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The Princeton Companion to Mathematics
Free Download The Princeton Companion to Mathematics
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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 contributorsPresents major ideas and branches of pure mathematics in a clear, accessible styleDefines and explains important mathematical concepts, methods, theorems, and open problemsIntroduces the language of mathematics and the goals of mathematical researchCovers number theory, algebra, analysis, geometry, logic, probability, and moreTraces the history and development of modern mathematicsProfiles more than ninety-five mathematicians who influenced those working todayExplores the influence of mathematics on other disciplinesIncludes bibliographies, cross-references, and a comprehensive indexContributors 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
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Product details
Hardcover: 1034 pages
Publisher: Princeton University Press; Third Printing Used edition (September 28, 2008)
Language: English
ISBN-10: 0691118809
ISBN-13: 978-0691118802
Product Dimensions:
8.1 x 2.5 x 10 inches
Shipping Weight: 6 pounds (View shipping rates and policies)
Average Customer Review:
4.5 out of 5 stars
84 customer reviews
Amazon Best Sellers Rank:
#127,217 in Books (See Top 100 in Books)
I love this book. I have the paper and kindle versions because they complement each other. It is because of books like this that make me eschew TV so I can buy more books. Don't try to understand everything the first time around, just read it and wonder at how many smart people there are and why you never seem to get to meet them. This book delivers shock and awe for people who like to think. There are no exercises to make you feel guilty about not doing them.
This wonderful volume is one of four works I always keep in digital or desk drawer reach while reading/studying/ referencing any other math book or journal article, the complete list being:-- Encyclopedia Of Mathematics (Science Encyclopedia)-- The Princeton Companion to Mathematics-- Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover Books on Mathematics)-- NIST Handbook of Mathematical Functions (Being of course the 2010 update of the Abramowitz classic above).Given these four, there is hardly a topic from among the current 495 math fields of study that isn't at least explained in enough detail to save LOTS of time on link expeditions. At minimum, these give head starts on alphabetized keywords that will quickly fill holes in any research project, class, or syllabus.
If you have a working math background and want to look at areas you never studied this is a great introduction. The preface says it was designed to introduce various areas of math to people with a math background in other areas. It works very well in that role. Although it displays only on my PC not on my paper-white the display is convenient and works very well. I am not a great typo hunter but have not found any.
This will keep me reading for years, and it's surprisingly well written. The problem with a book like this is that it can't really afford to go into depth (or it would grow to titanic size), but I guess that it's purpose is to expose people to interesting mathematics where they can get enough of a taste to know when to dive deeper. It does require discipline to stay on track at times, but it's worth pushing through (although I'm not finished yet).
Got my copy a week ago. What an exceptional book! Any of the random samples I read so far provides a informative, yet pleasant read. Gowers (Rouse Ball Professor of Mathematics in Cambridge) did a fantastic job in editing the many articles into a coherent and surprisingly accessible overview of modern mathematics. From inception to publication of this book took Gowers and his associate editors some 6 years. The amount of editorial attention given to this publication clearly shows and translated into a book that is - unlike any other math book I know of - easy to read and of high quality.This book provides lots of material that is of interest to non-mathematicians. As is mentioned in one of the other reviews here, this heavy volume does not contain a separate chapter on mathematical physics, yet as a physicist I found lots of material directly relevant to physics. There is a very interesting chapter on the general theory of relativity, and lots of material on quantum mechanics. Also fundamental concepts highly relevant in physics such as spherical harmonics, dynamical systems, deterministic chaotic behavior, phase transitions, Lie groups, etc. are covered in inviting shorter sections. Each of the subjects is introduced in such a way that the reader first gains an intuitive understanding of the concept, that subsequently gets deepened via a more rigorous approach.If only there was a similar 'companion' to modern physics! (The book of Oxford's Emeritus Rouse Ball professor Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe comes close, but falls short of being truly PCM's equivalent in physics.)If you're interested in math, don't hesitate and buy this book. (And be quick: I bought it here at Amazon for just over US$71. In the meantime, the price has increased already by more than US$5... ;-)
I haven't seen the printed version of this book, but it must be huge. This books covers a lot of topics in depth and you can regard it as a complement to the online Wikipedia pages or the Mathworld pages on the same subjects. I'm very happy with it, but I can't say that I've read the whole thing. It's a reference: very few people will ever read the whole thing.I'm an ex-math major picking his way through Galois Theory thirty years after graduation (and I wander into a lot of other topics, too). That's what I use this for. It would be interesting to hear what some research mathematicians think of it.
I own both the hardbound and the Kindle versions of this book. I really like the breadth and consistency of coverage of mathematics and mathematicians. Sure there's a lot of wiki content on the net for each topic but the consistency and quality of content isn't generally found in a single resource such as The Princeton Companion.The real issue is the poor Kindle version. many graphic elements that don't resize with changes in font size in the reader, insertion of a graphic for such things as |R for the Reals instead of typesetting it, white backgrounds on images that don't work with the sepia and black backgrounds and so on.It is really terrifically annoying that time and again books with heavy mathematical content beautifully typeset in physical or print replica editions are foisted off on readers in inadequately executed eReader formats such as mobi and ePub.If you check my reviews you'll find many Kindle formatted math books reviewed of which only the print replica versions are acceptable.
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