Notices of the American Mathematical Society

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Notices of the American Mathematical Society • ISSN 0002-9920 March 2003 Volume 50, Number 3 Disks That Are Double Spiral Staircases page 327 The RieITlann Hypothesis page 341 San Francisco Meeting page 423 Primitive curve painting (see page 356) Education is no longer just about classrooms and labs. With the growing diversity and complexity of educational programs, you need a software system that lets you efficiently deliver effective learning tools to literally, the world. Maple® now offers you a choice to address the reality of today's mathematics education. Maple® 8 - the standard Perfect for students in mathematics, sciences, and engineering. Maple® 8 offers all the power, flexibility, and resources your technical students need to manage even the most complex mathematical concepts. MapleNET™ -- online education ,.u A complete standards-based solution for authoring, nv3a~ _r.~ .::..,-;.-:.- delivering, and managing interactive learning modules \~.:...br *'r¥'''' S\l!t"AaITI(!\pU;; ,"", <If through browsers. Derived from the legendary Maple® .Att~~ .. <:t~~::,/, engine, MapleNefM is the only comprehensive solution "f'I!hlislJer~l!'Ct"\ :5 -~~~~~:--r---, for distance education in mathematics. Give your institution and your students cornpetitive edge. For a FREE 3D-day Maple® 8 Trial CD for Windows®, or to register for a FREE MapleNefM Online Seminar call 1/800 R67.6583 or e-mail [email protected]. ADVANCING MATHEMATICS WWW.MAPLESOFT.COM I [email protected]\I I WWW.MAPLEAPPS.COM I NORTH AMERICAN SALES 1/800 267. 6583 © 2003 Woter1oo Ma')Ir~ Inc Maple IS (J y<?glsterc() crademork of Woterloo Maple he Mar)leNet so troc1ema'k of Woter1oc' fV'lop'e Inr PII other trcde,nork$ (ye property o~ their respective ('wners Generic Polynomials Constructive Aspects of the Inverse Galois Problem Christian U. Jensen, Arne Ledet, and Noriko Yui Describes a constructive approach to the Inverse Galois problem. Explores a family of"generic" polynomials for certain finite groups, which give all Galois exten­ sions having the required group as their Galois group. The existence ofsuch generic polynomials is discussed, and where they do exist, a detailed treatment of their construction is given. Mathematical Sciences Research Institute Publications 45 0-521-81998-9 Hb $60.00 Topics in Graph Automorphisms and Generic Polynomials Reconstruction Christian lJ. Jensen Arne Ledet Josef Lauri and Raffae/e'Scapellato Noriko Yui Offers in-depth coverage ofselected a-reas ofgraph theoty?~ith a focus on symmetry properties ofgraphs. As l11uch as possible, the authors present results and proofs which are not often to be found in textbooks. Any student who has mastered the contents ofthis book will be well prepared for current research in many aspects of the theory ofgraph automorphisms and die reconstruction problem. London Mathematical Society Student Texts 54 0-521-82151-7 Hb $65.00 0-521-52903-4 Pb $23.00 Sets for Mathematics F. William Lawvere and Robert Rosebrugh This book uses categorical algebra to build a founda­ tion for the study ofgeometry, analysis, and algebra, starting from intuitive descriptions ofmathematically and physically common phenomena and advancing to a precise specification ofthe nature ofCategories ofSets. 0-521-80444-2 Hb $100.00 0-521-01060-8 Pb $35.00 The Changing Shape of Geometry Celebrating a Century of Geometry and Geometry Teaching Edited by Chris Pritchard Features enjoyable insights into all thing~ geometrical. Includes a wealth ofpopular articles including sections on Pythagoras, the golden ratio and recreational geometry. Contributors include a Nobel Laureate and a Pulitzer Prizewinner. Co-Published with the Mathematical Association ofAmerica 0-521-82451-6 Hb $90.00 0-521-53162-4 Pb $40.00 *prices subject to change Available in bookstores or from CAMBRIDGE UNIVERSITY PRESS T EXTBOO K S from Birkhiiuser An Introduction to Wavelet Analysis D. WALNUT, George Mason University, Fairfax, VA "This book can be recommended to everyone, especially to students looking for adetailed introduction to the subject. " --MATHEMATICAL REVnEWS Forthcoming! Forthcoming! "[This text] is carefully prepared, well-organized, and covers alarge part of the central theory... [there are] A Beginner's Guide to Mathematical Analysis, chapters on biorthogonal wavelets and wavelet packets, Finite Mathematics Volume I topics which are rare in wavelet books. Both are impor­ tant, and this feature in an extra argument in favour W.D. WALLIS, Southern Illinois University, Carbondale, IL Functions of One Variable of[this] book... the material is accessible [even] to This beginner's guide to finite math covers all the funda­ M. GIAQUINTA, Scuola Normale Superiore, Pisa, Italy; and less advanced readers... the book is anice addition to mentals of the subject with aview toward its many G. MODICA, Universita di Palermo, Italy the series. " --ZENTRALBLATT MATH applications. Concisely written for freshmen and sopho­ This book introduces the fundamental ideas and methods mores, the text presents topics in sequential order, 2001/472 PP./ 66 IllUS'/HARDCOVER/S69.95 of one-variable differential and integral calculus and its ISBN 0-8176-3962-4 beginning with a review of sets and numbers and proceed­ applications. With simple, direct and rigorous exposition, APPLIED AND NUMERICAL HARMONIC ANALYSIS ing to data sets, histograms, basic statistics, counting the book treats all the standard topics as well as basic arguments and the Binomial Theorem. This, in turn, leads ordinary differential equations, including one-dimensional to elementary probability. The book discusses matrices, motions and Kepler's laws, asymptotic expansion, and Forthcoming! vectors, linear programming, and graph theory with minimum principles in physics and geometry. Key fea­ particular emphasis on mathematical modeling; it further­ tures include full proofs motivated by numerous exam­ Lines and Curves more showcases several commercial applications of the ples, valuable historical accounts of the ideas and A Practical Geometry Handbook theoretical concepts. The book contains ample examples, methods, and beautiful illustrations. illustrations, and two sets of exercises per section, with v. GUTENMACHER, VISTAGY, Inc., Waltham, MA; 2003/APPROX. 352 PP., 166 ILlUS'/HARDCOVER/S79.95 (TENI) N.B. VASILYE~ deceased; and A. KUNDU, Saha Institute of accompanying solutions to the first set. Its applied Nuclear Physics, Calcutta, India (translator) emphasis and minimal prerequisites make the text ISBN 0-8176-4312-5 especially useful for business majors and students in the Lines and Curves is a unique adventure in the world of liberal arts. geometry. Unlike standard textbooks that use the subject Forthcoming! primarily to introduce axiomatic reasoning as illustrated 2003/APPROX. 330 PP., 40 ILlUS'/SOFTCOVER/S39.95 (TENI) by formal geometric proofs, Lines and Curves maintains ISBN 0-8176-4270-6 Basic Real Analysis solid mathematical rigor, but also strikes a balance H.H. SOHRAB, Towson State University, Towson, MD between whimsical artistry, storytelling, and surprising Basic Real Analysis demonstrates the richness and examples of geometric properties. This book includes New from the same author- depth of analysis: far more than merely a rigorous treat­ more than 200 fully-solved theoretical and practical A Beginner's Guide to ment of calculus, the text covers all the basic material, but problems in which formal geometry provides simple and extends well beyond standard texts to include a careful elegant insight, and points the reader toward important Discrete Mathematics discussion of topology, probability, number systems, areas of modern mathematics. This introduction to discrete mathematics features a integration theory, Banach and Hilbert space theory, and 2003/APPROX. 175 PP., 350 ILLUS'/SOFTCOVER/S34.95'(TENI) distinctly applied approach, beginning with a survey of Fourier series. In clear, well-written exposition, the ISBN 0-8176-4161-0 number systems, elementary set theory, discussion of author constructs the remarkable and useful Cantor set scientific notation, and the computer representation of and the Weierstrass nowhere differentiable function, numbers. The text proceeds to discuss basic counting and also proves the Weierstrass approximation theorem. Kac-Moody Groups, arguments, the Binomial Theorem, elementary probability, Different types of convergence, monotone functions, and induction, which leads to Boolean algebras and and the basics of functional analysis are presented as Their Flag Varieties and circuits. Graph study follows, including Euler and well. The book maintains a broad view of analysis and Hamilton cycles and trees, which serve as an example of a mathematics, contains numerous examples, and is ideal Representation Theory data structure. Matrices and vectors are defined. The for senior undergraduates and beginning graduate s. KUMAR, University ofNorth Carolina, Chapel Hill, NC students; it is a fine resource either in the classroom or book concludes with an introduction to cryptography, This comprehensive and self-contained text focuses on for self-study. including the RSA cryptosystem together with the neces­ the study of Kac-Moody groups and their flag varieties. sary elementary number theory. With many good exam­ 2003/APPROX. 400 PP'/HARDCOVER/S49.95 (TENI) The theory is developed from scratch, and the reader is ples, a full index, two sets of exercises in each section, ISBN 0-8176-4211-0 gently led to the forefront of the subject, treating the and solutions to the odd-numbered exercises, the book is algebro-geometric, topological,
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