Mathematical Sciences 2009 - Princeton University

1 Read newsworthy and lively commentary on our new blog at: for The Princeton Companion to Mathematics: This is a wonderful book. The content is overwhelming. Every practicing mathematician, everyone who uses mathematics, and everyone who is inter-ested in mathematics must have a copy of their own. Simon A. Levin, Princeton University The Princeton Companion to Mathemat-ics 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 math-ematics and mathematicians.

2 Endre S li, University of Oxford The Princeton Companion to Mathemat-ics 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 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, 1 Contents1 General Interest2 Annals of Mathematics Studies4 Princeton Mathematics Series5 London Mathematical Society Monographs5 Princeton Series in Applied Mathematics6 Princeton Graduate and Undergraduate Textbooks11 Princeton Lectures in Analysis12 Mathematical Sciences14 Mathematics and Social Sciences16 History and Philosophy of Science18 General Interest25 Books by Paul J.

3 Nahin26 Books by Julian Havil27 Books by Eli Maor28 Albert Einstein29 Index/Order FormProfessors who wish to consider a book from this catalog for course use may re-quest an examination copy. For more information please visit: of the books in this catalog are now being made available as e-book editions for the Amazon Kindle, Sony Reader, and in other formats that can be purchased from on-line booksellers. This icon listed with the title information for the print edition, indicates that an electronic edition is available. Princeton e-books are currently available only in North America. For more information, please visit our website at to the photos on the coverRow 1: Robert Clifford Gunning, Cathleen Synge Morawetz, George Olatokunbo Okikiolu, Andrei Okunkov, Alain Connes Row 2: Arlie Petters, Isadore Manual Singer, Maryam Mirzakhani, Curtis McMullen, John Willard Milnor Row 3: John Horton Conway, Edward Nelson, Mikhael Leonidovich Gromov, Jean-Pierre Serre, Kate Adebola Okikiolu Row 4: Avi Wigderson, William Alfred Massey, John N.

4 Mather, William Timothy Gowers, Marina Ratner Row 5: Sun-Yung Alice Chang, Adebisi Agboola, Ter-ence Chi-Chen Tao, Michele Vergne, Andrew Browder 1 NewThe Princeton Companion to MathematicsEdited by Timothy GowersJune Barrow-Green & Imre Leader, associate editorsThis 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 200 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.

5 Explore the impact of mathematics on other disciplines such as biology, finance, and music and much, much in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics, providing the context and broad perspective that are vital at a time of increasing specialization in the field. Packed with infor-mation and presented in an accessible style, this is an indispensable resource for undergradu-ate 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.

6 And more Traces the history and development of modern mathematics Profiles more than 95 mathematicians who influenced those working today Explores the influence of mathematics on other disciplines Includes bibliographies, cross-references, and a comprehensive indexTimothy Gowers is the Rouse Ball Professor of Mathematics at the University of Cambridge. June Barrow-Green is lecturer in the history of mathematics at the Open University . Imre Leader is professor of pure mathematics at the University of 1056 pages. 20 halftones. 160 line illus. Cl: 978-0-691-11880-2 $ | Annals of Mathematics StudiesForthcomingHigher Topos TheoryJacob LurieHigher category theory is generally regarded as technical and forbidding, but part of it is con-siderably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible.

7 In Higher Topos Theory, Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory s new language. The result is a powerful theory with applications in many areas of Lurie is associate professor of mathematics at Massachusetts Institute of 2009 . 960 pages. Pa: 978-0-691-14049-0 $ | Cl: 978-0-691-14048-3 $ | Hypoelliptic Laplacian and Ray-Singer MetricsJean-Michel Bismut & Gilles LebeauThis book presents the analytic foundations to the theory of the hypoelliptic Laplacian.

8 The hypoelliptic Laplacian, a second-order operator acting on the cotangent bundle of a compact manifold, is supposed to interpolate between the classical Laplacian and the geodesic flow. Jean-Michel Bismut and Gilles Lebeau establish the basic functional analytic properties of this opera-tor, which is also studied from the perspective of local index theory and analytic Bismut is professor of mathematics at the University of Paris-Sud. Gilles Lebeau is professor of mathematics at the University of Nice 376 pages. 4 line illus. Pa: 978-0-691-13732-2 $ | Cl: 978-0-691-13731-5 $ | Spaces of Degenerating Polarized Hodge StructuresKazuya Kato & Sampei UsuiIn 1970, Phillip Griffiths envisioned that points at infinity could be added to the classifying space D of polarized Hodge structures.

9 In this book, Kazuya Kato and Sampei Usui realize this dream by creating a logarithmic Hodge theory. They use the logarithmic structures begun by Fontaine-Illusie to revive nilpotent orbits as a logarithmic Hodge Kato is professor of mathematics at Kyoto University . Sampei Usui is professor of mathematics at Osaka 352 pages. 58 line illus. Pa: 978-0-691-13822-0 $ | Cl: 978-0-691-13821-3 $ | of Mathematics StudiesPhillip A. Griffiths, John N. Mather & Elias M. Stein, series editorsPrinceton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential Mathematical works of the twentieth century.

10 The series continues this tradition into the twenty-first century. To mark the continued success of the series, all books are available again in paperback. For a complete listing of all books in this series, please check our web site: receive notices about new books, subscribe for email at: Annals of Mathematics Studies 3 NewThe Structure of Affine BuildingsRichard M. WeissIn The Structure of Affine Buildings, Richard Weiss gives a detailed presentation of the complete proof of the classification of Bruhat-Tits buildings first completed by Jacques Tits in 1986. The book includes numerous results about auto-morphisms, completions, and residues of these buildings.