Notices of the American Mathematical Society ISSN 0002-9920 ABCD springer.com New and Noteworthy from Springer Random Curves Number Story of the American Mathematical Society AVAILABLE Journeys of a From Counting to ONLINE April 2008 Volume 55, Number 4 Mathematician Cryptography N. Koblitz , University of P. M. Higgins , University Journal of Washington, Seattle, WA, of Essex, UK Geometric USA Numbers have fascinated These autobiographical people for centuries. They Analysis Mathematics and memoirs of Neal Koblitz, are familiar to everyone, coinventor of one of the two most popular forms forming a central pillar of our understanding of Editor-in-Chief: S. G. Krantz Voting of encryption and digital signature, cover many the world, yet the number system was not JGA is a high-quality journal devoted to topics besides his own personal career in presented to us “gift-wrapped” but, rather, was publishing important new results at the interface page 448 mathematics and cryptography - travels to the developed over millennia. Peter Higgins distills of analysis, geometry and partial diff erential Soviet Union, Latin America, Vietnam and centuries of work into one delightful narrative equations. Founded 17 years ago by its current elsewhere, political activism, and academic that celebrates the mystery of numbers and Editor-in-Chief, Steven G. Krantz, the journal has controversies relating to math education, the explains how diff erent kinds of numbers arose maintained standards of innovation and C. P. Snow two-culture problem, and mistreat- and why they are useful. Full of historical Henri’s Crystal Ball excellence. JGA accepts papers in English, French, ment of women in academia. snippets and interesting examples, the book and German and has a strong international fl avor. ranges from simple number puzzles and magic page 458 2008. X, 392 p. 28 illus., 18 in color. Hardcover tricks, to showing how ideas about numbers ISSN 1050-6926 (print) ISBN 978-3-540-74077-3 7 $49.95 relate to real-world problems. ISSN 1559-002X (electronic) Journal No. 12220 The Mathematical 2008. XII, 324 p. 33 illus. Hardcover Victor L. Klee 3RD ISBN 978-1-84800-000-1 7 $25.00 Theory of Finite EDITION Mathematical Element Methods 2ND (1925–2007) Universal Algebra Physiology EDITION S. C. Brenner, Louisiana ND G. Grätzer , University of 2 J. Keener, University of Utah, page 467 EDITION State University, Baton Rouge, LA, USA; Manitoba, Winnipeg, MB, Canada Salt Lake City, UT, USA; J. Sneyd , L. R. Scott, University of Chicago, IL, USA Massey University, Auckland, New Zealand; Universal Algebra has become the The book will be useful to mathematicians as most authoritative, consistently relied on text in Mathematical Physiology provides an well as engineers and physical scientists and can a fi eld with applications in other branches of introduction into physiology using the tools and be used for a course that provides an introduc- algebra as well as other fi elds such as combina- perspectives of mathematical modeling and tion to basic functional analysis, approximation torics, geometry and computer science. analysis. This second edition provides coverage theory, and numerical analysis, while building of more recent models in the chapters, more upon and applying basic techniques of real This second edition includes new appendices stochastic approaches, including single channel variable theory. This expanded third edition (with contributions from B. Jonnson, analysis and Fokker-Plank and Langevin contains new chapters on additive Schwarz R. Quackenbush, W. Taylor, and G. Wenzel) as well equations and includes new chapters on Calcium preconditioners and adaptive meshes, and new as an extensive bibliography of over 1,250 papers Dynamics, Neuroendocrine Cells and Regulation exercises have also been added throughout. and books. of Cell Function. 2nd ed. 1979. 2nd printing 2008. Approx. 605 p. Review of the Second Edition 7 [ is is] a well- Review of the First Edition 7 Probably the best Volume 55, Number 4, Pages 441–552, April 2008 10 illus. Softcover written book. A great deal of material is covered, book ever written on the subject of mathematical ISBN 978-0-387-77486-2 7 $79.95 and students who have taken the trouble to physiology....It contains numerous exercises, master at least some of the advanced material in enough to keep even the most diligent student the later chapters would be well placed to embark busy...highly recommended to anybody interested on research in the area. 7 ZENTRALBLATT MATH in mathematical or theoretical physiology. Mathematical Reviews 3rd ed. 2008. XVIII, 402 p. 50 illus. (Texts in Applied 7 Mathematics, Volume 15) Hardcover 2nd ed. 2008. Approx. 1000 p. Hardcover ISBN 978-0-387-75933-3 7 $69.95 ISBN 978-0-387-75846-6 7 approx. $100 Sign Up for New Book Alerts at springer.com Easy Ways to Order for the Americas 7 Write: Springer Order Department, PO Box 2485, Secaucus, NJ 07096-2485, USA 7 Call: (toll free) 1-800-SPRINGER 7 Fax: 1-201-348-4505 7 Email: [email protected] or for outside the Americas 7 Write: Springer Distribution Center GmbH, Haberstrasse 7, 69126 Heidelberg, Germany 7 Call: +49 (0) 6221-345-4301 7 Fax: +49 (0) 6221-345-4229 7 Email: [email protected] 7 Prices are subject to change without notice. All prices are net prices. 013575x Chaos in the weak stability boundary (see page 549) Trim: 8.25" x 10.75" 112 pages on 40 lb Cougar Opaque • Spine: 1/4" • Print Cover on 9pt Carolina ,!4%8 ,!4%8 ,!4%8 Pro New & Forthcoming from Birkhäuser Integrable Systems in Selfdual Gauge Field Vortices The Center and Cyclicity Celestial Mechanics An Analytical Approach Problems DIARMUID Ó MATHÚNA, Dublin Institute for Advanced GABRIELLA TARANTELLO, Università di Roma ‘Tor A Computational Approach Studies, Dublin, Ireland Vergata’, Italy VALERY ROMANOVSKI, University of Maribor, Slovenia; This work focuses on the two integrable systems of This monograph discusses specifi c examples DOUGLAS SHAFER, University of North Carolina at Charlotte, NC, USA relevance to celestial mechanics, both of which date of selfdual gauge fi eld structures, including the back to the 18th century. Under discussion are the Chern–Simons model, the abelian–Higgs model, and Using a computational algebra approach, this work Kepler (two-body) problem and the Euler (two-fi xed Yang–Mills gauge fi eld theory. addresses the center and cyclicity problems as center) problem, the latter being the more complex The author builds a foundation for gauge theory and behaviors of dynamical systems and families of and more instructive, as it exhibits a richer and more selfdual vortices by introducing the basic mathematical polynomial systems. The text fi rst lays the groundwork varied solution structure. language of gauge theory and formulating examples of for computational algebra and gives the main properties The present work shows that the solutions to all of Chern–Simons–Higgs theories (in both abelian and of ideals in polynomial rings and their affi ne varieties these integrable problems can be put in a form that non-abelian settings). Thereafter, the electroweak followed by a discussion on the theory of normal forms admits the general representation of the orbits and theory and self-gravitating electroweak strings are and stability. The center and cyclicity problems are follows a defi nite shared pattern. examined. The fi nal chapters treat elliptic problems then explored in detail. Containing exercises as well involving Chern–Simmons models, concentration- as historical notes and algorithms, this self-contained 2008/APPROX. 240 PP./HARDCOVER compactness principles, and Maxwell–Chern–Simons text is suitable for an advanced graduate course in the ISBN 9780817640965/$89.95 TENT. vortices. Many open questions still remain in the fi eld subject as well as a reference for researchers. PROGRESS IN MATHEMATICAL PHYSICS, VOL. 51 and are examined in this work in connection with Liouville-type equations and systems. 2008/APPROX. 300 PP., 5 ILLUS./SOFTCOVER ISBN 9780817647261/$59.95 TENT. The Theory of the Top The goal of this text is to form an understanding of Volume I: Introduction to the Kinematics selfdual solutions arising in a variety of physical and Kinetics of the Top contexts and thus is ideal for graduate students and Vanishing and Finiteness FELIX KLEIN; ARNOLD SOMMERFELD researchers interested in partial differential equations Results in Geometric Analysis and mathematical physics. Translated by: RAYMOND J. NAGEM and GUIDO SANDRI, A Generalization of the Bochner Technique both Boston University, Boston, MA, USA 2008/APPROX. 340 PP./HARDCOVER STEFANO PIGOLA, Università dell’Insubria, Como, Italy; ISBN 9780817643102/$109.00 MARCO RIGOLI, Università di Milano, Italy; The Theory of the Top, Vol. I is the fi rst of a series of PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS ALBERTO G. SETTI, Università dell’Insubria, Como, Italy four self-contained English translations of the classic AND THEIR APPLICATIONS, VOL. 72 and defi nitive treatment of rigid body motion. Volume I This book describes very recent results involving focuses on providing fundamental background material an extensive use of analytical tools in the study of and basic theoretical concepts. Integration and Modern geometrical and topological properties of complete Riemannian manifolds. An extension of the Bochner Key features: Analysis technique to the noncompact setting is analyzed in • Complete and unabridged presentation with recent JOHN J. BENEDETTO, University of Maryland, College detail, yielding conditions which ensure that solutions Park, USA; WOJCIECH CZAJA, University of Maryland, advances and additional notes College Park, USA of geometrically signifi cant differential equations either • Annotations by the translators provide insights into are trivial (vanishing results) or give rise to fi nite- the nature of science and mathematics in the late This textbook begins with the fundamentals of dimensional vector spaces (fi niteness results). 19th century classical real variables and leads to Lebesgue’s defi nition of the integral, the theory of integration 2008/APPROX.