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.

Why Does Math Work ... If It's Not Real?
Why Does Math Work ... If It's Not Real?

Author: Dragan Radulović

Publisher: Cambridge University Press

Published: 2023-04-30

Total Pages: 167

ISBN-13: 1009063049

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According to G. H. Hardy, the 'real' mathematics of the greats like Fermat and Euler is 'useless,' and thus the work of mathematicians should not be judged on its applicability to real-world problems. Yet, mysteriously, much of mathematics used in modern science and technology was derived from this 'useless' mathematics. Mobile phone technology is based on trig functions, which were invented centuries ago. Newton observed that the Earth's orbit is an ellipse, a curve discovered by ancient Greeks in their futile attempt to double the cube. It is like some magic hand had guided the ancient mathematicians so their formulas were perfectly fitted for the sophisticated technology of today. Using anecdotes and witty storytelling, this book explores that mystery. Through a series of fascinating stories of mathematical effectiveness, including Planck's discovery of quanta, mathematically curious readers will get a sense of how mathematicians develop their concepts.

Topics in Algebra
Topics in Algebra

Author: I. N. Herstein

Publisher: John Wiley & Sons

Published: 1991-01-16

Total Pages: 405

ISBN-13: 0471010901

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New edition includes extensive revisions of the material on finite groups and Galois Theory. New problems added throughout.

Analytic Combinatorics
Analytic Combinatorics

Author: Philippe Flajolet

Publisher: Cambridge University Press

Published: 2009-01-15

Total Pages: 825

ISBN-13: 1139477161

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Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

Linear Algebra Done Right
Linear Algebra Done Right

Author: Sheldon Axler

Publisher: Springer Science & Business Media

Published: 1997-07-18

Total Pages: 276

ISBN-13: 9780387982595

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This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.

The Topos of Music
The Topos of Music

Author: Guerino Mazzola

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 1310

ISBN-13: 303488141X

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With contributions by numerous experts

Mathematics for Human Flourishing
Mathematics for Human Flourishing

Author: Francis Su

Publisher: Yale University Press

Published: 2020-01-07

Total Pages: 287

ISBN-13: 0300237138

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"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.

The Education of T.C. MITS
The Education of T.C. MITS

Author: Lillian R. Lieber

Publisher: Paul Dry Books

Published: 2007-06-01

Total Pages: 238

ISBN-13: 1589880331

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Whether you are stumped by the "commutative law" in algebra or a whiz at multiplying three-digit numbers in your head, this book opens the door to the wonders of mathematical imagining. By using simple language and intriguing illustrations drawn by her husband, Hugh, Lillian Lieber presents subtle mathematical concepts in an easy-to-understand way. Over sixty years after its release, this whimsical exploration of how to think in a mathematical mood will continue to delight math-lovers of all ages. Barry Mazur's new introduction is a tribute to the Liebers' influence on generations of mathematicians.

Birth of a Theorem
Birth of a Theorem

Author: Cédric Villani

Publisher: Macmillan + ORM

Published: 2015-04-14

Total Pages: 260

ISBN-13: 0374710236

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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 aTheorem 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 aTheorem. 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 aTheorem, Cédric Villani welcomes you into his.