How Not to Be Wrong
How Not to Be Wrong

Author: Jordan Ellenberg

Publisher: Penguin Press

Published: 2014-05-29

Total Pages: 480

ISBN-13: 1594205221

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A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.

How Mathematicians Think
How Mathematicians Think

Author: William Byers

Publisher: Princeton University Press

Published: 2010-05-02

Total Pages: 424

ISBN-13: 0691145997

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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.

Mathematics and Mathematicians
Mathematics and Mathematicians

Author: Lars Gårding

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 304

ISBN-13: 0821806122

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This book is about mathematics in Sweden between 1630 and 1950 - from S. Klingenstierna to M. Riesz, T. Carleman, and A. Beurling. It tells the story of how continental mathematics came to Sweden, how it was received, and how it inspired new results. The book contains a biography of Gosta Mittag-Leffler, the father of Swedish mathematics, who introduced the Weierstrassian theory of analytic functions and dominated a golden age from 1880 to 1910. Important results are analyzed and re-proved in modern notation, with explanations of their relations to mathematics at the time. The book treats Backlund transformations, Mittag-Leffler's theorem, the Phragmen-Lindelof theorem and Carleman's contributions to the spectral theorem, quantum mechanics, and the asymptotics of eigenvalues and eigenfunctions.

Mathematicians and Their Gods
Mathematicians and Their Gods

Author: Snezana Lawrence

Publisher: Oxford University Press, USA

Published: 2015

Total Pages: 305

ISBN-13: 0198703058

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This is a book on the relationship between mathematics and religious beliefs. This book shows that, throughout scientific history, mathematics has been used to make sense of the 'big' questions of life, and that religious beliefs sometimes drove mathematicians to do mathematics to help them make sense of the world

Mathematics for Human Flourishing
Mathematics for Human Flourishing

Author: Francis Su

Publisher: Yale University Press

Published: 2020-01-07

Total Pages: 287

ISBN-13: 0300248814

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Winner of the Mathematics Association of America's 2021 Euler Book Prize, this is an inclusive vision of mathematics—its beauty, its humanity, and its power to build virtues that help us all flourish“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"A good book is an entertaining read. A great book holds up a mirror that allows us to more clearly see ourselves and the world we live in. Francis Su’s Mathematics for Human Flourishing is both a good book and a great book."—MAA Reviews 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.

Inventing the Mathematician
Inventing the Mathematician

Author: Sara N. Hottinger

Publisher: SUNY Press

Published: 2016-03-01

Total Pages: 217

ISBN-13: 1438460090

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Considers how our ideas about mathematics shape our individual and cultural relationship to the field. Where and how do we, as a culture, get our ideas about mathematics and about who can engage with mathematical knowledge? Sara N. Hottinger uses a cultural studies approach to address how our ideas about mathematics shape our individual and cultural relationship to the field. She considers four locations in which representations of mathematics contribute to our cultural understanding of mathematics: mathematics textbooks, the history of mathematics, portraits of mathematicians, and the field of ethnomathematics. Hottinger examines how these discourses shape mathematical subjectivity by limiting the way some groups—including women and people of color—are able to see themselves as practitioners of math. Inventing the Mathematician provides a blueprint for how to engage in a deconstructive project, revealing the limited and problematic nature of the normative construction of mathematical subjectivity.

Secondary Mathematics for Mathematicians and Educators
Secondary Mathematics for Mathematicians and Educators

Author: Michael Weiss

Publisher: Routledge

Published: 2020-10-05

Total Pages: 359

ISBN-13: 1351587676

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In this engaging text, Michael Weiss offers an advanced view of the secondary mathematics curriculum through the prism of theory, analysis, and history, aiming to take an intellectually and mathematically mature perspective on the content normally taught in high school mathematics courses. Rather than a secondary mathematics textbook, Weiss presents here a textbook about the secondary mathematics curriculum, written for mathematics educators and mathematicians and presenting a long-overdue modern-day integration of the disparate topics and methods of secondary mathematics into a coherent mathematical theory. Areas covered include: Polynomials and polynomial functions; Geometry, graphs, and symmetry; Abstract algebra, linear algebra, and solving equations; Exponential and logarithmic functions; Complex numbers; The historical development of the secondary mathematics curriculum. Written using precise definitions and proofs throughout on a foundation of advanced content knowledge, Weiss offers a compelling and timely investigation into the secondary mathematics curriculum, relevant for preservice secondary teachers as well as graduate students and scholars in both mathematics and mathematics education.

Mathematics Form and Function
Mathematics Form and Function

Author: Saunders MacLane

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 486

ISBN-13: 1461248728

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This book records my efforts over the past four years to capture in words a description of the form and function of Mathematics, as a background for the Philosophy of Mathematics. My efforts have been encouraged by lec tures that I have given at Heidelberg under the auspices of the Alexander von Humboldt Stiftung, at the University of Chicago, and at the University of Minnesota, the latter under the auspices of the Institute for Mathematics and Its Applications. Jean Benabou has carefully read the entire manuscript and has offered incisive comments. George Glauberman, Car los Kenig, Christopher Mulvey, R. Narasimhan, and Dieter Puppe have provided similar comments on chosen chapters. Fred Linton has pointed out places requiring a more exact choice of wording. Many conversations with George Mackey have given me important insights on the nature of Mathematics. I have had similar help from Alfred Aeppli, John Gray, Jay Goldman, Peter Johnstone, Bill Lawvere, and Roger Lyndon. Over the years, I have profited from discussions of general issues with my colleagues Felix Browder and Melvin Rothenberg. Ideas from Tammo Tom Dieck, Albrecht Dold, Richard Lashof, and Ib Madsen have assisted in my study of geometry. Jerry Bona and B.L. Foster have helped with my examina tion of mechanics. My observations about logic have been subject to con structive scrutiny by Gert Miiller, Marian Boykan Pour-El, Ted Slaman, R. Voreadou, Volker Weispfennig, and Hugh Woodin.

A Book of Abstract Algebra
A Book of Abstract Algebra

Author: Charles C Pinter

Publisher: Courier Corporation

Published: 2010-01-14

Total Pages: 402

ISBN-13: 0486474178

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Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.