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The Princeton Companion to Mathematics Hardcover – 28 Sep 2008

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Product details

  • Hardcover: 1056 pages
  • Publisher: Princeton University Press (28 Sept. 2008)
  • Language: English
  • ISBN-10: 0691118809
  • ISBN-13: 978-0691118802
  • Product Dimensions: 25.4 x 20.6 x 6.4 cm
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (15 customer reviews)
  • Amazon Bestsellers Rank: 36,798 in Books (See Top 100 in Books)
  • See Complete Table of Contents

Product Description

Review


Winner of the 2011 Euler Book Prize, Mathematical Association of America



Honorable Mention for the 2008 PROSE Award for Single Volume Reference/Science, Association of American Publishers



One of Choice's Outstanding Academic Titles for 2009


"The Princeton Companion to Mathematics makes a heroic attempt to keep [abstract concepts] to a minimum . . . and conveys the breadth, depth and diversity of mathematics. It is impressive and well written and it's good value for [the] money."--Ian Stewart, The Times

"This is a panoramic view of modern mathematics. It is tough going in some places, but much of it is surprisingly accessible. A must for budding number-crunchers."--The Economist (Best Books of 2008)

"Although the editors' original goal of text that could be understood by anyone with a good background in high school mathematics provided short-lived, this wide-ranging account should reward undergraduate and graduate students and anyone curious about math as well as help research mathematicians understand the work of their colleagues in other specialties. The editors note some advantages a carefully organized printed reference may enjoy over a collection of Web pages, and this impressive volume supports their claim."--Science

"This impressive book represents an extremely ambitious and, I might add, highly successful attempt by Timothy Gowers and his coeditors, June Barrow-Green and Imre Leader, to give a current account of the subject of mathematics. It has something for nearly everyone, from beginning students of mathematics who would like to get some sense of what the subject is all about, all the way to professional mathematicians who would like to get a better idea of what their colleagues are doing. . . . If I had to choose just one book in the world to give an interested reader some idea of the scope, goals and achievements of modern mathematics, without a doubt this would be the one. So try it. I guarantee you'll like it!"--American Scientist

"Accessible, technically precise and thorough account of all math's major aspects. Students of math will find this book a helpful reference for understanding their classes; students of everything else will find helpful guides to understanding how math describes it all."--Tom Siegfried, Science News

"Once in a while a book comes along that should be on every mathematician's bookshelf. This is such a book. Described as a 'companion', this 1000-page tome is an authoritative and informative reference work that is also highly pleasurable to dip into. Much of it can be read with benefit by undergraduate mathematicians, while there is a great deal to engage professional mathematicians of all persuasions."--Robin Wilson, London Mathematical Society

"Imagine taking an overview of elementary and advanced mathematics, a history of mathematics and mathematicians, and a mathematical encyclopedia and combining them all into one comprehensive reference book. That is what Timothy Gowers, the 1998 Fields Medal laureate, has successfully accomplished in compiling and editing The Princeton Companion to Mathematics. At more than 1,000 pages and with nearly 200 entries written by some of the leading mathematicians of our time and specialists in their fields, this book is a one-of-a-kind reference for all things mathematics."--Mathematics Teacher

"Overall [The Princeton Companion to Mathematics] is an enormous achievement for which the authors deserve to be thanked. It contains a wealth of material, much of a kind one would not find elsewhere, and can be enjoyed by readers with man different backgrounds."--Simon Donaldson, Notices of the American Mathematical Society

"This is an enormously ambitious book, full of beautiful things; I would wish to keep it on my bedside table, but that could only be possible relays, since of course it is far too large. . . . To sum up, [The Princeton Companion to Mathematics] is really excellent. I know of no book that will give a young student a better idea of what mathematics is about. I am certain that this is the only single book that is likely to tell me what my colleagues are doing."--Bryan Birch, Notices of the American Mathematical Society

"The book is so rich and yet it is well done. A rare achievement indeed!"--Gil Kalai, Notices of the American Mathematical Society

"My advice to you, reader is to buy the book, open it to a random page, read, enjoy, and be enlightened."--Richard Kenyon, Notices of the American Mathematical Society

"Massive . . . endlessly fascinating."--Gregory McNamee, Bloomsbury Review

"This volume is an enormous, far-reaching effort to survey the current landscape of (pure) mathematics. Chief editor Gowers and associate editors Barrow-Green and Leader have enlisted scores of leading mathematicians worldwide to produce a gorgeous volume of longer essays and short, specific articles that convey some of the dense fabric of ideas and techniques of modern mathematics. . . . This volume should be on the shelf of every university and public library, and of every mathematician--professional and amateur alike."--S.J. Colley, Choice

"The Princeton Companion to Mathematics is a friendly, informative reference book that attempts to explain what mathematics is about and what mathematicians do. Over 200 entries by a panel of experts span such topics as: the origins of modern mathematics; mathematical concepts; branches of mathematics; mathematicians that contributed to the present state of the discipline; theorems and problems; the influences of mathematics and some perspectives. Its presentations are selective, satisfying, and complete within themselves but not overbearingly comprehensive. Any reader from a curious high school student to an experienced mathematician seeking information on a particular mathematical subject outside his or her field will find this book useful. The writing is clear and the examples and illustrations beneficial."--Frank Swetz, Convergence

"Every research mathematician, every university student of mathematics, and every serious amateur of mathematical science should own a least one copy of The Companion. Indeed, the sheer weight of the volume suggests that it is advisable to own two: one for work and one at home. . . . Even an academic sourpuss should be pleased with the attention to detail of The Companion's publishers, editors, and authors and with many judicious decisions about the level of exposition, level of detail, what to include and what to omit, and much more--which have led to a well-integrated and highly readable volume."--Jonathan M. Borwein, SIAM Review

"Edited by Gowers, a recipient of the Fields Medal, this volume contains almost 200 entries, commissioned especially for this book from the world's leading mathematicians. It introduces basic mathematical tools and vocabulary, traces the development of modern mathematics, defines essential terms and concepts, and puts them in context. . . . Packed with information presented in an accessible 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."--Library Journal

"The book I'm talking about is The Princeton Companion to Mathematics. If you are in an absolute rush, the short version of my post today is, buy this book. You don't have to click on the link with my referral if you don't want to, seriously just pick up a copy of this book, I can guarantee you that it will be love at first sight. . . . The Princeton Companion to Mathematics is not only a beautiful book from an aesthetic standpoint, with its heavy, high quality pages and sturdy binding, but above all it's a monumental piece of work. I have never seen a book like this before. . . . [T]he bible of mathematics. . . . I believe this is the kind of book that will still be in use a hundred years from now."--Antonio Cangiano, Math-Blog.com

"I'm completely charmed. This is one of those books that makes you wish you had a desert island to be marooned on."--Brian Hayes, bit-player.org

"This has been a long time coming, but the wait was worth it! After many years of slogging through textbooks that presented too many proofs and demonstrations that were left to the student or lacking numerous intermediate steps, after encountering numerous 'introductions' that were obtuse and highly theoretical and after digesting far too many explanations with maximal equations and minimal verbiage, we arrive at the happy medium. This book is a companion in every sense of the word and a very friendly one at that. . . . For a comprehensive overview of many areas of mathematics in a readable format, there has never been anything quite like this. I would urge a trip to the local library to have a look."--John A. Wass, Scientific Computing

"This book is supremely accessible. Many in the sugar industry with a fairly good grasp of mathematics will probably not struggle with it, and will invariably marvel at its richness and diversity. [A] great companion."--International Sugar Journal

"The book contains some valuable surveys of the main branches of mathematics that are written in an accessible style. Hence, it is recommended both to students of mathematics and researchers seeking to understand areas outside their specialties."--European Mathematical Society Newsletter

From the Back Cover


"This is a wonderful book. The content is overwhelming. Every practicing mathematician, everyone who uses mathematics, and everyone who is interested in mathematics must have a copy of their own."--Simon A. Levin, Princeton University


"The Princeton Companion to Mathematics fills a vital need. It is the only book of its kind."--Victor J. Katz, professor emeritus, University of the District of Columbia


"I think that this is a wonderful book, completely different from anything that has been written before about mathematics and mathematicians."--Endre Süli, University of Oxford


"The Princeton Companion to Mathematics is a much needed--and will become a much used--reference work. In fact, it will stand alone as the reference work in mathematics."--John J. Watkins, Colorado College



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Most Helpful Customer Reviews

60 of 61 people found the following review helpful By Mr. M. Bennet on 5 Nov. 2008
Format: Hardcover
I received a copy of this book for my birthday this year, and was immediately drawn towards the material on algebra with which I was most familiar. The most striking thing about the book as a whole, both in the bits I know well, and the bits I don't know much about, is the way in which it combines large portions of accessible text with substantial mathematical content - it is the lack of actual serious content which frustrates me most about popular books about maths (Fermat's Last Theorem and the Riemann Hypothesis have received the popular treatment with limited content). But in this companion there are clues to enable an enthusiast to engage with the material.

It is right to say, as the introduction does, that there is material in this book which will require some knowledge beyond what you might learn at school. But do not let that put you off (it is no more daunting than the physical size of the book, which mirrors only its extensive coverage). For the genius of this companion is in the way that it engages with real mathematics and how it is actually done by real mathematicians. It is not simply a presentation of particular subject matter (as in a text book) nor is it an encyclopedia of mathematics, for it seeks to convey an understanding of the nature and importance of pure mathematics, rather than simply definitions of the component parts - and through disciplined editing and clear exposition it sets a standard which will not easily be matched.

There is a huge amount which will challenge and excite a good A-level student.
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12 of 12 people found the following review helpful By I. W. Slater on 6 Jan. 2011
Format: Hardcover
I hesitated before buying this book, thinking that there would be little that I would understand. I have a degree in mathematics from Cambridge, but that was achieved 50 years ago and although I have kept my interest and read a number of popular books on the subject, I have never continued my studies and have forgotten most of what I once knew.

The book is a delight. Look inside and you will find a wide range of topics, ranging from a series of introductory articles to biographical and historical sections and including descriptions of the branches of the subject currently under investigation and the impact of mathematics on the practical world.

If you have an interest in mathematics and are tempted, do seriously consider buying this book. There will be (almost certainly) some parts that you find very difficult but there will be very many that give you a fascinating insight and great pleasure.
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36 of 39 people found the following review helpful By A. Marshall on 7 Oct. 2010
Format: Kindle Edition
This review applies only to the Kindle version.

The print edition of this book is a fantastic, weighty tome and is well worth every penny. Unfortunately the same cannot be said of the Kindle edition. For such a huge text, the failure to take advantage of hyperlinks makes browsing the book a frustrating experience. In addition, mathematical graphics and equations are rendered in low resolution and are virtually unreadable. As the Kindle device is perfectly capable of rendering high quality graphical content, this lapse is unforgiveable in an ebook costing this much.

Disappointing.
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1 of 1 people found the following review helpful By J G M REID on 13 Jan. 2014
Format: Kindle Edition Verified Purchase
My formal maths education ended 30 years ago with university level mathematics for engineering. A renewed interest had me looking for a book that explains how the many topics within mathematics are linked together, in a way that limits the use of the formal language of maths. The search is over....this is the book.

It is not a textbook, and you won't earn a college degree by reading it, but anyone reading part 1 will understand fundamentals which will make textbooks much easier to read. Part 2 is also a good path to understanding the history of mathematics, and both why and how it was developed to solve real problems that man has faced down the years.
Further sections explain key concepts in language as close to laymans's terms as possible, and give more detailed guides to major subtopics, significant contemporary questions, prominent figures, applications to other area of science and life as a mathematician.

The book is not 'light' reading in any sense. Maths can be inherently difficult, and the contents of the Companion are essays without illustrations. The hard copy is also physically daunting, which is why I would recommend the digital kindle version for each of access and use.

Nonetheless, if you have an interest in mathematics and have some level of maths education then, whether you use it as a guide to the subject or as a companion to deeper study, this is a book you should have.
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9 of 11 people found the following review helpful By Daniel J. Burridge on 23 Aug. 2009
Format: Hardcover
This is a great book. Its entries are well written by recognisable experts and at a high enough level so that people attempting research may use them as a starting point or even as a guide to the main people in the field. It can be read by the amateur too. Other good points are: the quality and depth of coverage, the connections made between fields, and the broad perpective it provides on the subject.
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