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Is Mathematics Inevitable?

Is Mathematics Inevitable?
Author: Underwood Dudley
Publisher:
Total Pages: 325
Release: 2008
Genre: Mathematics
ISBN: 9781470458621

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Is Mathematics Inevitable?

Is Mathematics Inevitable?
Author: Underwood Dudley
Publisher: MAA Press
Total Pages: 346
Release: 2008-04-29
Genre: Mathematics
ISBN:

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This is a collection of gems from the literature of mathematics that shine as brightly today as when they first appeared in print - they deserve to be seen and admired. The selections include two opposing views on the purpose of mathematics, the strong law of small numbers, the treatment of calculus in the 1771 Encyclopaedia Britannica, several proofs that the number of legs on a horse is infinite, a deserved refutation of the ridiculous Euler-Diderot anecdote, the real story of π and the Indiana legislature, the reason why Theodorus stopped proving that square roots were irrational when he got to the square root of 17, an excerpt from Mathematics Made Difficult, a glimpse into the mind of a calculating prodigy, and much more. There will be something here for anyone interested in mathematics.


How Not to Be Wrong

How Not to Be Wrong
Author: Jordan Ellenberg
Publisher: Penguin
Total Pages: 482
Release: 2015-05-26
Genre: Mathematics
ISBN: 0143127535

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“Witty, compelling, and just plain fun to read . . ." —Evelyn Lamb, Scientific American 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.


Science as It Could Have Been

Science as It Could Have Been
Author: Lena Soler
Publisher: University of Pittsburgh Press
Total Pages: 401
Release: 2016-02-19
Genre: Science
ISBN: 0822981157

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Could all or part of our taken-as-established scientific conclusions, theories, experimental data, ontological commitments, and so forth have been significantly different? Science as It Could Have Been focuses on a crucial issue that contemporary science studies have often neglected: the issue of contingency within science. It considers a number of case studies, past and present, from a wide range of scientific disciplines—physics, biology, geology, mathematics, and psychology—to explore whether components of human science are inevitable, or if we could have developed an alternative successful science based on essentially different notions, conceptions, and results. Bringing together a group of distinguished contributors in philosophy, sociology, and history of science, this edited volume offers a comprehensive analysis of the contingency/inevitability problem and a lively and up-to-date portrait of current debates in science studies.


Mathematics for the Nonmathematician

Mathematics for the Nonmathematician
Author: Morris Kline
Publisher: Courier Corporation
Total Pages: 676
Release: 2013-04-15
Genre: Mathematics
ISBN: 0486316130

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Erudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the fundamental concept, differential calculus, probability theory, much more. Exercises and problems.


Our Mathematical Universe

Our Mathematical Universe
Author: Max Tegmark
Publisher: Vintage
Total Pages: 434
Release: 2015-02-03
Genre: Science
ISBN: 0307744256

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Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.


Do the Math

Do the Math
Author: Philip B Persinger
Publisher: iUniverse
Total Pages: 257
Release: 2011-10-26
Genre: Fiction
ISBN: 1462014224

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What could be worse than losing the love of your life? Getting her back! William Teale is a brilliant professor of mathematics. His theory of inevitability posits that any human action, no matter how insignificant, might result in a disproportionately huge calamity. His wife, Virginia "Faye" Warner, is a world-famous romance novelist who specializes in reuniting soul mates after a tragic and prolonged separation. According to her math, "one past and two hearts plus one love equals four-ever." The Teale-Warner marriage is a thing of geometric and artistic perfection, a melding of the heart and the brain-amour and algebra. But when Faye's ghostwriter suffers a nervous breakdown and shakes all the arrows out of Cupid's quiver, Faye reintroduces her husband to love. Unfortunately, it's not with herself, but with the woman William had loved and lost years ago. Love is about to clash with inevitability, and it's unclear which will emerge victorious. Told in the off-beat voice of William's graduate intern, Roger, Do the Math reveals the curious relationship between logic and love and the delightful consequences of taking a chance.


Essays in the History of Lie Groups and Algebraic Groups

Essays in the History of Lie Groups and Algebraic Groups
Author: Armand Borel
Publisher: American Mathematical Soc.
Total Pages: 184
Release: 2001
Genre: Mathematics
ISBN: 0821802887

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Algebraic groups and Lie groups are important in most major areas of mathematics, occuring in diverse roles such as the symmetries of differential equations and as central figures in the Langlands program for number theory. In this book, Professor Borel looks at the development of the theory of Lie groups and algebraic groups, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. As the starting point of this passagefrom local to global, the author takes Lie's theory of local analytic transformation groups and Lie algebras. He then follows the globalization of the process in its two most important frameworks: (transcendental) differential geometry and algebraic geometry. Chapters II to IV are devoted to the former,Chapters V to VIII, to the latter.The essays in the first part of the book survey various proofs of the full reducibility of linear representations of $SL 2M$, the contributions H. Weyl to representation and invariant theory for Lie groups, and conclude with a chapter on E. Cartan's theory of symmetric spaces and Lie groups in the large.The second part of the book starts with Chapter V describing the development of the theory of linear algebraic groups in the 19th century. Many of the main contributions here are due to E. Study, E. Cartan, and above all, to L. Maurer. After being abandoned for nearly 50 years, the theory was revived by Chevalley and Kolchin and then further developed by many others. This is the focus of Chapter VI. The book concludes with two chapters on various aspects of the works of Chevalley on Lie groupsand algebraic groups and Kolchin on algebraic groups and the Galois theory of differential fields.The author brings a unique perspective to this study. As an important developer of some of the modern elements of both the differential geometric and the algebraic geometric sides of the theory, he has a particularly deep appreciation of the underlying mathematics. His lifelong involvement and his historical research in the subject give him a special appreciation of the story of its development.


Democracy and Mathematics Education

Democracy and Mathematics Education
Author: Kurt Stemhagen
Publisher: Routledge
Total Pages: 239
Release: 2021-05-06
Genre: Education
ISBN: 1000378136

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In Democracy and Mathematics Education, Kurt Stemhagen and Catherine Henney develop a way of thinking about the nature and purposes of math that is inclusive, participatory, and thoroughly human. They use these ideas to create a school mathematics experience that can enhance students’ math abilities and democratic potential. They locate mathematics’ origins in human activity and highlight the rich but often overlooked links between mathematical activity and democratic, social practices. Democratic mathematics education foregrounds student inquiry and brings to light the moral dimensions of a discipline that has both remarkable utility and inevitable limitations. For math educators, the book’s humanities approach helps to see the subject anew. For philosophers, it provides an important real world context for wrestling with perennial and timely questions, engaging democratic and evolutionary theory to transform school math. This alternative approach to mathematics and mathematics education provides a guide for how to use math to make democracy a larger part of school and wider social life. 2021 Winner of the AESA Critics’ Choice Book Award.


Inevitable Randomness in Discrete Mathematics

Inevitable Randomness in Discrete Mathematics
Author: J—zsef Beck
Publisher: American Mathematical Soc.
Total Pages: 267
Release: 2009-09-01
Genre: Mathematics
ISBN: 0821847562

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Mathematics has been called the science of order. The subject is remarkably good for generalizing specific cases to create abstract theories. However, mathematics has little to say when faced with highly complex systems, where disorder reigns. This disorder can be found in pure mathematical arenas, such as the distribution of primes, the $3n+1$ conjecture, and class field theory. The purpose of this book is to provide examples--and rigorous proofs--of the complexity law: (1) discrete systems are either simple or they exhibit advanced pseudorandomness; (2) a priori probabilities often exist even when there is no intrinsic symmetry. Part of the difficulty in achieving this purpose is in trying to clarify these vague statements. The examples turn out to be fascinating instances of deep or mysterious results in number theory and combinatorics. This book considers randomness and complexity. The traditional approach to complexity--computational complexity theory--is to study very general complexity classes, such as P, NP and PSPACE. What Beck does is very different: he studies interesting concrete systems, which can give new insights into the mystery of complexity. The book is divided into three parts. Part A is mostly an essay on the big picture. Part B is partly new results and partly a survey of real game theory. Part C contains new results about graph games, supporting the main conjecture. To make it accessible to a wide audience, the book is mostly self-contained.