2010; 236 pp; softcover
ISBN-13: 978-0-8218-4928-6
Expected publication date is July 16, 2010.
Szpiro's book provides a delightful, well-written, eclectic selection of mathematical tidbits that makes excellent airplane reading for anyone with an interest in mathematics, regardless of their mathematical background. Excellent gift material.
--Keith Devlin, Stanford University, author of The Unfinished Game and The Language of Mathematics
It is great to have collected in one volume the many varied, insightful and often surprising mathematical stories that George Szpiro has written in his mathematical columns for the newspapers through the years.
--Marcus du Sautoy, Oxford University, author of The Music of the Primes and Symmetry: A Journey into the Patterns of Nature
Mathematics is thriving. Not only have long-standing problems, such as the Poincare conjecture, been solved, but mathematics is an important element of many modern conveniences, such as cell phones, CDs, and secure transactions over the Internet. For good or for bad, it is also the engine that drives modern investment strategies. Fortunately for the general public, mathematics and its modern applications can be intelligible to the non-specialist, as George Szpiro shows in A Mathematical Medley.
In stories of a few pages each, Szpiro describes in layman's terms mathematical problems that have recently been solved (or thought to have been solved), research that was published in scientific journals, and mathematical observations about contemporary life. Anecdotal stories about the lives of mathematicians and stories about famous old problems are interspersed among other vignettes.
This book is intended for true general readers who are interested in any sort of mathematics.
A baker's dozen
Math for math's sake
Math applied to real life
Personalities
In the air
Training the brain
Games, gifts, and other diversions
Choosing and dividing
Money, and making it
Interdisciplinary matters
References
Clay Mathematics Proceedings, Volume: 9
2010; 187 pp; softcover
ISBN-13: 978-0-8218-5191-3
Expected publication date is July 17, 2010.
The subject of algebraic cycles has its roots in the study of divisors, extending as far back as the nineteenth century. Since then, and in particular in recent years, algebraic cycles have made a significant impact on many fields of mathematics, among them number theory, algebraic geometry, and mathematical physics. The present volume contains articles on all of the above aspects of algebraic cycles. It also contains a mixture of both research papers and expository articles, so that it would be of interest to both experts and beginners in the field.
Graduate students and research mathematicians interested in algebraic geometry.
Transcendental aspects
D. Arapura -- The Hodge theoretic fundamental group and its cohomology
X. Chen and J. D. Lewis -- The real regulator for a self-product of a general surface
E. M. Friedlander and C. Haesemeyer -- Lipschitz cocycles and Poincare duality
C. Pedrini -- On the motive of a K3 surface
C. Schnell -- Two observations about normal functions
Positive characteristics and arithmetic
J.-L. Colliot-Thelene and T. Szamuely -- Autour de la conjecture de Tate a coefficients Z_{ell} pour les varietes sur les corps finis
H. Gangl -- Regulators via iterated integrals (numerical computations)
A. S. Merkurjev -- Zero-cycles on algebraic tori
A. Miller -- Chow-Kunneth projectors and ell-adic cohomology
Connections with mathematical physics
S. Bloch -- Motives associated to sums of graphs
L. Guo, S. Paycha, B. Xie, and B. Zhang -- Double shuffle relations and renormalization of multiple zeta values
CBMS Regional Conference Series in Mathematics, Number: 113
2010; 118 pp; softcover
ISBN-13: 978-0-8218-4986-6
Expected publication date is July 9, 2010.
This book is the companion to the CBMS lectures of Scott Wolpert at Central Connecticut State University. The lectures span across areas of research progress on deformations of hyperbolic surfaces and the geometry of the Weil-Petersson metric. The book provides a generally self-contained course for graduate students and postgraduates. The exposition also offers an update for researchers; material not otherwise found in a single reference is included.
A unified approach is provided for an array of results. The exposition covers Wolpert's work on twists, geodesic-lengths and the Weil-Petersson symplectic structure; Wolpert's expansions for the metric, its Levi-Civita connection and Riemann tensor. The exposition also covers Brock's twisting limits, visual sphere result and pants graph quasi isometry, as well as the Brock-Masur-Minsky construction of ending laminations for Weil-Petersson geodesics. The rigidity results of Masur-Wolf and Daskalopoulos-Wentworth, following the approach of Yamada, are included. The book concludes with a generally self-contained treatment of the McShane-Mirzakhani length identity, Mirzakhani's volume recursion, approach to Witten-Kontsevich theory by hyperbolic geometry, and prime simple geodesic theorem.
Lectures begin with a summary of the geometry of hyperbolic surfaces and approaches to the deformation theory of hyperbolic surfaces. General expositions are included on the geometry and topology of the moduli space of Riemann surfaces, the CAT(0) geometry of the augmented Teichmuller space, measured geodesic and ending laminations, the deformation theory of the prescribed curvature equation, and the Hermitian description of Riemann tensor. New material is included on estimating orbit sums as an approach for the potential theory of surfaces.
Graduate students and research mathematicians interested in Riemann surfaces, moduli spaces of Riemann surfaces, and Teichmuller theory.
Preliminaries
Teichmuller space and horizontal strip deformations
Geodesic-lengths, twists and symplectic geometry
Geometry of the augmented Teichmuller space, part 1
Geometry of the augmented Teichmuller space, part 2
Geometry of the augmented Teichmuller space, part 3
Deformations of hyperbolic metrics and the curvature tensor
Collar expansions and exponential-distance sums
Train tracks and the Mirzakhani volume recursion
Mirzakhani prime simple geodesic theorem
Bibliography
Index
AMS Chelsea Publishing, Volume: 370
2010; 222 pp; hardcover
ISBN-13: 978-0-8218-5193-7
Expected publication date is August 21, 2010.
Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within.
The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea--transversality--the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main results. In this way, they present intelligent treatments of important theorems, such as the Lefschetz fixed-point theorem, the Poincare-Hopf index theorem, and Stokes theorem.
The book has a wealth of exercises of various types. Some are routine explorations of the main material. In others, the students are guided step-by-step through proofs of fundamental results, such as the Jordan-Brouwer separation theorem. An exercise section in Chapter 4 leads the student through a construction of de Rham cohomology and a proof of its homotopy invariance.
The book is suitable for either an introductory graduate course or an advanced undergraduate course.
Undergraduate and graduate students interested in differential topology
Manifolds and smooth maps
Transversality and intersection
Oriented intersection theory
Integration on manifolds
Measure zero and Sard's theorem
Classification of compact one-manifolds
Bibliography
Index
Contemporary Mathematics, Volume: 517
2010; 413 pp; softcover
ISBN-13: 978-0-8218-4869-2
Expected publication date is July 8, 2010.
These proceedings reflect the special session on Experimental Mathematics held January 5, 2009, at the Joint Mathematics Meetings in Washington, DC as well as some papers specially solicited for this volume.
Experimental Mathematics is a recently structured field of Mathematics that uses the computer and advanced computing technology as a tool to perform experiments. These include the analysis of examples, testing of new ideas, and the search of patterns to suggest results and to complement existing analytical rigor.
The development of a broad spectrum of mathematical software products, such as MathematicaR and MapleTM, has allowed mathematicians of diverse backgrounds and interests to use the computer as an essential tool as part of their daily work environment.
This volume reflects a wide range of topics related to the young field of Experimental Mathematics. The use of computation varies from aiming to exclude human input in the solution of a problem to traditional mathematical questions for which computation is a prominent tool.
Graduate students and research mathematicians interested in computational aspects of mathematics.
G. Almkvist -- The art of finding Calabi-Yau differential equations
T. Amdeberhan -- A note on a question due to A. Garsia
D. H. Bailey and J. M. Borwein -- Experimental computation with oscillatory integrals
D. H. Bailey, J. M. Borwein, D. Broadhurst, and W. Zudilin -- Experimental mathematics and mathematical physics
S. T. Boettner -- An extension of the parallel Risch algorithm
R. P. Boyer and W. M. Y. Goh -- Appell polynomials and their zero attractors
O-Y. Chan and D. Manna -- Congruences for Stirling numbers of the second kind
M. W. Coffey -- Expressions for harmonic number exponential generating functions
R. E. Crandall -- Theory of log-rational integrals
S. Garoufalidis and X. Sun -- A new algorithm for the recursion of hypergeometric multisums with improved universal denominator
I. Gonzalez, V. H. Moll, and A. Straub -- The method of brackets. Part 2: Examples and applications
J. G. Goyanesa -- History of the formulas and algorithms for pi
J. Guillera -- A matrix form of Ramanujan-type series for 1/pi
K. Kohl and F. Stan -- An algorithmic approach to the Mellin transform method
C. Koutschan -- Eliminating human insight: An algorithmic proof of Stembridge's TSPP theorem
M. L. Lapidus and R. G. Niemeyer -- Towards the Koch snowflake fractal billiard: Computer experiments and mathematical conjectures
L. A. Medina and D. Zeilberger -- An experimental mathematics perspective on the old, and still open, question of when to stop?
M. J. Mossinghoff -- The distance to an irreducible polynomial
S. Northshield -- Square roots of 2 x 2 matrices
O. Oloa -- On a series of Ramanujan
P. Raff and D. Zeilberger -- Finite analogs of Szemeredi's theorems
A. V. Sills -- Towards an automation of the circle method
J. H. Silverman -- The greatest common divisor of a^n-1 and b^n-1 and the Ailon-Rudnick conjecture
J. Sondow and K. Schalm -- Which partial sums of the Taylor series for e are convergents to e? (and a link to the primes 2, 5, 13, 37, 463). II
C. Hillar, L. Garcia-Puente, A. M. Del Campo, J. Ruffo, Z. Teitler, S. L. Johnson, and F. Sottile -- Experimentation at the frontiers of reality in Schubert calculus
Y. Yang and W. Zudilin -- On Sp_4 modularity of Picard-Fuchs differential equations for Calabi-Yau threefolds