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Title The Princeton Companion to Mathematics
Author Timothy Gowers
Publisher Princeton University Press
Release Date 2010-07-18
Category Mathematics
Total Pages 1056
ISBN 1400830397
Language English, Spanish, and French
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Book Summary:

This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more. Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics. Accessible in style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties. Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors Presents major ideas and branches of pure mathematics in a clear, accessible style Defines and explains important mathematical concepts, methods, theorems, and open problems Introduces the language of mathematics and the goals of mathematical research Covers number theory, algebra, analysis, geometry, logic, probability, and more Traces the history and development of modern mathematics Profiles more than ninety-five mathematicians who influenced those working today Explores the influence of mathematics on other disciplines Includes bibliographies, cross-references, and a comprehensive index Contributors incude: Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Béla Bollobás, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, José Ferreirós, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvêa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolò Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, János Kollár, T. W. Körner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-François Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lützen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rüdiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, Doron Zeilberger

Title The Princeton Companion to Applied Mathematics
Author Nicholas J. Higham
Publisher Princeton University Press
Release Date 2015-09-15
Category Mathematics
Total Pages 1016
ISBN 9781400874477
Language English, Spanish, and French
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Book Summary:

This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index

Title Mathematics A Very Short Introduction
Author Timothy Gowers
Publisher Oxford Paperbacks
Release Date 2002-08-22
Category Mathematics
Total Pages 143
ISBN 0192853619
Language English, Spanish, and French
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Book Summary:

The aim of this volume is to explain the differences between research-level mathematics and the maths taught at school. Most differences are philosophical and the first few chapters are about general aspects of mathematical thought.

Mathematics For Physics by Michael Stone

Title Mathematics for Physics
Author Michael Stone
Publisher Cambridge University Press
Release Date 2009-07-09
Category Science
Total Pages 86
ISBN 9781139480611
Language English, Spanish, and French
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Book Summary:

An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.

Mathematics by A. D. Aleksandrov

Title Mathematics
Author A. D. Aleksandrov
Publisher Courier Corporation
Release Date 2012-05-07
Category Mathematics
Total Pages 1120
ISBN 9780486157870
Language English, Spanish, and French
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Book Summary:

Major survey offers comprehensive, coherent discussions of analytic geometry, algebra, differential equations, calculus of variations, functions of a complex variable, prime numbers, linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.

A Princeton Companion by Alexander Leitch

Title A Princeton Companion
Author Alexander Leitch
Publisher Princeton University Press
Release Date 2015-03-08
Category History
Total Pages 572
ISBN 9781400870011
Language English, Spanish, and French
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Book Summary:

In this unusual and unique volume, Alexander Leitch provides a warm, often witty, and always informative reference book on Princeton University. The collection of approximately 400 articles, alphabetically arranged and written by some seventy faculty members and alumni in addition to the author, covers all aspects of Princeton life in the past as well as in the present. Of special interest are the biographies of eminent Princetonians, including the University's presidents, well-known trustees, distinguished deans, famous alumni, and some of Princeton's most prominent and popular professors. Other articles in the book embrace a wide range of topics: histories of academic departments, programs, and research units; descriptions of the honor system, the preceptorial method, the four-course plan, and coeducation; a historical survey of the University's acquisition of land and the development of its campus, together with articles on its principal buildings; pieces on student activities; accounts of alumni activities; articles on athletics; portraits of notable personalities; and commentaries on a host of lighter topics such as the cane spree, beer jackets, the Faculty Song, the proctors, and Veterans of Future Wars. Among the most important articles are one summarizing Woodrow Wilson's Sesquicentennial address, "Princeton in the Nation's Service," and a dozen others recording faculty and alumni achievements toward the goal encompassed by that phrase. Originally published in 1978. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Heavenly Mathematics by Glen Van Brummelen

Title Heavenly Mathematics
Author Glen Van Brummelen
Publisher Princeton University Press
Release Date 2017-04-04
Category Mathematics
Total Pages 216
ISBN 9780691175997
Language English, Spanish, and French
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Book Summary:

"Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high schools until the 1950s. Today, however, it is rarely taught. Heavenly Mathematics traces the rich history of this forgotten art, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth."--Jacket.

From Here To Infinity by Ian Stewart

Title From Here to Infinity
Author Ian Stewart
Publisher Oxford Paperbacks
Release Date 1996
Category Literary Criticism
Total Pages 310
ISBN 0192832026
Language English, Spanish, and French
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Book Summary:

A retitled and revised edition of Ian Stewart's The Problem of Mathematics, this is the perfect guide to today's mathematics. Read about the latest discoveries, including Andrew Wile's amazing proof of Fermat's Last Theorem, the newest advances in knot theory, the Four Colour Theorem, Chaos Theory, and fake four-dimensial spaces. See how simple concepts from probability theory shed light on the National Lottery and tell you how to maximize your winnings. Discover howinfinitesimals become respectable, why there are different kinds of infinity, and how to square the circle with the mathematical equivalent of a pair of scissors.

Title The Princeton Companion to Atlantic History
Author Joseph C. Miller
Publisher Princeton University Press
Release Date 2015-01-18
Category Reference
Total Pages 568
ISBN 9781400852215
Language English, Spanish, and French
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Book Summary:

The first encyclopedic reference to Atlantic history Between the fifteenth and nineteenth centuries, the connections among Africa, the Americas, and Europe transformed world history—through maritime exploration, commercial engagements, human migrations and settlements, political realignments and upheavals, cultural exchanges, and more. This book, the first encyclopedic reference work on Atlantic history, takes an integrated, multicontinental approach that emphasizes the dynamics of change and the perspectives and motivations of the peoples who made it happen. The entries—all specially commissioned for this volume from an international team of leading scholars—synthesize the latest scholarship on central themes, including economics, migration, politics, war, technologies and science, the physical environment, and culture. Part one features five major essays that trace the changes distinctive to each chronological phase of Atlantic history. Part two includes more than 125 entries on key topics, from the seemingly familiar viewed in unfamiliar and provocative ways (the Seven Years' War, trading companies) to less conventional subjects (family networks, canon law, utopias). This is an indispensable resource for students, researchers, and scholars in a range of fields, from early American, African, Latin American, and European history to the histories of economics, religion, and science. The first encyclopedic reference on Atlantic history Features five major essays and more than 125 alphabetical entries Provides essential context on major areas of change: Economies (for example, the slave trade, marine resources, commodities, specie, trading companies) Populations (emigrations, Native American removals, blended communities) Politics and law (the law of nations, royal liberties, paramount chiefdoms, independence struggles in Haiti, the Hispanic Americas, the United States, and France) Military actions (the African and Napoleonic wars, the Seven Years' War, wars of conquest) Technologies and science (cartography, nautical science, geography, healing practices) The physical environment (climate and weather, forest resources, agricultural production, food and diets, disease) Cultures and communities (captivity narratives, religions and religious practices) Includes original contributions from Sven Beckert, Holly Brewer, Peter A. Coclanis, Seymour Drescher, Eliga H. Gould, David S. Jones, Wim Klooster, Mark Peterson, Steven Pincus, Richard Price and Sophia Rosenfeld, and many more Contains illustrations, maps, and bibliographies

Mathematicians by Mariana Ruth Cook

Title Mathematicians
Author Mariana Ruth Cook
Publisher American Mathematical Soc.
Release Date 2018
Category History and biography -- History of mathematics and mathematicians -- Contemporary
Total Pages 199
ISBN 1470448386
Language English, Spanish, and French
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Book Summary:

Photographs accompanied by autobiographical text written by each mathematician.

The Calculus Lifesaver by Adrian Banner

Title The Calculus Lifesaver
Author Adrian Banner
Publisher Princeton University Press
Release Date 2007-03-25
Category Mathematics
Total Pages 728
ISBN 9780691130880
Language English, Spanish, and French
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Book Summary:

For many students, calculus can be the most mystifying and frustrating course they will ever take. Based upon Adrian Banner's popular calculus review course at Princeton University, this book provides students with the essential tools they need not only to learn calculus, but also to excel at it.

From Music To Mathematics by Gareth E. Roberts

Title From Music to Mathematics
Author Gareth E. Roberts
Publisher JHU Press
Release Date 2016-02-15
Category Mathematics
Total Pages 320
ISBN 9781421419190
Language English, Spanish, and French
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Book Summary:

Taking a "music first" approach, Gareth E. Roberts's From Music to Mathematics will inspire students to learn important, interesting, and at times advanced mathematics. Ranging from a discussion of the geometric sequences and series found in the rhythmic structure of music to the phase-shifting techniques of composer Steve Reich, the musical concepts and examples in the book motivate a deeper study of mathematics. Comprehensive and clearly written, From Music to Mathematics is designed to appeal to readers without specialized knowledge of mathematics or music. Students are taught the relevant concepts from music theory (notation, scales, intervals, the circle of fifths, tonality, etc.), with the pertinent mathematics developed alongside the related musical topic. The mathematics advances in level of difficulty from calculating with fractions, to manipulating trigonometric formulas, to constructing group multiplication tables and proving a number is irrational. Topics discussed in the book include • Rhythm • Introductory music theory • The science of sound • Tuning and temperament • Symmetry in music • The Bartók controversy • Change ringing • Twelve-tone music • Mathematical modern music • The Hemachandra–Fibonacci numbers and the golden ratio • Magic squares • Phase shifting Featuring numerous musical excerpts, including several from jazz and popular music, each topic is presented in a clear and in-depth fashion. Sample problems are included as part of the exposition, with carefully written solutions provided to assist the reader. The book also contains more than 200 exercises designed to help develop students' analytical skills and reinforce the material in the text. From the first chapter through the last, readers eager to learn more about the connections between mathematics and music will find a comprehensive textbook designed to satisfy their natural curiosity.

Title Mathematical Statistical Mechanics
Author Colin J. Thompson
Publisher Princeton University Press
Release Date 2015-03-08
Category Science
Total Pages 290
ISBN 9781400868681
Language English, Spanish, and French
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Book Summary:

While most introductions to statistical mechanics are either too mathematical or too physical, Colin Thompson's book combines mathematical rigor with familiar physical materials. Following introductory chapters on kinetic theory, thermodynamics, the Gibbs ensembles, and the thermodynamic limit, later chapters discuss the classical theories of phase transitions, the Ising model, algebraic methods and combinatorial methods for solving the two-dimensional model in zero field, and some applications of the Ising model to biology. Originally published in 1979. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Title The Princeton Companion to Classical Japanese Literature
Author Earl Roy Miner
Publisher Princeton University Press
Release Date 2020-09-01
Category Literary Criticism
Total Pages 86
ISBN 9780691218380
Language English, Spanish, and French
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Book Summary:

The description for this book, The Princeton Companion to Classical Japanese Literature, will be forthcoming.

Encyclopedia Of Mathematics by James Stuart Tanton

Title Encyclopedia of Mathematics
Author James Stuart Tanton
Publisher Infobase Publishing
Release Date 2009-01-01
Category Mathematics
Total Pages 577
ISBN 9781438110080
Language English, Spanish, and French
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Book Summary:

Encyclopedia of Mathematics is a comprehensive one-volume encyclopedia designed for high school through early college students. More than 1,000 entries, numerous essays, and more than 125 photographs and illustrations cover the principal areas and issues that characterize this "new" area of science. This valuable resource unites disparate ideas and provides the meaning, history, context, and relevance behind each one. The easy-to-use format makes finding straightforward and natural answers to questions within arithmetic simple. Encyclopedia of Mathematics also gives historical context to mathematical concepts, with entries discussing ancient Arabic, Babylonian, Chinese, Egyptian, Greek, Hindu, and Mayan mathematics, as well as entries providing biographical descriptions of important people in the development of mathematics.

The Calculus Of Friendship by Steven Strogatz

Title The Calculus of Friendship
Author Steven Strogatz
Publisher Princeton University Press
Release Date 2011-03-07
Category Mathematics
Total Pages 184
ISBN 1400830885
Language English, Spanish, and French
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Book Summary:

The Calculus of Friendship is the story of an extraordinary connection between a teacher and a student, as chronicled through more than thirty years of letters between them. What makes their relationship unique is that it is based almost entirely on a shared love of calculus. For them, calculus is more than a branch of mathematics; it is a game they love playing together, a constant when all else is in flux. The teacher goes from the prime of his career to retirement, competes in whitewater kayaking at the international level, and loses a son. The student matures from high school math whiz to Ivy League professor, suffers the sudden death of a parent, and blunders into a marriage destined to fail. Yet through it all they take refuge in the haven of calculus--until a day comes when calculus is no longer enough. Like calculus itself, The Calculus of Friendship is an exploration of change. It's about the transformation that takes place in a student's heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. Written by a renowned teacher and communicator of mathematics, The Calculus of Friendship is warm, intimate, and deeply moving. The most inspiring ideas of calculus, differential equations, and chaos theory are explained through metaphors, images, and anecdotes in a way that all readers will find beautiful, and even poignant. Math enthusiasts, from high school students to professionals, will delight in the offbeat problems and lucid explanations in the letters. For anyone whose life has been changed by a mentor, The Calculus of Friendship will be an unforgettable journey.

Title Why Is There Philosophy of Mathematics At All
Author Ian Hacking
Publisher Cambridge University Press
Release Date 2014-01-30
Category Science
Total Pages 212
ISBN 9781107729827
Language English, Spanish, and French
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Book Summary:

This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities.

Title Calculus in 3D Geometry Vectors and Multivariate Calculus
Author Zbigniew Nitecki
Publisher American Mathematical Soc.
Release Date 2018-10-16
Category Calculus
Total Pages 405
ISBN 9781470443603
Language English, Spanish, and French
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Book Summary:

Calculus in 3D is an accessible, well-written textbook for an honors course in multivariable calculus for mathematically strong first- or second-year university students. The treatment given here carefully balances theoretical rigor, the development of student facility in the procedures and algorithms, and inculcating intuition into underlying geometric principles. The focus throughout is on two or three dimensions. All of the standard multivariable material is thoroughly covered, including vector calculus treated through both vector fields and differential forms. There are rich collections of problems ranging from the routine through the theoretical to deep, challenging problems suitable for in-depth projects. Linear algebra is developed as needed. Unusual features include a rigorous formulation of cross products and determinants as oriented area, an in-depth treatment of conics harking back to the classical Greek ideas, and a more extensive than usual exploration and use of parametrized curves and surfaces. Zbigniew Nitecki is Professor of Mathematics at Tufts University and a leading authority on smooth dynamical systems. He is the author of Differentiable Dynamics, MIT Press; Differential Equations, A First Course (with M. Guterman), Saunders; Differential Equations with Linear Algebra (with M. Guterman), Saunders; and Calculus Deconstructed, AMS.

Title Handbook of Writing for the Mathematical Sciences Third Edition
Author Nicholas J. Higham
Publisher SIAM
Release Date 2019-12-16
Category Mathematics
Total Pages 375
ISBN 9781611976106
Language English, Spanish, and French
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Book Summary:

Handbook of Writing for the Mathematical Sciences provides advice on all aspects of scientific writing, with a particular focus on writing mathematics. Its readable style and handy format, coupled with an extensive bibliography and comprehensive index, make it useful for everyone from undergraduates to seasoned professionals. This third edition revises, updates, and expands the best-selling second edition to reflect modern writing and publishing practices and builds on the author's extensive experience in writing and speaking about mathematics. Some of its key features include coverage of fundamentals of writing, including English usage, revising a draft, and writing when your first language is not English; thorough treatment of mathematical writing, including how to choose notation, how to choose between words and symbols, and how to format equations; and many tips for exploiting LaTeX and BibTeX. Higham also provides advice on how to write and publish a paper, covering the entire publication process, and includes anecdotes, quotes, and unusual facts that enliven the presentation. The new edition has been reorganized to make the book easier to use for reference; treats modern developments in publishing such as open access, DOIs, and ORCID; and contains more on poster design, including e-posters and the poster blitz. The new edition also includes five new chapters on the following topics: · workflow covering text editors, markup languages, version control, and much more; · the principles of indexing and how to prepare an index in LaTeX; · reviewing a paper, book proposal, or book; · writing a book, including advice on choosing a publisher and LaTeX tips particular to books; and · writing a blog post.

Title Foundations of Mathematics
Author Philip Brown
Publisher Stylus Publishing, LLC
Release Date 2016-03-14
Category Mathematics
Total Pages 382
ISBN 9781944534417
Language English, Spanish, and French
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Book Summary:

Foundations of Mathematics offers the university student or interested reader a unique reference book by covering the basics of algebra, trigonometry, geometry, and calculus. There are many instances in the book to demonstrate the interplay and interconnectedness of these topics. The book presents definitions and examples throughout for clear, easy learning. Numerous exercises are included at the ends of the chapters, and readers are encouraged to complete all of them as an essential part of working through the book. It offers a unique experience for readers to understand different areas of mathematics in one clear, concise text. Instructors’ resources are available upon adoption. Features: •Covers the basics of algebra, trigonometry, geometry, and calculus •Includes all of the mathematics needed to learn calculus •Demonstrates the interplay and interconnectedness of these topics •Uses numerous examples and exercises to reinforce concepts