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Birkhäuser Mathematics Bulletin 2 | 2006 Editorial Contents 2 Matters Birkhäuser Mathematics Bulletin 2 | 2006 Editorial Contents 2 Matters Dear friends of Birkhäuser, Birkhäuser Verlag AG Logic 3 Viaduktstrasse 42 Number Theory 3 it is with great pleasure that we present to you CH – 4051 Basel Algebra 4 today our Mathematics Bulletin in its new look. Tel: +41 / 61 / 2 05 07 07 Geometry / Topology 7 Birkhäuser’s new company logo, the red book Fax: +41 / 61 / 2 05 07 92 Analysis 9 mark, stands for our competence in publishing and Editors: our core values. An innovation-driven approach, Dr. Thomas Hempfling Mathematical Physics 19 together with reliability of content and trustworthy Executive Editor Numerical and services will make the difference in the area of Mathematics/Physics Computational Mathematics 20 sciences where the high speed of information flow [email protected] Applications of lies at the basis of success. If you are a Birkhäuser Dr. Stefan Göller Mathematics 21 author, you will have experienced our individual Editor Engineering 26 approach we particularly take care of. Proud of a Computational Sciences and Statistics 27 publishing history since 1879, we continue to be at Engineering, History of Science Computer Science 29 the forefront of research publishing with our new [email protected] corporate identity. History and Philosophy of Science 30 Strengthening our publishing activities in fields New series: that show a rapid development, I would like to point Modern Birkhäuser Classics 33 out to you our new journals such as the Journal Birkhäuser Boston, Inc. 675, Massachussets Avenue New Journals in 2007 37 of Fixed Point Theory and Applications, Logica Cambridge, MA 02139 / USA Order Form 39 Universalis, Mathematics in Computer Science and Complex Analysis and Operator Theory. Editors: Our bulletin aspires to be a precious source of Ann Kostant Birkhäuser Mathematics Bulletin 2/2006, Project-No. 5004S (11/2006) information for you. An online version is also Executive Editor available on our website www.birkhauser.ch. Mathematics/Physics All EUR prices are net prices subject to local [email protected] I will be glad to receive your comments or VAT, except for postage prices for journals (VAT included). suggestions, and, if you would like to find out more Tom Grasso CHF prices are gross prices. about being an author with Birkhäuser, please Editor Prices and other details are subject to change contact my colleagues in editorial or me personally Computational Sciences without notice. at [email protected]. and Engineering [email protected] Sincerely yours, Dr. Sven Fund www.birkhauser.ch Logic BiomedicineNumber Theory 3 Bagaria, J., Universitat de Barcelona, subsystems of axiomatic set theory, Fine, B., Fairfield University, First treatment in book form Spain / Todorcevic, S., University definable versions of large cardinals, Fairfield, CT, USA / Rosenberger, G., of the AKS algorithm that of Toronto, ON, Canada (Eds) and selection theory for open covers of Universität Dortmund, Germany shows that primality testing topological spaces. As for the research Set Theory Number Theory is of polynomial time papers, they range from topics such as Many interesting side topics, such as Centre de Recerca Matemàtica the number of near-coherence classes An Introduction via the Distribution primality testing and cryptography, Barcelona, 2003-2004 of ultrafilters, the consistency strength of Primes Fermat and Mersenne numbers, of bounded forcing axioms, Pk (l) and Carmichael numbers 2006. VI, 406 p. Hardcover combinatorics, some applications of 2007. XVI, 342 p. 12 illus. Softcover EUR 98.– / CHF 158.– morasses, subgroups of Abelian Polish EUR 48.– / CHF 78.– The book’s user-friendly style, ISBN 978-3-7643-7691-8 groups, adding club subsets of w2 ISBN 978-0-8176-4472-7 historical context, and wide range of TM – Trends in Mathematics with finite conditions, the consistency Due in November 2006 exercises from simple to quite difficult strength of mutual stationarity, Textbook (with solutions and hints provided for and new axioms of set theory. select ones) make it ideal for self study This volume complements the This book provides an introduction as well as classroom use. Intended lectures on Ramsey Methods in and overview of number theory based for upper level undergraduates Analysis that appeared as separate on the distribution and properties and beginning graduate students, book (ISBN 978-3-7643-7264-4). of primes. This unique approach the only prerequisites are a basic provides both a firm background knowledge of calculus, multivariable Of interest to: in the standard material as well as calculus, and some linear algebra. All Postgraduates and an overview of the whole discipline. necessary concepts from abstract researchers in set theory All the essential topics are covered: algebra and complex analysis fundamental theorem of arithmetic, are introduced in the book. This volume has its origins in the theory of congruences, quadratic Research Programme on Set Theory reciprocity, arithmetic functions, Of interest to: and its Applications that took place and the distribution of primes. Advanced undergraduates, graduate at the Centre de Recerca Matemática students, mathematicians, researchers, (CRM) Barcelona from September Key Topics and Features: number theorists, cryptographers 2003 to July 2004. It consists of Solid introduction to analytic two parts. The first contains survey number theory, including full papers on some of the mainstream proofs of Dirichlet’s Theorem and areas of set theory, and the second the Prime Number Theorem contains original research papers. Solid treatment of algebraic The survey papers cover topics as number theory, including a Omega-logic, applications of set complete presentation of theory to lattice theory and Boolean primes, prime factorizations in algebras, real-valued measurable algebraic number fields, and cardinals, complexity of sets and unique factorization of ideals relations in continuum theory, weak Number Theory Algebra 4 Ginzburg, V., University of Of interest to: Brady, N., University of Oklahoma, act upon. The second part is thus Chicago, IL, USA (Ed.) Graduate students, researchers, Norman, OK, USA / Short, H., Université dedicated to Dehn functions, negatively mathematicians, math physicists, de Provence, Marseille, France / curved groups, in particular, CAT(0) Algebraic Geometry algebraists, algebraic geometers, Riley, T., Cornell University, groups, cubings and cubical complexes. and Number Theory number theorists, students and Ithaca, NY, USA In the last part, filling functions are In Honor of Vladimir Drinfeld's colleagues of Drinfeld who know presented from geometric, algebraic 50th Birthday the impact of his work throughout The Geometry of the and algorithmic points of view, how the mathematical community Word Problem for Finitely filling functions interact is discussed, 2006. XVIII, 643 p. 19 illus. Hardcover Generated Groups and applications to nilpotent groups, EUR 108.– / CHF 172.– hyperbolic groups and asymptotic ISBN 978-0-8176-4471-0 2007. Approx. 200 p. Softcover cones are given. Many examples PM – Progress in Mathematics, Vol. 253 EUR 28.– / CHF 44.– and open problems are included. ISBN 978-3-7643-7949-0 One of the most creative ACM – Advanced Courses in Of interest to: mathematicians of our times, Mathematics – CRM Barcelona Graduate and postgraduate students in Vladimir Drinfeld received the Due in November 2006 (computational) algebra and geometry Fields Medal in 1990 for his Textbook groundbreaking contributions to the Langlands program and to The origins of the word problem are the theory of quantum groups. in group theory, decidability and These ten original articles by complexity, but, through the vision prominent mathematicians, dedicated of M. Gromov and the language to Drinfeld on the occasion of his 50th of filling functions, the topic now birthday, broadly reflect the range of impacts the world of large-scale Drinfeld's own interests in algebra, geometry, including topics such as algebraic geometry, and number theory. soap films, isoperimetry, coarse invariants and curvature. Contributors: The first part introduces van A. Eskin, V.V. Fock, E. Frenkel, Kampen diagrams in Cayley graphs D. Gaitsgory, V. Ginzburg, A.B. of finitely generated, infinite groups; Goncharov, E. Hrushovski, Y. Ihara, it discusses the van Kampen D. Kazhdan, M. Kisin, I. Krichever, lemma, the isoperimetric functions G. Laumon, Yu.I. Manin, A. Okounkov, or Dehn functions, the theory of V. Schechtman, and M.A. Tsfasman. small cancellation groups and an introduction to hyperbolic groups. One of the main tools in geometric group theory is the study of spaces, in particular geodesic spaces and manifolds, such that the groups Algebra 5 Girard, P.R., INSA Lyon, France Knapp, A.W., State University of with a separate 90-page section New York, Stony Brook, NY, USA giving hints or complete solutions Quaternions, Clifford Algebras for most of the problems and Relativistic Physics Basic Algebra The exposition proceeds from the particular to the general, 2007. Approx. 200 p. Softcover 2006. XXIV, 718 p. 42 illus. Hardcover often providing examples well EUR 29.90 / CHF 48.– EUR 58.– / CHF 92.– before a theory that incorporates ISBN 978-3-7643-7790-8 ISBN 978-0-8176-3248-9 them; includes blocks of problems Due in Winter 2006/07 COR – Cornerstones that introduce additional topics Textbook Textbook and applications for further study Applications to science and The use of Clifford algebras in Basic Algebra and Advanced Algebra engineering
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