A Certain Ambiguity

A Mathematical Novel

Author: Gaurav Suri,Hartosh Singh Bal

Publisher: Princeton University Press

ISBN: 9781400834778

Category: Fiction

Page: 296

View: 4508

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While taking a class on infinity at Stanford in the late 1980s, Ravi Kapoor discovers that he is confronting the same mathematical and philosophical dilemmas that his mathematician grandfather had faced many decades earlier--and that had landed him in jail. Charged under an obscure blasphemy law in a small New Jersey town in 1919, Vijay Sahni is challenged by a skeptical judge to defend his belief that the certainty of mathematics can be extended to all human knowledge--including religion. Together, the two men discover the power--and the fallibility--of what has long been considered the pinnacle of human certainty, Euclidean geometry. As grandfather and grandson struggle with the question of whether there can ever be absolute certainty in mathematics or life, they are forced to reconsider their fundamental beliefs and choices. Their stories hinge on their explorations of parallel developments in the study of geometry and infinity--and the mathematics throughout is as rigorous and fascinating as the narrative and characters are compelling and complex. Moving and enlightening, A Certain Ambiguity is a story about what it means to face the extent--and the limits--of human knowledge.

A Certain Ambiguity

A Mathematical Novel

Author: Gaurav Suri,Hartosh Singh Bal

Publisher: Princeton University Press

ISBN: 0691127093

Category: Fiction

Page: 281

View: 2488

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While taking a class on infinity at Stanford in the late 1980s, Ravi Kapoor discovers that he is confronting the same mathematical and philosophical dilemmas that his mathematician grandfather had faced many decades earlier--and that had landed him in jail. Charged under an obscure blasphemy law in a small New Jersey town in 1919, Vijay Sahni is challenged by a skeptical judge to defend his belief that the certainty of mathematics can be extended to all human knowledge--including religion. Together, the two men discover the power--and the fallibility--of what has long been considered the pinnacle of human certainty, Euclidean geometry. As grandfather and grandson struggle with the question of whether there can ever be absolute certainty in mathematics or life, they are forced to reconsider their fundamental beliefs and choices. Their stories hinge on their explorations of parallel developments in the study of geometry and infinity--and the mathematics throughout is as rigorous and fascinating as the narrative and characters are compelling and complex. Moving and enlightening, A Certain Ambiguity is a story about what it means to face the extent--and the limits--of human knowledge.

How Mathematicians Think

Using Ambiguity, Contradiction, and Paradox to Create Mathematics

Author: William Byers

Publisher: Princeton University Press

ISBN: 9780691145990

Category: Mathematics

Page: 424

View: 9091

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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.

Water Close Over Us: A Journey along the Narmada

Author: Hartosh Singh Bal

Publisher: Harper Collins

ISBN: 935029706X

Category: Social Science

Page: 252

View: 3398

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A journey to the centre of the Indian identity The Narmada is the only river in India to merit a parikrama. The traditional journey takes more than three years and ends where it begins, having covered more than 2,600 kilometres. Bal follows the parikrama to study the stories of the clash of cultures along the river. It is here that the agriculturist encountered the forest dweller, the Indo-European north faced the Dravidian south, the Afghan battled the Gond and the dam builders confronted the environmentalists. Perhaps, then, it is no coincidence that the Adi Sankara attained the realization of Advaita - non-duality - on these banks. As the author seeks to understand whether such reconciliation is possible in every case, the stories he encounters take on a life of their own - from Osho's relatives who still safeguard his memory in sari shops to the king of a small island who spends moonlit nights firing bullets into the river.

Pythagoras' Revenge

A Mathematical Mystery

Author: Arturo Sangalli

Publisher: Princeton University Press

ISBN: 9780691049557

Category: Fiction

Page: 183

View: 8927

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The celebrated mathematician and philosopher Pythagoras left no writings. But what if he had and the manuscript had never been found? Where would it be located? Two mathematicians, one American, one British, set out, unbeknownst to each other, to find the missing manuscript.

Viewpoints

Mathematical Perspective and Fractal Geometry in Art

Author: Marc Frantz,Annalisa Crannell

Publisher: Princeton University Press

ISBN: 9781400839056

Category: Mathematics

Page: 248

View: 9562

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An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a plethora of pedagogical and learning opportunities for instructors and students. Viewpoints focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. Investigating facets of the three-dimensional world in order to understand mathematical concepts behind the art, the textbook explores art topics including comic, anamorphic, and classical art, as well as photography, while presenting such mathematical ideas as proportion, ratio, self-similarity, exponents, and logarithms. Straightforward problems and rewarding solutions empower students to make accurate, sophisticated drawings. Personal essays and short biographies by contemporary artists are interspersed between chapters and are accompanied by images of their work. These fine artists--who include mathematicians and scientists--examine how mathematics influences their art. Accessible to students of all levels, Viewpoints encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery. Classroom-tested activities and problem solving Accessible problems that move beyond regular art school curriculum Multiple solutions of varying difficulty and applicability Appropriate for students of all mathematics and art levels Original and exclusive essays by contemporary artists Forthcoming: Instructor's manual (available only to teachers)

Mathematics of Games and Gambling

Author: Edward W. Packel

Publisher: MAA

ISBN: 9780883856468

Category: Mathematics

Page: 175

View: 2734

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The new edition of a favourite, featuring fresh material such as betting in sport and bluffing in poker.

Is God a Mathematician?

Author: Mario Livio

Publisher: Simon and Schuster

ISBN: 9781416594437

Category: Mathematics

Page: 320

View: 5421

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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.

The Mathematician's Shiva

A Novel

Author: Stuart Rojstaczer

Publisher: Penguin

ISBN: 0143126318

Category: Fiction

Page: 366

View: 4969

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" A comic, bittersweet tale of family evocative of The Yiddish Policemen's Union and Everything Is Illuminated Alexander "Sasha" Karnokovitch and his family would like to mourn the passing of his mother, Rachela, with modesty and dignity. But Rachela, a famous Polish e;migre; mathematician and professor at the University of Wisconsin, is rumored to have solved the million-dollar, Navier-Stokes Millennium Prize Problem. Rumor also has it that she spitefully took the solution to her grave. To Sasha's chagrin, a ragtag group of socially challenged mathematicians arrives in Madison and crashes the shiva, vowing to do whatever it takes to find the solution-even if it means prying up the floorboards for Rachela's notes. Written by a trained geophysicist, this hilarious and multi-layered debut novel brims with colorful characters and brilliantly captures humanity's drive not just to survive, but to solve the impossible"--

The Parrot's Theorem

A Novel

Author: Denis Guedj

Publisher: Macmillan

ISBN: 1466851678

Category: Fiction

Page: 352

View: 4542

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Mr. Ruche, a Parisian bookseller, receives a bequest from a long lost friend in the Amazon of a vast library of math books, which propels him into a great exploration of the story of mathematics. Meanwhile Max, whose family lives with Mr. Ruche, takes in a voluble parrot who will discuss math with anyone. When Mr. Ruche learns of his friend's mysterious death in a Brazilian rainforest, he decides that with the parrot's help he will use these books to teach Max and his brother and sister the mysteries of Euclid's Elements, Pythagoras's Theorem and the countless other mathematical wonders. But soon it becomes clear that Mr. Ruche has inherited the library for reasons other than enlightenment, and before he knows it the household is racing to prevent the parrot and vital, new theorems from falling into the wrong hands. An immediate bestseller when first published in France, The Parrot's Theorem charmingly combines a straightforward history of mathematics and a first-rate murder mystery.

The Fractal Murders

Author: Mark Cohen

Publisher: Mysterious Press

ISBN: 0446507350

Category: Fiction

Page: 320

View: 1146

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Jane Smythe, a math professor specializing in fractal geometry, is shocked to learn that three professors with the same specialty have died amid mysterious circumstances. That's where Pepper Keane, an ex-Marine turned PI with an encyclopedic knowledge of rock 'n' roll, comes in. He finds himself attracted to Professor Smythe and is determined to discover the root of these incidents. At first, he can't find any evidence that the three dead mathematicians even knew each other. But Keane, with the help of his hacker best friend and exercise guru brother, continues to dig. Suspects begin to appear and then multiply as they race through the rocky terrain of Colorado to Mexico, Boston, and Nebraska - with the main suspect an FBI agent who is also Keane's worst enemy.

Poetry of the Universe

Author: Robert Osserman

Publisher: Anchor

ISBN: 0307790584

Category: Science

Page: 224

View: 6295

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In the bestselling literary tradition of Lewis Thomas's Lives of a Cell and James Watson's The Double Helix, Poetry of the Universe is a delightful and compelling narrative charting the evolution of mathematical ideas that have helped to illuminate the nature of the observable universe. In a richly anecdotal fashion, the book explores teh leaps of imagination and vision in mathematics that have helped pioneer our understanding of the world around us.

Turing (A Novel about Computation)

Author: Christos H. Papadimitriou

Publisher: MIT Press

ISBN: 9780262250788

Category: Fiction

Page: 296

View: 9668

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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.

Introduction to Mathematical Thinking

Author: Keith J. Devlin

Publisher: N.A

ISBN: 9780615653631

Category: Mathematics

Page: 92

View: 1826

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In the twenty-first century, everyone can benefit from being able to think mathematically. This is not the same as "doing math." The latter usually involves the application of formulas, procedures, and symbolic manipulations; mathematical thinking is a powerful way of thinking about things in the world -- logically, analytically, quantitatively, and with precision. It is not a natural way of thinking, but it can be learned.Mathematicians, scientists, and engineers need to "do math," and it takes many years of college-level education to learn all that is required. Mathematical thinking is valuable to everyone, and can be mastered in about six weeks by anyone who has completed high school mathematics. Mathematical thinking does not have to be about mathematics at all, but parts of mathematics provide the ideal target domain to learn how to think that way, and that is the approach taken by this short but valuable book.The book is written primarily for first and second year students of science, technology, engineering, and mathematics (STEM) at colleges and universities, and for high school students intending to study a STEM subject at university. Many students encounter difficulty going from high school math to college-level mathematics. Even if they did well at math in school, most are knocked off course for a while by the shift in emphasis, from the K-12 focus on mastering procedures to the "mathematical thinking" characteristic of much university mathematics. Though the majority survive the transition, many do not. To help them make the shift, colleges and universities often have a "transition course." This book could serve as a textbook or a supplementary source for such a course.Because of the widespread applicability of mathematical thinking, however, the book has been kept short and written in an engaging style, to make it accessible to anyone who seeks to extend and improve their analytic thinking skills. Going beyond a basic grasp of analytic thinking that everyone can benefit from, the STEM student who truly masters mathematical thinking will find that college-level mathematics goes from being confusing, frustrating, and at times seemingly impossible, to making sense and being hard but doable.Dr. Keith Devlin is a professional mathematician at Stanford University and the author of 31 previous books and over 80 research papers. His books have earned him many awards, including the Pythagoras Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. He is known to millions of NPR listeners as "the Math Guy" on Weekend Edition with Scott Simon. He writes a popular monthly blog "Devlin's Angle" for the Mathematical Association of America, another blog under the name "profkeithdevlin", and also blogs on various topics for the Huffington Post.

Fictional Minds

Author: Alan Palmer

Publisher: U of Nebraska Press

ISBN: 9780803237438

Category: Literary Collections

Page: 275

View: 8647

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"Readers create a continuing consciousness out of scattered references to a particular character and read this consciousness as an "embedded narrative" within the whole narrative of the novel. The combination of these embedded narratives forms the plot. This perspective on narrative enables us to explore hitherto neglected aspects of fictional minds such as dispositions, emotions, and action. It also highlights the social public and dialogic mind and the "mind beyond the skin." For example much of our thought is intermental, or joint, group or shared; even our identity is to an extent socially distributed.".

Letters to a Young Mathematician

Author: Ian Stewart

Publisher: Basic Books

ISBN: 0465008410

Category: Mathematics

Page: 224

View: 7082

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Mathematician Ian Stewart tells readers what he wishes he had known when he was a student. He takes up subjects ranging from the philosophical to the practical-what mathematics is and why it’s worth doing, the relationship between logic and proof, the role of beauty in mathematical thinking, the future of mathematics, how to deal with the peculiarities of the mathematical community, and many others.

Entertaining Mathematical Puzzles

Author: Martin Gardner

Publisher: Courier Corporation

ISBN: 9780486252117

Category: Juvenile Nonfiction

Page: 112

View: 502

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Playing with mathematical riddles can be an intriguing and fun-filled pastime — as popular science writer Martin Gardner proves in this entertaining collection. Puzzlists need only an elementary knowledge of math and a will to resist looking up the answer before trying to solve a problem. Written in a light and witty style, Entertaining Mathematical Puzzles is a mixture of old and new riddles, grouped into sections that cover a variety of mathematical topics: money, speed, plane and solid geometry, probability, topology, tricky puzzles, and more. The probability section, for example, points out that everything we do, everything that happens around us, obeys the laws of probability; geometry puzzles test our ability to think pictorially and often, in more than one dimension; while topology, among the "youngest and rowdiest branches of modern geometry," offers a glimpse into a strange dimension where properties remain unchanged, no matter how a figure is twisted, stretched, or compressed. Clear and concise comments at the beginning of each section explain the nature and importance of the math needed to solve each puzzle. A carefully explained solution follows each problem. In many cases, all that is needed to solve a puzzle is the ability to think logically and clearly, to be "on the alert for surprising, off-beat angles...that strange hidden factor that everyone else had overlooked." Fully illustrated, this engaging collection will appeal to parents and children, amateur mathematicians, scientists, and students alike, and may, as the author writes, make the reader "want to study the subject in earnest" and explains "some of the inviting paths that wind away from the problems into lusher areas of the mathematical jungle." 65 black-and-white illustrations.

Naming Infinity

A True Story of Religious Mysticism and Mathematical Creativity

Author: Loren Graham,Jean-Michel Kantor

Publisher: Harvard University Press

ISBN: 0674032934

Category: History

Page: 239

View: 373

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Looks at the competition between French and Russian mathematicians over the nature of infinity during the twentieth century.

The Indian Clerk

A Novel

Author: David Leavitt

Publisher: Bloomsbury Publishing USA

ISBN: 9781596918405

Category: Fiction

Page: 496

View: 894

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Based on the remarkable true story of G. H. Hardy and Srinivasa Ramanujan, and populated with such luminaries such as D. H. Lawrence, Bertrand Russell, and Ludwig Wittgenstein, The Indian Clerk takes this extraordinary slice of history and transforms it into an emotional and spellbinding story about the fragility of human connection and our need to find order in the world. A literary masterpiece, it appeared on four bestseller lists, including the Los Angeles Times, and received dazzling reviews from every major publication in the country.

Why Do Buses Come in Threes?

The Hidden Maths of Everyday Life

Author: Rob Eastaway

Publisher: Pavilion Books

ISBN: 1909396621

Category: Mathematics

Page: 300

View: 8181

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With a foreword by Tim Rice, this book will change the way you see the world. Why is it better to buy a lottery ticket on a Friday? Why are showers always too hot or too cold? And what's the connection between a rugby player taking a conversion and a tourist trying to get the best photograph of Nelson's Column? These and many other fascinating questions are answered in this entertaining and highly informative book, which is ideal 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 even life-saving techniques have links with intriguing mathematical problems, as you will find explained here. Whether you have a PhD in astrophysics or haven't touched a maths problem since your school days, this book will give you a fresh understanding of the world around you.