How Not to be Wrong

The Power of Mathematical Thinking

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Author: Jordan Ellenberg

Publisher: Penguin

ISBN: 0143127535

Category: Business & Economics

Page: 480

View: 9371

"Using the mathematician's method of analyzing life and exposing the hard-won insights of the academic community to the layman, minus the jargon ... Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need"--

How Not to be Wrong

The Power of Mathematical Thinking

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Author: Jordan Ellenberg

Publisher: Penguin Press HC

ISBN: 1594205221

Category: Mathematics

Page: 468

View: 8626

The columnist for Slate's popular "Do the Math" celebrates the logical, illuminating nature of math in today's world, sharing in accessible language mathematical approaches that demystify complex and everyday problems.

How Not to Be Wrong

The Power of Mathematical Thinking

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Author: Jordan Ellenberg

Publisher: Penguin

ISBN: 0698163842

Category: Mathematics

Page: 480

View: 8564

The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.

The Grasshopper King

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Author: Jordan Ellenberg

Publisher: Coffee House Press

ISBN: 1566893860

Category: Fiction

Page: 200

View: 398

This debut novel is a profoundly absurd campus satire about immortality, obsession, obscurity, and true love.

Algorithms to Live By

The Computer Science of Human Decisions

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Author: Brian Christian,Tom Griffiths

Publisher: Macmillan

ISBN: 1627790365

Category: Business & Economics

Page: 368

View: 1460

A fascinating exploration of how insights from computer algorithms can be applied to our everyday lives, helping to solve common decision-making problems and illuminate the workings of the human mind All our lives are constrained by limited space and time, limits that give rise to a particular set of problems. What should we do, or leave undone, in a day or a lifetime? How much messiness should we accept? What balance of new activities and familiar favorites is the most fulfilling? These may seem like uniquely human quandaries, but they are not: computers, too, face the same constraints, so computer scientists have been grappling with their version of such issues for decades. And the solutions they've found have much to teach us. In a dazzlingly interdisciplinary work, acclaimed author Brian Christian and cognitive scientist Tom Griffiths show how the algorithms used by computers can also untangle very human questions. They explain how to have better hunches and when to leave things to chance, how to deal with overwhelming choices and how best to connect with others. From finding a spouse to finding a parking spot, from organizing one's inbox to understanding the workings of memory, Algorithms to Live By transforms the wisdom of computer science into strategies for human living.

Professor Stewart's Cabinet of Mathematical Curiosities

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Author: Ian Stewart

Publisher: Profile Books

ISBN: 1847651283

Category: Mathematics

Page: 320

View: 3015

School maths is not the interesting part. The real fun is elsewhere. Like a magpie, Ian Stewart has collected the most enlightening, entertaining and vexing 'curiosities' of maths over the years... Now, the private collection is displayed in his cabinet. There are some hidden gems of logic, geometry and probability -- like how to extract a cherry from a cocktail glass (harder than you think), a pop up dodecahedron, the real reason why you can't divide anything by zero and some tips for making money by proving the obvious. Scattered among these are keys to unlocking the mysteries of Fermat's last theorem, the Poincar Conjecture, chaos theory, and the P/NP problem for which a million dollar prize is on offer. There are beguiling secrets about familiar names like Pythagoras or prime numbers, as well as anecdotes about great mathematicians. Pull out the drawers of the Professor's cabinet and who knows what could happen...

The Joy of SET

The Many Mathematical Dimensions of a Seemingly Simple Card Game

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Author: Liz McMahon,Gary Gordon,Hannah Gordon,Rebecca Gordon

Publisher: Princeton University Press

ISBN: 1400884489

Category: Mathematics

Page: 320

View: 8350

Have you ever played the addictive card game SET? Have you ever wondered about the connections between games and mathematics? If the answer to either question is "yes," then The Joy of SET is the book for you! The Joy of SET takes readers on a fascinating journey into this seemingly simple card game and reveals its surprisingly deep and diverse mathematical dimensions. Absolutely no mathematical background is necessary to enjoy this book—all you need is a sense of curiosity and adventure! Originally invented in 1974 by Marsha Falco and officially released in 1991, SET has gained a widespread, loyal following. SET's eighty-one cards consist of one, two, or three symbols of different shapes (diamond, oval, squiggle), shadings (solid, striped, open), and colors (green, purple, red). In order to win, players must identify “sets” of three cards for which each characteristic is the same—or different—on all the cards. SET’s strategic and unique design opens connections to a plethora of mathematical disciplines, including geometry, modular arithmetic, combinatorics, probability, linear algebra, and computer simulations. The Joy of SET looks at these areas as well as avenues for further mathematical exploration. As the authors show, the relationship between SET and mathematics runs in both directions—playing this game has generated new mathematics, and the math has led to new questions about the game itself. The first book devoted to the mathematics of one of today’s most popular card games, The Joy of SET will entertain and enlighten the game enthusiast in all of us.

Love and Math

The Heart of Hidden Reality

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Author: Edward Frenkel

Publisher: Basic Books

ISBN: 0465069959

Category: Mathematics

Page: 288

View: 6543

What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren’t even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we’ve never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space. Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before. At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

Power-Up

Unlocking the Hidden Mathematics in Video Games

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Author: Matthew Lane

Publisher: Princeton University Press

ISBN: 1400884829

Category: Mathematics

Page: 264

View: 8692

A fun and lively look at the mathematical ideas concealed in video games Did you know that every time you pick up the controller to your PlayStation or Xbox, you are entering a game world steeped in mathematics? Power-Up reveals the hidden mathematics in many of today's most popular video games and explains why mathematical learning doesn't just happen in the classroom or from books—you're doing it without even realizing it when you play games on your cell phone. In this lively and entertaining book, Matthew Lane discusses how gamers are engaging with the traveling salesman problem when they play Assassin's Creed, why it is mathematically impossible for Mario to jump through the Mushroom Kingdom in Super Mario Bros., and how The Sims teaches us the mathematical costs of maintaining relationships. He looks at mathematical pursuit problems in classic games like Missile Command and Ms. Pac-Man, and how each time you play Tetris, you're grappling with one of the most famous unsolved problems in all of mathematics and computer science. Along the way, Lane discusses why Family Feud and Pictionary make for ho-hum video games, how realism in video games (or the lack of it) influences learning, what video games can teach us about the mathematics of voting, the mathematics of designing video games, and much more. Power-Up shows how the world of video games is an unexpectedly rich medium for learning about the beautiful mathematical ideas that touch all aspects of our lives—including our virtual ones.

Introduction to Mathematical Thinking

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Author: Keith J. Devlin

Publisher: N.A

ISBN: 9780615653631

Category: Mathematics

Page: 92

View: 6083

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.

The Computer as Crucible

An Introduction to Experimental Mathematics

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Author: Jonathan Borwein,Keith Devlin

Publisher: CRC Press

ISBN: 1439876916

Category: Mathematics

Page: 170

View: 8118

Keith Devlin and Jonathan Borwein, two well-known mathematicians with expertise in different mathematical specialties but with a common interest in experimentation in mathematics, have joined forces to create this introduction to experimental mathematics. They cover a variety of topics and examples to give the reader a good sense of the current state of play in the rapidly growing new field of experimental mathematics. The writing is clear and the explanations are enhanced by relevant historical facts and stories of mathematicians and their encounters with the field over time.

How to Bake Pi

An Edible Exploration of the Mathematics of Mathematics

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Author: Eugenia Cheng

Publisher: Basic Books

ISBN: 0465051693

Category: Mathematics

Page: 304

View: 7646

"Whimsical...rigorous and insightful." -- New York Times Book Review What is math? How exactly does it work? And what do three siblings trying to share a cake have to do with it? In How to Bake Pi, math professor Eugenia Cheng provides an accessible introduction to the logic and beauty of mathematics, powered, unexpectedly, by insights from the kitchen. We learn how the béchamel in a lasagna can be a lot like the number five, and why making a good custard proves that math is easy but life is hard. At the heart of it all is Cheng's work on category theory, a cutting-edge "mathematics of mathematics," that is about figuring out how math works. Combined with her infectious enthusiasm for cooking and true zest for life, Cheng's perspective on math is a funny journey through a vast territory no popular book on math has explored before. So, what is math? Let's look for the answer in the kitchen.

What We Cannot Know

Explorations at the Edge of Knowledge

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Author: Marcus du Sautoy

Publisher: Fourth Estate

ISBN: 9780007576593

Category:

Page: 320

View: 9338

'Brilliant and fascinating. No one is better at making the recondite accessible and exciting' Bill Bryson Britain's most famous mathematician takes us to the edge of knowledge to show us what we cannot know. Is the universe infinite? Do we know what happened before the Big Bang? Where is human consciousness located in the brain? And are there more undiscovered particles out there, beyond the Higgs boson? In the modern world, science is king: weekly headlines proclaim the latest scientific breakthroughs and numerous mathematical problems, once indecipherable, have now been solved. But are there limits to what we can discover about our physical universe? In this very personal journey to the edges of knowledge, Marcus du Sautoy investigates how leading experts in fields from quantum physics and cosmology, to sensory perception and neuroscience, have articulated the current lie of the land. In doing so, he travels to the very boundaries of understanding, questioning contradictory stories and consulting cutting edge data. Is it possible that we will one day know everything? Or are there fields of research that will always lie beyond the bounds of human comprehension? And if so, how do we cope with living in a universe where there are things that will forever transcend our understanding? In What We Cannot Know, Marcus du Sautoy leads us on a thought-provoking expedition to the furthest reaches of modern science. Prepare to be taken to the edge of knowledge to find out if there's anything we truly cannot know.

Dataclysm

Who We Are (When We Think No One's Looking)

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Author: Christian Rudder

Publisher: Fourth Estate

ISBN: 9780007494439

Category:

Page: 304

View: 3266

An irreverent, provocative, and visually fascinating look at what our online lives reveal about who we really are - and how this deluge of data will transform the science of human behaviour.

Storm in a Teacup: The Physics of Everyday Life

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Author: Helen Czerski

Publisher: W. W. Norton & Company

ISBN: 0393248976

Category: Science

Page: 336

View: 8507

“[Czerski’s] quest to enhance humanity’s everyday scientific literacy is timely and imperative.”—Science Storm in a Teacup is Helen Czerski’s lively, entertaining, and richly informed introduction to the world of physics. Czerski provides the tools to alter the way we see everything around us by linking ordinary objects and occurrences, like popcorn popping, coffee stains, and fridge magnets, to big ideas like climate change, the energy crisis, or innovative medical testing. She provides answers to vexing questions: How do ducks keep their feet warm when walking on ice? Why does it take so long for ketchup to come out of a bottle? Why does milk, when added to tea, look like billowing storm clouds? In an engaging voice at once warm and witty, Czerski shares her stunning breadth of knowledge to lift the veil of familiarity from the ordinary.

Fluke

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Author: Joseph Mazur

Publisher: Oneworld Publications

ISBN: 1780749015

Category: Mathematics

Page: 256

View: 2046

What are the chances?! This exclamation greets the scarcely believable coincidence – you’re picked up by the same taxi driver several years and thousands of miles apart or, in a second-hand bookshop far from home, you find your own childhood copy of Winnie-the-Pooh on the shelf. But the unlikely is more probable than you think. Against every fibre of common sense, the fact is that it’s quite likely that some squirrel, somewhere, will be struck by lightning as it crosses the road. The chaos and unpredictability of our lives is an illusion. There is a rational order to the universe, and it’s called mathematics. Fluke is a fascinating investigation into the true nature of chance, a must-read for maths enthusiasts and avid storytellers alike, it tears down the veil of improbability to reveal the wonderfully possible.

Birth of a Theorem

A Mathematical Adventure

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Author: Cédric Villani

Publisher: Farrar, Straus and Giroux

ISBN: 0374710236

Category: Biography & Autobiography

Page: 272

View: 9946

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.

A Mathematician Reads the Newspaper

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Author: John Allen Paulos,John Paulos

Publisher: Basic Books

ISBN: 0465050670

Category: Mathematics

Page: 240

View: 9995

In this lively volume, mathematician John Allen Paulos employs his singular wit to guide us through an unlikely mathematical jungle—the pages of the daily newspaper. From the Senate and sex to celebrities and cults, Paulos takes stories that may not seem to involve math at all and demonstrates how mathematical naïveté can put readers at a distinct disadvantage. Whether he’s using chaos theory to puncture economic and environmental predictions, applying logic to clarify the hazards of spin doctoring and news compression, or employing arithmetic and common sense to give us a novel perspective on greed and relationships, Paulos never fails to entertain and enlighten.

Math Goes to the Movies

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Author: Burkard Polster,Marty Ross

Publisher: JHU Press

ISBN: 142140608X

Category: Mathematics

Page: 304

View: 2152

This fascinating behind-the-scenes look at movie math shows how fun and illuminating equations can be.

How Mathematicians Think

Using Ambiguity, Contradiction, and Paradox to Create Mathematics

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Author: William Byers

Publisher: Princeton University Press

ISBN: 9780691145990

Category: Mathematics

Page: 424

View: 5759

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.