and the rivalry and antagonism which torment those who pursue impossible goals.

Uncle Petros and Goldbach's Conjecture

Uncle Petros and Goldbach's Conjecture Pdf/ePub eBook Author: Apostolos Doxiadis
Editor: Bloomsbury Publishing USA
ISBN: 9781608196449
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Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis Summary

In this critically acclaimed international bestseller, Petros Papachristos, a mathematical prodigy, has devoted much of his life trying to prove one of the greatest mathematical challenges of all time: Goldbach's Conjecture, the deceptively simple claim that every even number greater than two is the sum of two primes. His feverish and singular pursuit of this goal has come to define his life. Now an old man, he is looked on with suspicion and shame by his family-until his ambitious young nephew intervenes. Seeking to understand his uncle's mysterious mind, the narrator of this novel unravels his story, a dramatic tale set against a tableau of brilliant historical figures-among them G. H. Hardy, the self-taught Indian genius Srinivasa Ramanujan, and a young Kurt Gödel. Meanwhile, as Petros recounts his own life's work, a bond is formed between uncle and nephew, pulling each one deeper into mathematical obsession, and risking both of their sanity.

The Math Gene

The Math Gene Pdf/ePub eBook Author: Keith Devlin
Editor: Basic Books
ISBN: 0786725087
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The Math Gene by Keith Devlin Summary

Why is math so hard? And why, despite this difficulty, are some people so good at it? If there's some inborn capacity for mathematical thinking—which there must be, otherwise no one could do it —why can't we all do it well? Keith Devlin has answers to all these difficult questions, and in giving them shows us how mathematical ability evolved, why it's a part of language ability, and how we can make better use of this innate talent.He also offers a breathtakingly new theory of language development—that language evolved in two stages, and its main purpose was not communication—to show that the ability to think mathematically arose out of the same symbol-manipulating ability that was so crucial to the emergence of true language. Why, then, can't we do math as well as we can speak? The answer, says Devlin, is that we can and do—we just don't recognize when we're using mathematical reasoning.

Turing (A Novel about Computation)

Turing (A Novel about Computation) Pdf/ePub eBook Author: Christos H. Papadimitriou
Editor: MIT Press
ISBN: 0262250780
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Turing (A Novel about Computation) by Christos H. Papadimitriou Summary

The world of computation according to Turing, an interactive tutoring program, as told to star-crossed lovers: a novel. Our hero is Turing, an interactive tutoring program and namesake (or virtual emanation?) of Alan Turing, World War II code breaker and father of computer science. In this unusual novel, Turing's idiosyncratic version of intellectual history from a computational point of view unfolds in tandem with the story of a love affair involving Ethel, a successful computer executive, Alexandros, a melancholy archaeologist, and Ian, a charismatic hacker. After Ethel (who shares her first name with Alan Turing's mother) abandons Alexandros following a sundrenched idyll on Corfu, Turing appears on Alexandros's computer screen to unfurl a tutorial on the history of ideas. He begins with the philosopher-mathematicians of ancient Greece—"discourse, dialogue, argument, proof... can only thrive in an egalitarian society"—and the Arab scholar in ninth-century Baghdad who invented algorithms; he moves on to many other topics, including cryptography and artificial intelligence, even economics and developmental biology. (These lessons are later critiqued amusingly and developed further in postings by a fictional newsgroup in the book's afterword.) As Turing's lectures progress, the lives of Alexandros, Ethel, and Ian converge in dramatic fashion, and the story takes us from Corfu to Hong Kong, from Athens to San Francisco—and of course to the Internet, the disruptive technological and social force that emerges as the main locale and protagonist of the novel. Alternately pedagogical and romantic, Turing (A Novel about Computation) should appeal both to students and professionals who want a clear and entertaining account of the development of computation and to the general reader who enjoys novels of ideas.

Headlong

Headlong Pdf/ePub eBook Author: Michael Frayn
Editor: Faber & Faber
ISBN: 0571249191
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Headlong by Michael Frayn Summary

Shortlisted for the Man Booker Prize Headlong begins when Martin Clay, a young would-be art historian, believes he has discovered a missing masterpiece. The owner of the painting is oblivious to its potential and asks Martin to help him sell it, leaving Martin with the chance of a lifetime: if he could only separate the painter from its owner, he would be able to perform a great public service, to make his professional reputation, perhaps even rather a lot of money as well. But is the painting really what Martin believes it to be? As Martin is drawn further into this moral and intellectual labyrinth, events start to spiral out of control . . . Shortlisted for the Man Booker Prize, Whitbread Novel Award and the James Tait Black Memorial Prize for fiction, Headlong is an ingeniously comic thriller that follows a young philosophy lectuerer's obsessive race through the art world in search of an elusive masterpiece. Michael Frayn's other novels include Spies, which won the Whitbread Best Novel award, and Skios, which was longlisted for the Booker Prize.

Quest: An Autobiography

Quest: An Autobiography Pdf/ePub eBook Author: Leopold Infeld
Editor: American Mathematical Soc.
ISBN: 0821840738
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Quest: An Autobiography by Leopold Infeld Summary

Leopold Infeld was one of the nine eminent scientists who, together with Albert Einstein, signed Bertrand Russell's famous letter warning that in this nuclear age, only a ban on war itself could save this planet (July, 1955). Infeld was born in the Jewish ghetto of Cracow, Poland in 1898, and this autobiography contains a vivid description of this long-since-vanished world. He was assistant to and then a scientific collaborator with Albert Einstein at the Institute for Advanced Study, Princeton, NJ (1936-1938), and this collaboration continued for twelve years while Infeld was at the University of Toronto. In 1938 he wrote a book together with Albert Einstein that became a number one bestseller, The Evolution of Physics. Infeld was lecturer and then Professor of Applied Mathematics at the University of Toronto from 1938--1950. From 1945-1950 he gave many lectures all over Canada on the elementary physics of the atom bomb, warning that Russia would soon have the bomb and urging that the short period of U.S. monopoly be used constructively, for peace. In 1950 he left Canada to become Professor of Theoretical Physics at the University of Warsaw as well as the founding director of the Institute of Theoretical Physics at that university, where he remained until 1967, the year before he died.

Birth of a Theorem

Birth of a Theorem Pdf/ePub eBook Author: Cédric Villani
Editor: Farrar, Straus and Giroux
ISBN: 0374710236
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Birth of a Theorem by Cédric Villani Summary

In 2010, French mathematician Cédric Villani received the Fields Medal, the most coveted prize in mathematics, in recognition of a proof which he devised with his close collaborator Clément Mouhot to explain one of the most surprising theories in classical physics. Birth of a Theorem is Villani's own account of the years leading up to the award. It invites readers inside the mind of a great mathematician as he wrestles with the most important work of his career. But you don't have to understand nonlinear Landau damping to love Birth of a Theorem. It doesn't simplify or overexplain; rather, it invites readers into collaboration. Villani's diaries, emails, and musings enmesh you in the process of discovery. You join him in unproductive lulls and late-night breakthroughs. You're privy to the dining-hall conversations at the world's greatest research institutions. Villani shares his favorite songs, his love of manga, and the imaginative stories he tells his children. In mathematics, as in any creative work, it is the thinker's whole life that propels discovery—and with Birth of a Theorem, Cédric Villani welcomes you into his.

Between Logic and Reality

Between Logic and Reality Pdf/ePub eBook Author: Majda Trobok,Nenad Miščević,Berislav Žarnić
Editor: Springer Science & Business Media
ISBN: 9789400723900
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Between Logic and Reality by Majda Trobok,Nenad Miščević,Berislav Žarnić Summary

Is reality logical and is logic real? What is the origin of logical intuitions? What is the role of logical structures in the operations of an intelligent mind and in communication? Is the function of logical structure regulative or constitutive or both in concept formation? This volume provides analyses of the logic-reality relationship from different approaches and perspectives. The point of convergence lies in the exploration of the connections between reality – social, natural or ideal – and logical structures employed in describing or discovering it. Moreover, the book connects logical theory with more concrete issues of rationality, normativity and understanding, thus pointing to a wide range of potential applications. The papers collected in this volume address cutting-edge topics in contemporary discussions amongst specialists. Some essays focus on the role of indispensability considerations in the justification of logical competence, and the wide range of challenges within the philosophy of mathematics. Others present advances in dynamic logical analysis such as extension of game semantics to non-logical part of vocabulary and development of models of contractive speech act.

That's Maths

That's Maths Pdf/ePub eBook Author: Peter Lynch
Editor: Gill & Macmillan Ltd
ISBN: 0717169561
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That's Maths by Peter Lynch Summary

From atom bombs to rebounding slinkies, open your eyes to the mathematical magic in the everyday. Mathematics isn’t just for academics and scientists, a fact meteorologist and blogger Peter Lynch has spent the past several years proving through his Irish Times newspaper column and blog, That’s Maths. Here, he shows how maths is all around us, with chapters on the beautiful equations behind designing a good concert venue, predicting the stock market and modelling the atom bomb, as well as playful meditations on everything from coin-stacking to cartography. If you left school thinking maths was boring, think again!

Mathematical Cultures

Mathematical Cultures Pdf/ePub eBook Author: Brendan Larvor
Editor: Birkhäuser
ISBN: 3319285823
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Mathematical Cultures by Brendan Larvor Summary

This collection presents significant contributions from an international network project on mathematical cultures, including essays from leading scholars in the history and philosophy of mathematics and mathematics education.​ Mathematics has universal standards of validity. Nevertheless, there are local styles in mathematical research and teaching, and great variation in the place of mathematics in the larger cultures that mathematical practitioners belong to. The reflections on mathematical cultures collected in this book are of interest to mathematicians, philosophers, historians, sociologists, cognitive scientists and mathematics educators.

How Mathematicians Think

How Mathematicians Think Pdf/ePub eBook Author: William Byers
Editor: Princeton University Press
ISBN: 1400833957
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How Mathematicians Think by William Byers Summary

To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.

Elementary Number Theory: Primes, Congruences, and Secrets

Elementary Number Theory: Primes, Congruences, and Secrets Pdf/ePub eBook Author: William Stein
Editor: Springer Science & Business Media
ISBN: 0387855254
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Elementary Number Theory: Primes, Congruences, and Secrets by William Stein Summary

This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predetermined secret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem.

Flatterland

Flatterland Pdf/ePub eBook Author: Ian Stewart
Editor: Basic Books
ISBN: 0786723289
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Flatterland by Ian Stewart Summary

First there was Edwin A. Abbott's remarkable Flatland, published in 1884, and one of the all-time classics of popular mathematics. Now, from mathematician and accomplished science writer Ian Stewart, comes what Nature calls "a superb sequel." Through larger-than-life characters and an inspired story line, Flatterland explores our present understanding of the shape and origins of the universe, the nature of space, time, and matter, as well as modern geometries and their applications. The journey begins when our heroine, Victoria Line, comes upon her great-great-grandfather A. Square's diary, hidden in the attic. The writings help her to contact the Space Hopper, who tempts her away from her home and family in Flatland and becomes her guide and mentor through ten dimensions. In the tradition of Alice in Wonderland and The Phantom Toll Booth, this magnificent investigation into the nature of reality is destined to become a modern classic.

Prime Numbers

Prime Numbers Pdf/ePub eBook Author: Richard Crandall,Carl B. Pomerance
Editor: Springer Science & Business Media
ISBN: 1468493167
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Prime Numbers by Richard Crandall,Carl B. Pomerance 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

Little Infamies

Little Infamies Pdf/ePub eBook Author: Panos Karnezis
Editor: Farrar, Straus and Giroux
ISBN: 1429923431
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Little Infamies by Panos Karnezis Summary

Cunning, fantastical tales about a Greek village of the imagination, from a startling new talent Panos Karnezis' remarkable stories are all set in the same nameless Greek village. His characters are the people who live there--the priest, the whore, the doctor, the seamstress, the mayor--and the occasional animal: a centaur, a parrot that recites Homer, a horse called History. Their lives intersect, as lives do in a small place, and they know each other's secrets: the hidden crimes, the mysteries, the little infamies that men commit. Karnezis observes his villagers with a worldly eye, and creates a place where magic invariably loses out to harsh reality, a place full of passion, cruelty, and deep reserves of black humor. These stories recall the masters of the form--the wit and sophisticated playfulness of Saki and the primal fatalism of Prosper Merimee--but they are utterly original and prove that Karnezis is one of the freshest new voices in English fiction.

Unflattening

Unflattening Pdf/ePub eBook Author: Nick Sousanis
Editor: Harvard University Press
ISBN: 0674425642
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Unflattening by Nick Sousanis Summary

The primacy of words over images has deep roots in Western culture. But what if the two are inextricably linked in meaning-making? In this experiment in visual thinking, drawn in comics, Nick Sousanis defies conventional discourse to offer readers a stunning work of graphic art and a serious inquiry into the ways humans construct knowledge.

Riot at the Calc Exam and Other Mathematically Bent Stories

Riot at the Calc Exam and Other Mathematically Bent Stories Pdf/ePub eBook Author: Colin Conrad Adams
Editor: American Mathematical Soc.
ISBN: 0821848178
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Riot at the Calc Exam and Other Mathematically Bent Stories by Colin Conrad Adams Summary

What's so funny about math? Lots! Especially if you're mathematically bent. In the world of Colin Adams, differential equations bring on tears of laughter. Hollywood producers hire algebraic geometers to punch up a script. In this world, math and humor are synonymous. Riot at the Calc Exam is a proof of this fact. A collection of humorous math stories, this book gives a window into mathematics and the culture of mathematicians. Appropriate for mathematicians, math students, math teachers, lay people with an interest in mathematics, and indeed everyone else. This book is a romp through the wild world of mathematics.

Kappa Quartet

Kappa Quartet Pdf/ePub eBook Author: Daryl Qilin Yam
Editor: Epigram Books
ISBN: 9814757764
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Kappa Quartet by Daryl Qilin Yam Summary

Kevin is a young man without a soul, holidaying in Tokyo; Mr Five, the enigmatic kappa, is the man he so happens to meet. Little does Kevin know that kappas—the river demons of Japanese folklore—desire nothing more than the souls of other humans. Set between Singapore and Japan, Kappa Quartet is split into eight discrete sections, tracing the rippling effects of this chance encounter across a host of other characters, connected and bound to one another in ways both strange and serendipitous. Together they ask one another: what does it mean to be in possession of something nobody has seen before?

Perfect Rigour

Perfect Rigour Pdf/ePub eBook Author: Masha Gessen
Editor: Icon Books Ltd
ISBN: 1848313098
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Perfect Rigour by Masha Gessen Summary

In 2006, an eccentric Russian mathematician named Grigori Perelman solved one of the world's greatest intellectual puzzles. The Poincare conjecture is an extremely complex topological problem that had eluded the best minds for over a century. In 2000, the Clay Institute in Boston named it one of seven great unsolved mathematical problems, and promised a million dollars to anyone who could find a solution. Perelman was awarded the prize this year - and declined the money. Journalist Masha Gessen was determined to find out why. Drawing on interviews with Perelman's teachers, classmates, coaches, teammates, and colleagues in Russia and the US - and informed by her own background as a math whiz raised in Russia - she set out to uncover the nature of Perelman's astonishing abilities. In telling his story, Masha Gessen has constructed a gripping and tragic tale that sheds rare light on the unique burden of genius.

Professor Stewart's Hoard of Mathematical Treasures

Professor Stewart's Hoard of Mathematical Treasures Pdf/ePub eBook Author: Ian Stewart
Editor: Basic Books
ISBN: 0465021379
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Professor Stewart's Hoard of Mathematical Treasures by Ian Stewart Summary

Opening another drawer in his Cabinet of Curiosities, renowned mathematics professor Ian Stewart presents a new medley of games, paradoxes, and riddles in Professor Stewart's Hoard of Mathematical Treasures. With wit and aplomb, Stewart mingles casual puzzles with grander forays into ancient and modern mathematical thought. Amongst a host of arcane and astonishing facts about every kind of number from irrational and imaginary to complex and cuneiform, we learn: – How to organize chaos – How matter balances anti-matter – How to turn a sphere inside out (without creasing it) – How to calculate pi by observing the stars – ...and why you can't comb a hairy ball. Along the way Stewart offers the reader tantalizing glimpses of the mathematics underlying life and the universe. Mind-stretching, enlightening, and endlessly amusing, Professor Stewart's Hoard of Mathematical Treasures will stimulate, delight, and enthrall.

What Lot's Wife Saw

What Lot's Wife Saw Pdf/ePub eBook Author: Ioanna Bourazopoulou
Editor: Black & White Publishing
ISBN: 1845025482
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What Lot's Wife Saw by Ioanna Bourazopoulou Summary

It's been twenty-five years since the Overflow flooded Southern Europe, drowning Rome, Vienna and Istanbul, and turning Paris into a major port. At the Dead Sea, the earth has opened up to reveal a strange violet salt to which the world has become addicted, and a colony has been established by the mysterious Consortium of Seventy-Five to control the supply. Run by murderers, fugitives and liars, the Colony is a haven to those fleeing Europe - especially the privileged "Purple Stars". But when the governor of the Colony dies suddenly and mysteriously, the six officials turn on each other, sparking a terrifying chain of events which threatens the very existence of the Colony. In Paris, Phileas Book, the greatest crossword compiler of his age and creator of the Epistleword, is recruited by the sinister Consortium. Presented with the epistolary confessions of the six, he is ordered to sift truth from lies to find out who killed the unpopular Governor Bera. But as Phileas starts to unravel the mystery, he begins to realise that these are no ordinary letters and that nothing less than the course of human history is at stake.What Lot's Wife Saw is an astonishing and beautifully written novel about the fear, sin and guilt that lurks in the dark corridors of the human conscience. It is a story on an epic scale about betrayal, sacrifice and unconditional love, and a darkly humorous parable recalling the Biblical tales of God's terrible rage and the fate that befell those who suffered it. But, above all, it is an enthralling vision of a nightmarish world which only the power of humanity can change.

How Long Is a Piece of String?

How Long Is a Piece of String? Pdf/ePub eBook Author: Rob Eastaway
Editor: Portico
ISBN: 1909396613
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How Long Is a Piece of String? by Rob Eastaway Summary

Why do weather forecasters get it wrong? What are the best tactics for playing "Who Wants to be a Millionaire?" and "The Weakest Link"? And what is the link between a tin of baked beans and a men's urinal? These and many other questions are answered in this book. It is for anyone wanting to remind themselves - or discover for the first time - that maths is relevant to almost everything we do. Dating, cooking, travelling by car, gambling and ranking sportsmen all have links with intriguing mathematical problems that are explained in this book. It reveals the secrets behind some of the best con tricks and the hidden workings of the taxi meter, and explains how epidemics start and stop.

The Three-Body Problem

The Three-Body Problem Pdf/ePub eBook Author: Catherine Shaw
Editor: Allison & Busby
ISBN: 074901444X
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The Three-Body Problem by Catherine Shaw Summary

Cambridge, 1888. When schoolmistress Vanessa Duncan learns of a murder at St John's College, little does she know that she will become deeply entangled in the mystery. Dr Geoffrey Akers, Fellow in Pure Mathematics, has been found dead, struck down by a violent blow to the head. What could provoke such a brutal act? Vanessa, finding herself in amongst Cambridge's brightest scholarly minds, discovers that the motive may lie in mathematics itself. Drawn closer to the case by a blossoming friendship with mathematician Arthur Weatherburn, Vanessa begins to investigate. When she learns of Sir Isaac Newton's elusive 'n-body problem' and the prestigious prize offered to anyone with a solution, things begin to make sense. But with further deaths occurring and the threat of an innocent man being condemned, Vanessa must hurry with her calculations...

Math with Bad Drawings

Math with Bad Drawings Pdf/ePub eBook Author: Ben Orlin
Editor: Black Dog & Leventhal
ISBN: 0316509027
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Math with Bad Drawings by Ben Orlin Summary

A hilarious reeducation in mathematics-full of joy, jokes, and stick figures-that sheds light on the countless practical and wonderful ways that math structures and shapes our world. In Math With Bad Drawings, Ben Orlin reveals to us what math actually is; its myriad uses, its strange symbols, and the wild leaps of logic and faith that define the usually impenetrable work of the mathematician. Truth and knowledge come in multiple forms: colorful drawings, encouraging jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Orlin shows us how to think like a mathematician by teaching us a brand-new game of tic-tac-toe, how to understand an economic crises by rolling a pair of dice, and the mathematical headache that ensues when attempting to build a spherical Death Star. Every discussion in the book is illustrated with Orlin's trademark "bad drawings," which convey his message and insights with perfect pitch and clarity. With 24 chapters covering topics from the electoral college to human genetics to the reasons not to trust statistics, Math with Bad Drawings is a life-changing book for the math-estranged and math-enamored alike.

Imagining Numbers

Imagining Numbers Pdf/ePub eBook Author: Barry Mazur
Editor: Farrar, Straus and Giroux
ISBN: 1429931469
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Imagining Numbers by Barry Mazur Summary

How the elusive imaginary number was first imagined, and how to imagine it yourself Imagining Numbers (particularly the square root of minus fifteen) is Barry Mazur's invitation to those who take delight in the imaginative work of reading poetry, but may have no background in math, to make a leap of the imagination in mathematics. Imaginary numbers entered into mathematics in sixteenth-century Italy and were used with immediate success, but nevertheless presented an intriguing challenge to the imagination. It took more than two hundred years for mathematicians to discover a satisfactory way of "imagining" these numbers. With discussions about how we comprehend ideas both in poetry and in mathematics, Mazur reviews some of the writings of the earliest explorers of these elusive figures, such as Rafael Bombelli, an engineer who spent most of his life draining the swamps of Tuscany and who in his spare moments composed his great treatise "L'Algebra". Mazur encourages his readers to share the early bafflement of these Renaissance thinkers. Then he shows us, step by step, how to begin imagining, ourselves, imaginary numbers.

Prime Suspects

Prime Suspects Pdf/ePub eBook Author: Andrew Granville,Jennifer Granville
Editor: Princeton University Press
ISBN: 0691188734
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Prime Suspects by Andrew Granville,Jennifer Granville Summary

An outrageous graphic novel that investigates key concepts in mathematics Integers and permutations—two of the most basic mathematical objects—are born of different fields and analyzed with separate techniques. Yet when the Mathematical Sciences Investigation team of crack forensic mathematicians, led by Professor Gauss, begins its autopsies of the victims of two seemingly unrelated homicides, Arnie Integer and Daisy Permutation, they discover the most extraordinary similarities between the structures of each body. Prime Suspects is a graphic novel that takes you on a voyage of forensic discovery, exploring some of the most fundamental ideas in mathematics. Travel with Detective von Neumann as he leaves no clue unturned, from shepherds’ huts in the Pyrenees to secret societies in the cafés of Paris, from the hidden codes in the music of the stones to the grisly discoveries in Finite Fields. Tremble at the ferocity of the believers in deep and rigid abstraction. Feel the frustration—and the excitement—of our young heroine, Emmy Germain, as she blazes a trail for women in mathematical research and learns from Professor Gauss, the greatest forensic detective of them all. Beautifully drawn and exquisitely detailed, Prime Suspects is unique, astonishing, and witty—a once-in-a-lifetime opportunity to experience mathematics like never before.

Mathematical Logic

Mathematical Logic Pdf/ePub eBook Author: George Tourlakis
Editor: John Wiley & Sons
ISBN: 1118030699
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Mathematical Logic by George Tourlakis Summary

A comprehensive and user-friendly guide to the use of logic inmathematical reasoning Mathematical Logic presents a comprehensive introductionto formal methods of logic and their use as a reliable tool fordeductive reasoning. With its user-friendly approach, this booksuccessfully equips readers with the key concepts and methods forformulating valid mathematical arguments that can be used touncover truths across diverse areas of study such as mathematics,computer science, and philosophy. The book develops the logical tools for writing proofs byguiding readers through both the established "Hilbert" style ofproof writing, as well as the "equational" style that is emergingin computer science and engineering applications. Chapters havebeen organized into the two topical areas of Boolean logic andpredicate logic. Techniques situated outside formal logic areapplied to illustrate and demonstrate significant facts regardingthe power and limitations of logic, such as: Logic can certify truths and only truths. Logic can certify all absolute truths (completeness theorems ofPost and Gödel). Logic cannot certify all "conditional" truths, such as thosethat are specific to the Peano arithmetic. Therefore, logic hassome serious limitations, as shown through Gödel'sincompleteness theorem. Numerous examples and problem sets are provided throughout thetext, further facilitating readers' understanding of thecapabilities of logic to discover mathematical truths. In addition,an extensive appendix introduces Tarski semantics and proceeds withdetailed proofs of completeness and first incompleteness theorems,while also providing a self-contained introduction to the theory ofcomputability. With its thorough scope of coverage and accessible style,Mathematical Logic is an ideal book for courses inmathematics, computer science, and philosophy at theupper-undergraduate and graduate levels. It is also a valuablereference for researchers and practitioners who wish to learn howto use logic in their everyday work.

Between Logic and Reality

Between Logic and Reality Pdf/ePub eBook Author: Majda Trobok,Nenad Miščević,Berislav Žarnić
Editor: Springer Science & Business Media
ISBN: 9789400723900
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Between Logic and Reality by Majda Trobok,Nenad Miščević,Berislav Žarnić Summary

Is reality logical and is logic real? What is the origin of logical intuitions? What is the role of logical structures in the operations of an intelligent mind and in communication? Is the function of logical structure regulative or constitutive or both in concept formation? This volume provides analyses of the logic-reality relationship from different approaches and perspectives. The point of convergence lies in the exploration of the connections between reality – social, natural or ideal – and logical structures employed in describing or discovering it. Moreover, the book connects logical theory with more concrete issues of rationality, normativity and understanding, thus pointing to a wide range of potential applications. The papers collected in this volume address cutting-edge topics in contemporary discussions amongst specialists. Some essays focus on the role of indispensability considerations in the justification of logical competence, and the wide range of challenges within the philosophy of mathematics. Others present advances in dynamic logical analysis such as extension of game semantics to non-logical part of vocabulary and development of models of contractive speech act.

Success with Mathematics

Success with Mathematics Pdf/ePub eBook Author: Heather Cooke
Editor: Routledge
ISBN: 1134426542
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Success with Mathematics by Heather Cooke Summary

Many students find the leap between school and university level mathematics to be significantly greater than they expected. Success with Mathematics has been devised and written especially in order to help students bridge that gap. It offers clear, practical guidance from experienced teachers of mathematics in higher education on such key issues as: * getting started * ways of studying * assessment * mathematical communication * learning by doing * using ICT * using calculators * what next. After reading this book, students will find themselves better prepared for the change in pace, rigour and abstraction they encounter in degree level mathematics. They will also find themselves able to broaden their learning strategies and improve their self-directed study skills. This book is essential reading for anyone following, or about to undertake, a degree in mathematics, or other degree courses with mathematical content.

The Whole Truth About Whole Numbers

The Whole Truth About Whole Numbers Pdf/ePub eBook Author: Sylvia Forman,Agnes M. Rash
Editor: Springer
ISBN: 3319110357
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The Whole Truth About Whole Numbers by Sylvia Forman,Agnes M. Rash Summary

The Whole Truth About Whole Numbers is an introduction to the field of Number Theory for students in non-math and non-science majors who have studied at least two years of high school algebra. Rather than giving brief introductions to a wide variety of topics, this book provides an in-depth introduction to the field of Number Theory. The topics covered are many of those included in an introductory Number Theory course for mathematics majors, but the presentation is carefully tailored to meet the needs of elementary education, liberal arts, and other non-mathematical majors. The text covers logic and proofs, as well as major concepts in Number Theory, and contains an abundance of worked examples and exercises to both clearly illustrate concepts and evaluate the students’ mastery of the material.

Primality Testing for Beginners

Primality Testing for Beginners Pdf/ePub eBook Author: Lasse Rempe-Gillen, Rebecca Waldecker
Editor: American Mathematical Soc.
ISBN: 0821898833
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Primality Testing for Beginners by Lasse Rempe-Gillen, Rebecca Waldecker Summary

How can you tell whether a number is prime? What if the number has hundreds or thousands of digits? This question may seem abstract or irrelevant, but in fact, primality tests are performed every time we make a secure online transaction. In 2002, Agrawal, Kayal, and Saxena answered a long-standing open question in this context by presenting a deterministic test (the AKS algorithm) with polynomial running time that checks whether a number is prime or not. What is more, their methods are essentially elementary, providing us with a unique opportunity to give a complete explanation of a current mathematical breakthrough to a wide audience. Rempe-Gillen and Waldecker introduce the aspects of number theory, algorithm theory, and cryptography that are relevant for the AKS algorithm and explain in detail why and how this test works. This book is specifically designed to make the reader familiar with the background that is necessary to appreciate the AKS algorithm and begins at a level that is suitable for secondary school students, teachers, and interested amateurs. Throughout the book, the reader becomes involved in the topic by means of numerous exercises.

Learning and Teaching Mathematics in The Global Village

Learning and Teaching Mathematics in The Global Village Pdf/ePub eBook Author: Marcel Danesi
Editor: Springer
ISBN: 331932280X
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Learning and Teaching Mathematics in The Global Village by Marcel Danesi Summary

This book provides a fundamental reassessment of mathematics education in the digital era. It constitutes a new mindset of how information and knowledge are processed by introducing new interconnective and interactive pedagogical approaches. Math education is catching up on technology, as courses and materials use digital sources and resources more and more. The time has come to evaluate this new dynamic, which transcends all previous use of ancillary devices to supplement classroom math instruction. Interactivity and interconnectivity with the online world of math and math texts (such as television programs and internet sites) can be integrated with our traditional modes for delivery of math instruction. This book looks at how this integration can unfold practically by applying these relevant pedagogical principles to elementary topics such as numeration, arithmetic, algebra, story problems, combinatorics, and basic probability theory. The book further exemplifies how mathematics can be connected to topics in popular culture, information technologies, and other such domains.

Is God a Mathematician?

Is God a Mathematician? Pdf/ePub eBook Author: Mario Livio
Editor: Simon and Schuster
ISBN: 1416594434
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Is God a Mathematician? by Mario Livio Summary

Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.

A Factotum in the Book Trade

A Factotum in the Book Trade Pdf/ePub eBook Author: Marius Kociejowski
Editor: Biblioasis
ISBN: 177196457X
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A Factotum in the Book Trade by Marius Kociejowski Summary

The bookshop is, and will always be, the soul of the trade. What happens there does not happen elsewhere. The multifariousness of human nature is more on show there than anywhere else, and I think it’s because of books, what they are, what they release in ourselves, and what they become when we make them magnets to our desires. A memoir of a life in the antiquarian book trade, A Factotum in the Book Trade is a journey between the shelves—and then behind the counter, into the overstuffed basement, and up the spine-stacked attic stairs of your favourite neighbourhood bookshop. From his childhood in rural Ontario, where at the village jumble sale he bought poetry volumes for their pebbled-leather covers alone, to his all-but-accidental entrance into the trade in London and the career it turned into, poet and travel writer Marius Kociejowski recounts his life among the buyers, sellers, customers, and literary nobility—the characters, fictional and not—who populate these places we all love. Cataloging their passions and pleasures, oddities and obsessions, A Factotum in the Book Trade is a journey through their lives, and a story of the serendipities and collisions of fate, the mundane happenings and indelible encounters, the friendships, feuds, losses, and elations that characterize the business of books—and, inevitably, make up an unforgettable life.

Conversations with a Mathematician

Conversations with a Mathematician Pdf/ePub eBook Author: Gregory J. Chaitin
Editor: Springer Science & Business Media
ISBN: 1447101855
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Conversations with a Mathematician by Gregory J. Chaitin Summary

The author, G. J. Chaitin, shows that God plays dice not only in quantum mechanics but also in the foundations of mathematics. According to Chaitin there exist mathematical facts that are true for no reason. This fascinating and provocative text contains a collection of his most wide-ranging and non-technical lectures and interviews. It will be of interest to anyone concerned with the philosophy of mathematics, the similarities and differences between physics and mathematics, and mathematics as art.

A Mathematical Medley

A Mathematical Medley Pdf/ePub eBook Author: George Szpiro
Editor: American Mathematical Soc.
ISBN: 082184928X
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A Mathematical Medley by George Szpiro Summary

Szpiro's book provides a delightful, well-written, eclectic selection of mathematical tidbits that makes excellent airplane reading for anyone with an interest in mathematics, regardless of their mathematical background. Excellent gift material. --Keith Devlin, Stanford University, author of The Unfinished Game and The Language of Mathematics It is great to have collected in one volume the many varied, insightful and often surprising mathematical stories that George Szpiro has written in his mathematical columns for the newspapers through the years. --Marcus du Sautoy, Oxford University, author of The Music of the Primes and Symmetry: A Journey into the Patterns of Nature Mathematics is thriving. Not only have long-standing problems, such as the Poincare conjecture, been solved, but mathematics is an important element of many modern conveniences, such as cell phones, CDs, and secure transactions over the Internet. For good or for bad, it is also the engine that drives modern investment strategies. Fortunately for the general public, mathematics and its modern applications can be intelligible to the non-specialist, as George Szpiro shows in A Mathematical Medley. In stories of a few pages each, Szpiro describes in layman's terms mathematical problems that have recently been solved (or thought to have been solved), research that was published in scientific journals, and mathematical observations about contemporary life. Anecdotal stories about the lives of mathematicians and stories about famous old problems are interspersed among other vignettes.

Mathematics Wizard Srinivasa Ramanujan

Mathematics Wizard Srinivasa Ramanujan Pdf/ePub eBook Author: Narendra Govil
Editor: Prabhat Prakashan
ISBN: 9390366739
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Mathematics Wizard Srinivasa Ramanujan by Narendra Govil Summary

The book depicts the interesting story of a mysterious Indian mathematician, Srinivasa Ramanujan, with no college education, whose mathematics in a series of letters to a Cambridge Mathematician, G.H. Hardy, shook the entire mathematics community. It is an exciting journey of a poor, self-taught and god-gifted mathematician who by the age of 31 became the youngest Fellow of Royal Society of London. Even after almost 100 years of his death at the age of 32, his results mysteriously find applications in modern world such as in the study of black holes, quantum gravity, cryptography and many others. Ramanujan's life story and work has inspired numerous people and generations of mathematicians around the globe and continue to excite even today. We hope that the book will reach the current generation and generate interest in mathematics.--Provided by publisher.

Goldbach’s Problem

Goldbach’s Problem Pdf/ePub eBook Author: Michael Th. Rassias
Editor: Springer
ISBN: 3319579142
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Goldbach’s Problem by Michael Th. Rassias Summary

Important results surrounding the proof of Goldbach's ternary conjecture are presented in this book. Beginning with an historical perspective along with an overview of essential lemmas and theorems, this monograph moves on to a detailed proof of Vinogradov's theorem. The principles of the Hardy-Littlewood circle method are outlined and applied to Goldbach's ternary conjecture. New results due to H. Maier and the author on Vinogradov's theorem are proved under the assumption of the Riemann hypothesis. The final chapter discusses an approach to Goldbach's conjecture through theorems by L. G. Schnirelmann. This book concludes with an Appendix featuring a sketch of H. Helfgott's proof of Goldbach's ternary conjecture. The Appendix also presents some biographical remarks of mathematicians whose research has played a seminal role on the Goldbach ternary problem. The author's step-by-step approach makes this book accessible to those that have mastered classical number theory and fundamental notions of mathematical analysis. This book will be particularly useful to graduate students and mathematicians in analytic number theory, approximation theory as well as to researchers working on Goldbach's problem.

Number Theory

Number Theory Pdf/ePub eBook Author: John J. Watkins
Editor: Princeton University Press
ISBN: 1400848741
FileSize: 1198kb
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Number Theory by John J. Watkins Summary

The natural numbers have been studied for thousands of years, yet most undergraduate textbooks present number theory as a long list of theorems with little mention of how these results were discovered or why they are important. This book emphasizes the historical development of number theory, describing methods, theorems, and proofs in the contexts in which they originated, and providing an accessible introduction to one of the most fascinating subjects in mathematics. Written in an informal style by an award-winning teacher, Number Theory covers prime numbers, Fibonacci numbers, and a host of other essential topics in number theory, while also telling the stories of the great mathematicians behind these developments, including Euclid, Carl Friedrich Gauss, and Sophie Germain. This one-of-a-kind introductory textbook features an extensive set of problems that enable students to actively reinforce and extend their understanding of the material, as well as fully worked solutions for many of these problems. It also includes helpful hints for when students are unsure of how to get started on a given problem. Uses a unique historical approach to teaching number theory Features numerous problems, helpful hints, and fully worked solutions Discusses fun topics like Pythagorean tuning in music, Sudoku puzzles, and arithmetic progressions of primes Includes an introduction to Sage, an easy-to-learn yet powerful open-source mathematics software package Ideal for undergraduate mathematics majors as well as non-math majors Digital solutions manual (available only to professors)

Do I Count?

Do I Count? Pdf/ePub eBook Author: Gunter M. Ziegler
Editor: CRC Press
ISBN: 146656492X
FileSize: 1798kb
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Do I Count? by Gunter M. Ziegler Summary

The subject of mathematics is not something distant, strange, and abstract that you can only learn about—and often dislike—in school. It is in everyday situations, such as housekeeping, communications, traffic, and weather reports. Taking you on a trip into the world of mathematics, Do I Count? Stories from Mathematics describes in a clear and captivating way the people behind the numbers and the places where mathematics is made. Written by top scientist and engaging storyteller Günter M. Ziegler and translated by Thomas von Foerster, the book presents mathematics and mathematicians in a manner that you have not previously encountered. It guides you on a scenic tour through the field, pointing out which beds were useful in constructing which theorems and which notebooks list the prizes for solving particular problems. Forgoing esoteric areas, the text relates mathematics to celebrities, history, travel, politics, science and technology, weather, clever puzzles, and the future. Can bees count? Is 13 bad luck? Are there equations for everything? What’s the real practical value of the Pythagorean Theorem? Are there Sudoku puzzles with fewer than 17 entries and just one solution? Where and how do mathematicians work? Who invented proofs and why do we need them? Why is there no Nobel Prize for mathematics? What kind of life did Paul Erdős lead? Find out the answers to these and other questions in this entertaining book of stories. You’ll see that everyone counts, but no computation is needed.

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