Mathematics Without Numbers

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Math Without Numbers

Author : Milo Beckman
Publisher : Penguin
ISBN 13 : 1524745561
Total Pages : 225 pages
Book Rating : 4.5/5 (247 download)

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Book Synopsis Math Without Numbers by : Milo Beckman

Download or read book Math Without Numbers written by Milo Beckman and published by Penguin. This book was released on 2022-01-11 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: An illustrated tour of the structures and patterns we call "math" The only numbers in this book are the page numbers. Math Without Numbers is a vivid, conversational, and wholly original guide to the three main branches of abstract math—topology, analysis, and algebra—which turn out to be surprisingly easy to grasp. This book upends the conventional approach to math, inviting you to think creatively about shape and dimension, the infinite and infinitesimal, symmetries, proofs, and how these concepts all fit together. What awaits readers is a freewheeling tour of the inimitable joys and unsolved mysteries of this curiously powerful subject. Like the classic math allegory Flatland, first published over a century ago, or Douglas Hofstadter's Godel, Escher, Bach forty years ago, there has never been a math book quite like Math Without Numbers. So many popularizations of math have dwelt on numbers like pi or zero or infinity. This book goes well beyond to questions such as: How many shapes are there? Is anything bigger than infinity? And is math even true? Milo Beckman shows why math is mostly just pattern recognition and how it keeps on surprising us with unexpected, useful connections to the real world. The ambitions of this book take a special kind of author. An inventive, original thinker pursuing his calling with jubilant passion. A prodigy. Milo Beckman completed the graduate-level course sequence in mathematics at age sixteen, when he was a sophomore at Harvard; while writing this book, he was studying the philosophical foundations of physics at Columbia under Brian Greene, among others.

Mathematics without Numbers

Author : Geoffrey Hellman
Publisher : Clarendon Press
ISBN 13 : 019152011X
Total Pages : 172 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Mathematics without Numbers by : Geoffrey Hellman

Download or read book Mathematics without Numbers written by Geoffrey Hellman and published by Clarendon Press. This book was released on 1989-10-12 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geoffrey Hellman presents a detailed interpretation of mathematics as the investigation of structural possibilities, as opposed to absolute, Platonic objects. After dealing with the natural numbers and analysis, he extends his approach to set theory, and shows how to dispense with a fixed universe of sets. Finally, he addresses problems of application to the physical world.

How Not to Be Wrong

Author : Jordan Ellenberg
Publisher : Penguin
ISBN 13 : 0143127535
Total Pages : 482 pages
Book Rating : 4.1/5 (431 download)

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Book Synopsis How Not to Be Wrong by : Jordan Ellenberg

Download or read book How Not to Be Wrong written by Jordan Ellenberg and published by Penguin. This book was released on 2015-05-26 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: “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 without Numbers

Author : Hartry Field
Publisher : Oxford University Press
ISBN 13 : 0191083771
Total Pages : 176 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis Science without Numbers by : Hartry Field

Download or read book Science without Numbers written by Hartry Field and published by Oxford University Press. This book was released on 2016-10-13 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Science Without Numbers caused a stir in philosophy on its original publication in 1980, with its bold nominalist approach to the ontology of mathematics and science. Hartry Field argues that we can explain the utility of mathematics without assuming it true. Part of the argument is that good mathematics has a special feature ("conservativeness") that allows it to be applied to "nominalistic" claims (roughly, those neutral to the existence of mathematical entities) in a way that generates nominalistic consequences more easily without generating any new ones. Field goes on to argue that we can axiomatize physical theories using nominalistic claims only, and that in fact this has advantages over the usual axiomatizations that are independent of nominalism. There has been much debate about the book since it first appeared. It is now reissued in a revised contains a substantial new preface giving the author's current views on the original book and the issues that were raised in the subsequent discussion of it.

Mathematics without Apologies

Author : Michael Harris
Publisher : Princeton University Press
ISBN 13 : 0691175837
Total Pages : 468 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Mathematics without Apologies by : Michael Harris

Download or read book Mathematics without Apologies written by Michael Harris and published by Princeton University Press. This book was released on 2017-05-30 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: An insightful reflection on the mathematical soul What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers—for the sake of truth, beauty, and practical applications—this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources. Drawing on his personal experiences and obsessions as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, Michael Harris reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, he touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party? Disarmingly candid, relentlessly intelligent, and richly entertaining, Mathematics without Apologies takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond.

A Mind for Numbers

Author : Barbara A. Oakley
Publisher : TarcherPerigee
ISBN 13 : 039916524X
Total Pages : 338 pages
Book Rating : 4.3/5 (991 download)

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Book Synopsis A Mind for Numbers by : Barbara A. Oakley

Download or read book A Mind for Numbers written by Barbara A. Oakley and published by TarcherPerigee. This book was released on 2014-07-31 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. In her book, she offers you the tools needed to get a better grasp of that intimidating but inescapable field.

Mathematics for Human Flourishing

Author : Francis Su
Publisher : Yale University Press
ISBN 13 : 0300237138
Total Pages : 287 pages
Book Rating : 4.3/5 (2 download)

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Book Synopsis Mathematics for Human Flourishing by : Francis Su

Download or read book Mathematics for Human Flourishing written by Francis Su and published by Yale University Press. This book was released on 2020-01-07 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.

Numbers Rule

Author : George Szpiro
Publisher : Princeton University Press
ISBN 13 : 0691209081
Total Pages : 240 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis Numbers Rule by : George Szpiro

Download or read book Numbers Rule written by George Szpiro and published by Princeton University Press. This book was released on 2020-11-03 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author takes the general reader on a tour of the mathematical puzzles and paradoxes inherent in voting systems, such as the Alabama Paradox, in which an increase in the number of seats in the Congress could actually lead to a reduced number of representatives for a state, and the Condorcet Paradox, which demonstrates that the winner of elections featuring more than two candidates does not necessarily reflect majority preferences. Szpiro takes a roughly chronological approach to the topic, traveling from ancient Greece to the present and, in addition to offering explanations of the various mathematical conundrums of elections and voting, also offers biographical details on the mathematicians and other thinkers who thought about them, including Plato, Pliny the Younger, Pierre Simon Laplace, Thomas Jefferson, John von Neumann, and Kenneth Arrow.

Really Big Numbers

Author : Richard Evan Schwartz
Publisher : American Mathematical Soc.
ISBN 13 : 1470414252
Total Pages : 192 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Really Big Numbers by : Richard Evan Schwartz

Download or read book Really Big Numbers written by Richard Evan Schwartz and published by American Mathematical Soc.. This book was released on 2014-06-30 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the American Mathematical Society's first-ever book for kids (and kids at heart), mathematician and author Richard Evan Schwartz leads math lovers of all ages on an innovative and strikingly illustrated journey through the infinite number system. By means of engaging, imaginative visuals and endearing narration, Schwartz manages the monumental task of presenting the complex concept of Big Numbers in fresh and relatable ways. The book begins with small, easily observable numbers before building up to truly gigantic ones, like a nonillion, a tredecillion, a googol, and even ones too huge for names! Any person, regardless of age, can benefit from reading this book. Readers will find themselves returning to its pages for a very long time, perpetually learning from and growing with the narrative as their knowledge deepens. Really Big Numbers is a wonderful enrichment for any math education program and is enthusiastically recommended to every teacher, parent and grandparent, student, child, or other individual interested in exploring the vast universe of numbers.

Math Without Numbers

Author : William S. Veatch
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781539503392
Total Pages : 354 pages
Book Rating : 4.5/5 (33 download)

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Book Synopsis Math Without Numbers by : William S. Veatch

Download or read book Math Without Numbers written by William S. Veatch and published by Createspace Independent Publishing Platform. This book was released on 2016-11-09 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Math Without Numbers - The Mathematics of Ideas. Volume 1 - Foundations. This Volume 1 in the "Math Without Numbers" series explores the nature of Ideas, from both a practical and an abstract mathematical point of view. The book demonstrates that mathematics can explain "how" we think, but cannot tell us "what" to think or how to act. The author applies principles of Set Theory to Ideas, and illustrates how Ideas form structures that are well-known in the field of Mathematics, including Partitions/Equivalence Classes, Groups, Boolean Algebras, Rings, Lattices, and Topologies. The book touches on Logic, Argumentation, and Debate, which are topics that will be explored in detail in Volumes 2 and 3. The discussion is original and accessible, and includes material appropriate for anyone with a background in basic high school math, as well as more advanced material for those looking for a challenge. The book begins at an introductory level, but proceeds to discuss more complex material for those interested in making language more precise and unambiguous. Much of the focus is on Lattices and Boolean Algebras/Rings, as applied to Ideas rather than numbers. There are many similarities to the relatively new field of mathematics called Formal Concept Analysis, although Math Without Numbers focuses on building a foundation in Set Theory and Logic. This book is intended for anyone interested in Set Theory, the Philosophy of Mathematics, the Philosophy of Language, Critical Thinking, Logic, and/or Artificial Intelligence. Those who like solving word puzzles will enjoy the Math Without Numbers series, which attempts to solve one of the greatest puzzles of all time: the Mathematics of Ideas.

Numbers

Author : Heinz-Dieter Ebbinghaus
Publisher : Springer Science & Business Media
ISBN 13 : 9780387974972
Total Pages : 424 pages
Book Rating : 4.9/5 (749 download)

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Book Synopsis Numbers by : Heinz-Dieter Ebbinghaus

Download or read book Numbers written by Heinz-Dieter Ebbinghaus and published by Springer Science & Business Media. This book was released on 1991 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about all kinds of numbers, from rationals to octonians, reals to infinitesimals. It is a story about a major thread of mathematics over thousands of years, and it answers everything from why Hamilton was obsessed with quaternions to what the prospect was for quaternionic analysis in the 19th century. It glimpses the mystery surrounding imaginary numbers in the 17th century and views some major developments of the 20th century.

Are Numbers Real?

Author : Brian Clegg
Publisher : Macmillan
ISBN 13 : 1250081041
Total Pages : 303 pages
Book Rating : 4.2/5 (5 download)

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Book Synopsis Are Numbers Real? by : Brian Clegg

Download or read book Are Numbers Real? written by Brian Clegg and published by Macmillan. This book was released on 2016-12-06 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an accessible, in-depth look at the history of numbers and their applications in life and science, from math's surreal presence in the virtual world to the debates about the role of math in science.

Power in Numbers

Author : Talithia Williams
Publisher : Quarto Publishing Group USA
ISBN 13 : 0760360286
Total Pages : 227 pages
Book Rating : 4.7/5 (63 download)

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Book Synopsis Power in Numbers by : Talithia Williams

Download or read book Power in Numbers written by Talithia Williams and published by Quarto Publishing Group USA. This book was released on 2018-04-10 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: From rocket scientists to code breakers, “fascinating stories” of women who overcame obstacles, shattered stereotypes, and pursued their passion for math (Notices of the American Mathematical Society). With more than 200 photos and original interviews with several of the amazing women covered, Power in Numbers: The Rebel Women of Mathematics is a full-color volume that puts a spotlight on the influence of women on the development of mathematics over the last two millennia. Each biography reveals the life of a different female mathematician, from her childhood and early influences to the challenges she faced and the great achievements she made in spite of them. Learn how: After her father terminated her math lessons, Sofia Kovalevskaya snuck algebra books into her bed to read at night Emmy Noether became an invaluable resource to Albert Einstein while she was in the Navy Native American rocket scientist Mary Golda Ross developed designs for fighter jets and missiles in a top-secret unit Katherine Johnson’s life-or-death calculations at NASA meant that astronauts such as Alan Shepard and John Glenn made it home alive Shakuntala Devi multiplied massive numbers in her head so her family could eat at night Pamela Harris proved her school counselors wrong when they told her she would only succeed as a bilinguial secretary Carla Cotwright-Williams began her life in the dangerous streets of South-Central Los Angeles before skyrocketing to a powerful career with the Department of Defense in Washington, DC These women are a diverse group, but their stories have one thing in common: At some point on their journeys, someone believed in them—and made them think the impossible was perhaps not so impossible. “A quick read . . . full of dramatic stories and eye-catching illustrations.” —MAA Reviews “I found myself marveling at the personal anecdotes and quotes throughout the book.” —Notices of the American Mathematical Society

Exploring the World of Mathematics

Author : John Hudson Tiner
Publisher : New Leaf Publishing Group
ISBN 13 : 161458155X
Total Pages : 159 pages
Book Rating : 4.6/5 (145 download)

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Book Synopsis Exploring the World of Mathematics by : John Hudson Tiner

Download or read book Exploring the World of Mathematics written by John Hudson Tiner and published by New Leaf Publishing Group. This book was released on 2004-07-01 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numbers surround us. Just try to make it through a day without using any. It's impossible: telephone numbers, calendars, volume settings, shoe sizes, speed limits, weights, street numbers, microwave timers, TV channels, and the list goes on and on. The many advancements and branches of mathematics were developed through the centuries as people encountered problems and relied upon math to solve them. For instance: What timely invention was tampered with by the Caesars and almost perfected by a pope? Why did ten days vanish in September of 1752? How did Queen Victoria shorten the Sunday sermons at chapel? What important invention caused the world to be divided into time zones? What simple math problem caused the Mars Climate Orbiter to burn up in the Martian atmosphere? What common unit of measurement was originally based on the distance from the equator to the North Pole? Does water always boil at 212? Fahrenheit? What do Da Vinci's Last Supper and the Parthenon have in common? Why is a computer glitch called a "bug"? It's amazing how ten simple digits can be used in an endless number of ways to benefit man. The development of these ten digits and their many uses is the fascinating story you hold in your hands: Exploring the World of Mathematics.

What Is Mathematics, Really?

Author : Reuben Hersh
Publisher : Oxford University Press
ISBN 13 : 0198027362
Total Pages : 368 pages
Book Rating : 4.1/5 (98 download)

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Book Synopsis What Is Mathematics, Really? by : Reuben Hersh

Download or read book What Is Mathematics, Really? written by Reuben Hersh and published by Oxford University Press. This book was released on 1997-08-21 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

Mathematics Without Numbers

Author : Geoffrey Hellman
Publisher : Oxford University Press on Demand
ISBN 13 : 0198240341
Total Pages : 167 pages
Book Rating : 4.1/5 (982 download)

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Book Synopsis Mathematics Without Numbers by : Geoffrey Hellman

Download or read book Mathematics Without Numbers written by Geoffrey Hellman and published by Oxford University Press on Demand. This book was released on 1989 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops a structuralist understanding of mathematics, as an alternative to set- or type-theoretic foundations, that respects classical mathematical truth while minimizing Platonist commitments to abstract entities.

The Wonder Book of Geometry

Author : David Acheson
Publisher : Oxford University Press
ISBN 13 : 0192585371
Total Pages : 240 pages
Book Rating : 4.1/5 (925 download)

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Book Synopsis The Wonder Book of Geometry by : David Acheson

Download or read book The Wonder Book of Geometry written by David Acheson and published by Oxford University Press. This book was released on 2020-10-22 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: How can we be sure that Pythagoras's theorem is really true? Why is the 'angle in a semicircle' always 90 degrees? And how can tangents help determine the speed of a bullet? David Acheson takes the reader on a highly illustrated tour through the history of geometry, from ancient Greece to the present day. He emphasizes throughout elegant deduction and practical applications, and argues that geometry can offer the quickest route to the whole spirit of mathematics at its best. Along the way, we encounter the quirky and the unexpected, meet the great personalities involved, and uncover some of the loveliest surprises in mathematics.