Paper | October 2010
216 pp. | 6 x 9 | 18 halftones. 143 line illus.
ISBN13: 978-0-691-14822-9
Math--the application of reasonable logic to reasonable assumptions--usually produces reasonable results. But sometimes math generates astonishing paradoxes--conclusions that seem completely unreasonable or just plain impossible but that are nevertheless demonstrably true: Conclusions that, for example, tell us that a losing sports team can become a winning one by adding worse players than its opponents. Or that the thirteenth of the month is more likely to be a Friday than any other day. Or that cones can roll unaided uphill. In Nonplussed!--a delightfully eclectic collection of paradoxes from many different areas of math--popular-math writer Julian Havil reveals the math that shows the truth of these and many other unbelievable ideas.
Nonplussed! pays special attention to problems from probability and statistics, areas where intuition can easily be wrong. These problems include the vagaries of tennis scoring, what can be deduced from tossing a needle, and disadvantageous games that form winning combinations. Other chapters address everything from the historically important Torricelli's Trumpet to the mind-warping implications of objects that live on high dimensions. Readers learn about the colorful history and people associated with many of these problems in addition to their mathematical proofs.
Nonplussed! will appeal to anyone with a calculus background who enjoys popular math books or puzzles.
Julian Havil is a former Master at Winchester College, England, where he taught mathematics for more than thirty years. He is the author of Gamma: Exploring Euler's Constant and Impossible?: Surprising Solutions to Counterintuitive Conundrums (both Princeton).
Preface xi
Acknowledgements xiii
Introduction 1
Chapter 1: Three Tennis Paradoxes 4
Chapter 2: The Uphill Roller 16
Chapter 3: The Birthday Paradox 25
Chapter 4: The Spin of a Table 37
Chapter 5: Derangements 46
Chapter 6: Conway's Chequerboard Army 62
Chapter 7: The Toss of a Needle 68
Chapter 8: Torricelli's Trumpet 82
Chapter 9: Nontransitive Effects 92
Chapter 10: A Pursuit Problem 105
Chapter 11: Parrondo's Games 115
Chapter 12: Hyperdimensions 127
Chapter 13: Friday the 13th 151
Chapter 14: Fractran 162
The Motifs 180
Appendix A: The Inclusion-Exclusion Principle 187
Appendix B: The Binomial Inversion Formula 189
Appendix C: Surface Area and Arc Length 193
Index 195
Cloth | November 2010
160 pp. | 6 x 9 | 55 line illus. 11 tables.
978-0-691-14503-7
This book lays out the theoretical groundwork for personalized search and reputation management, both on the Web and in peer-to-peer and social networks. Representing much of the foundational research in this field, the book develops scalable algorithms that exploit the graphlike properties underlying personalized search and reputation management, and delves into realistic scenarios regarding Web-scale data.
Sep Kamvar focuses on eigenvector-based techniques in Web search, introducing a personalized variant of Google's PageRank algorithm, and he outlines algorithms--such as the now-famous quadratic extrapolation technique--that speed up computation, making personalized PageRank feasible. Kamvar suggests that Power Method-related techniques ultimately should be the basis for improving the PageRank algorithm, and he presents algorithms that exploit the convergence behavior of individual components of the PageRank vector. Kamvar then extends the ideas of reputation management and personalized search to distributed networks like peer-to-peer and social networks. He highlights locality and computational considerations related to the structure of the network, and considers such unique issues as malicious peers. He describes the EigenTrust algorithm and applies various PageRank concepts to P2P settings. Discussion chapters summarizing results conclude the book's two main sections.
Cloth | December 2010
720 pp. | 6 x 9 | 8 line illus.
ISBN13: 978-0-691-14704-8
This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gabor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows for the first book-length treatment of orthogonal polynomials for measures supported on a finite number of intervals on the real line.
In addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle (OPUC) and orthogonal polynomials on the real line (OPRL), Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC.
Barry Simon is the IBM Professor of Mathematics and Theoretical Physics at the California Institute of Technology. His books include Methods of Modern Mathematical Physics and Orthogonal Polynomials on the Unit Circle.
Cloth | February 2011
432 pp. | 6 x 9 | 59 halftones.
ISBN13: 978-0-691-14247-0
Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions--and inspire more love and hatred--than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. Loving and Hating Mathematics is about the hidden human, emotional, and social forces that shape mathematics and affect the experiences of students and mathematicians. Written in a lively, accessible style, and filled with gripping stories and anecdotes, Loving and Hating Mathematics brings home the intense pleasures and pains of mathematical life.
These stories challenge many myths, including the notions that mathematics is a solitary pursuit and a "young man's game," the belief that mathematicians are emotionally different from other people, and even the idea that to be a great mathematician it helps to be a little bit crazy. Reuben Hersh and Vera John-Steiner tell stories of lives in math from their very beginnings through old age, including accounts of teaching and mentoring, friendships and rivalries, love affairs and marriages, and the experiences of women and minorities in a field that has traditionally been unfriendly to both. Included here are also stories of people for whom mathematics has been an immense solace during times of crisis, war, and even imprisonment--as well as of those rare individuals driven to insanity and even murder by an obsession with math.
This is a book for anyone who wants to understand why the most rational of human endeavors is at the same time one of the most emotional.
Reuben Hersh is professor emeritus of mathematics at the University of New Mexico and the coauthor of The Mathematical Experience, which won the National Book Award. He is also the author of What Is Mathematics, Really? Vera John-Steiner is professor emerita of linguistics and education at the University of New Mexico. Her books include Notebooks of the Mind, which won the William James Book Award from the American Psychological Association.
Paper | January 2011
360 pp. | 5 1/2 x 8 1/2 | 20 line illus.
ISBN13: 978-0-691-14841-0
This anthology brings together the year's finest writing on mathematics from around the world. Featuring promising new voices alongside some of the foremost names in mathematics, The Best Writing on Mathematics makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here readers will discover why Freeman Dyson thinks some mathematicians are birds while others are frogs; why Keith Devlin believes there's more to mathematics than proof; what Nick Paumgarten has to say about the timing patterns of New York City's traffic lights (and why jaywalking is the most mathematically efficient way to cross Sixty-sixth Street); what Samuel Arbesman can tell us about the epidemiology of the undead in zombie flicks; and much, much more.
In addition to presenting the year's most memorable writing on mathematics, this must-have anthology also includes a foreword by esteemed mathematician William Thurston and an informative introduction by Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it's headed.
Mircea Pitici is a PhD candidate in mathematics education at Cornell University. He teaches mathematics courses and writing seminars at Cornell and Ithaca College.