Birkhäuser Mathematics Autumn 2007 1 New and noteworthy books and journals New Highlights Autumn 2007 2nd ed. see page 118 see page 39 see page 125 see page 15 see page 43 see page 29 2 Contents Logic 4 Combinatorics 7 Number Theory / Lattice Theory 9 Algebra and Representation Theory 14 Geometry / Topology 28 Analysis / Operator Theory 39 Differential Equations / Dynamical Systems 63 Systems and Control 77 Probability and Statistics 81 Mathematical Physics / Physics 89 Numerical and Computational Mathematics / Applications 94 Of general interest 118 History of Science 121 Titel in deutscher Sprache / German-language titles 130 Series Index 139 Series in Pure and Applied Mathematics 140 Series in History of Science 155 Journals 158 Authors and Editors Index 164 Contact Information 168 3 Logic 2nd ed. Completeness Theory for Logica Universalis Propositional Logics Towards a General Theory of Logic Pogorzelski, W.A., University of Bialystok, Beziau, J.-Y., University of Neuchâtel, Poland / Wojtylak, P., Silesian University Switzerland (Ed.) Katowice, Poland Universal Logic is not a new logic, but a SUL – Studies in Universal Logic general theory of logics, considered as mathematical structures. The name was Due in December 2007 introduced about ten years ago, but the subject is as old as the beginning of modern The book develops the theory of one logic: Alfred Tarski and other Polish logicians of the most important notions in the such as Adolf Lindenbaum developed a methodology of formal systems. Particularly, general theory of logics at the end of the completeness plays an important role in 1920s based on consequence operations propositional logic where many variants and logical matrices. The subject was of the notion have been defined. Global revived after the flowering of thousands of variants of the notion mean the possibility new logics during the last thirty years: there of getting all correct and reliable schemata was a need for a systematic theory of logics of inference. Its local variants refer to the to put some order in this chaotic multiplicity. notion of truth given by some semantics. This book contains recent works on A uniform theory of completeness in its universal logic by first-class researchers general and local meaning is carried out and from all around the world. The book is full it generalizes and systematizes some variety of new and challenging ideas that will guide of the notion of completeness such as Post- the future of this exciting subject. It will be completeness, structural completeness of interest for people who want to better and many others. This approach allows understand what logic is. Tools and concepts also for a more profound view upon some are provided here for those who want to essential properties (e.g. two-valuedness) of study classes of already existing logics or propositional systems. For these purposes, want to design and build new ones. the theory of logical matrices, and the theory 2007. 246 p. Softcover of consequence operations is exploited. EUR 49.90 / CHF 78.– / ISBN 978-3-7643-8353-4 2008. Approx. 180 p. Softcover EUR 49.90 / CHF 85.– / ISBN 978-3-7643-8517-0 4 A Beginner's Guide to Discrete Mathematics Wallis, W.D. "Wallis's book on discrete mathematics is a resource for an introductory course in a subject fundamental to both mathematics and computer science, a course that is expected not only to cover certain specific Universal Algebraic Logic topics but also to introduce students to Dedicated to the Unity of Science important modes of thought specific to each Andréka, H. / Németi, I. / Sain, I., all discipline… Lower-division undergraduates Hungarian Academy of Sciences, Budapest, through graduate students." Choice Hungary 2003. 352 p. 43 illus. Softcover EUR 48.– / CHF 85.– / ISBN 978-0-8176-4269-3 SUL – Studies in Universal Logic A Beginner's Guide to Due in January 2008 Finite Mathematics For Business, Management, and the The three main themes of this book are (i) universal logic and the question of what Social Sciences logic is, (ii) universal algebraic logic and Wallis, W.D. duality theories between the world of logics and the world of algebra, and (iii) algebraic "Requiring little mathematical background logic proper including algebras of relations beyond high school algebra, the text will be of various ranks, Tarski's cylindric algebras, especially useful for business and liberal arts relation algebras, Halmos' polyadic algebras majors. Its straightforward treatment of the and other kinds of algebras of logic. essential concepts in finite mathematics will appeal to a wide audience of students and Besides Tarskian algebraizations of teachers." Zentralblatt MATH logics, category theoretical perspectives are also touched upon. Following the 2004. XII, 354 p. Softcover EUR 44.90 / CHF 75.– / ISBN 978-0-8176-4270-9 Tarskian tradition, besides the connections between logic and algebra, related logical connections with geometry and eventually Foundations of Logic and spacetime geometry leading up to relativity Mathematics are also part of the perspective of the Applications to Computer Science and book. An introductory chapter contains the Cryptography necessary algebraic basics, this can be used Nievergelt, Y. in its own right as a quick introduction to universal algebra. "The book under review covers the topics 2008. Approx. 260 p. Softcover which can usually be found in textbooks EUR 59.90 / CHF 105.– / ISBN 978-3-7643-8505-7 of discrete mathematics for students in computer science or mathematics … as well as more advanced topics in mathematical logic ... While the range of topics is relatively standard, the way they are presented is highly original. ...This is a valuable reference 5 Logic text and a useful companion for anybody presents one or more major theorems with wondering how basic mathematical concepts detailed and nontrivial proofs, and states can be rigorously developed within set without proof one or two other important theory." Mathematical Reviews results. At the end of every chapter is an ample collection of exercises." 2001. XVI, 415 p. 22 illus. Hardcover Mathematical Reviews EUR 84.– / CHF 140.– / ISBN 978-0-8176-4249-5 "...surprisingly, despite the extremely basic nature of the subject, this monograph has Handbook of Logic and Proof essentially no competition. But fortunately Techniques for Computer Science the first entry proves a gem. Undergraduate mathematics and computer science Krantz, S. G. majors will find the first chapters offering background that will serve them well in "This is really what it promises to be – a good many courses. The rest of the book, which handbook: supple, self-contained, providing features many open problems, constitutes the necessary and sufficient working an accessible and stimulating invitation to resources … it is more than [one] expect[s]: research … Highly recommended." Choice the rigor of usefulness and conciseness 2003. XVII, 391 p. 35 illus. Hardcover exceeds or equals … the pleasure of reading EUR 68.– / CHF 120.– / ISBN 978-0-8176-4128-3 it." Zentralblatt MATH 2002. XIX, 245 p. 16 illus. Hardcover Proofs and Fundamentals EUR 54.90 / CHF 90.– / ISBN 978-0-8176-4220-4 A First Course in Abstract Mathematics In Search of Infinity Bloch, E. D. Vilenkin, N.Y. "Perhaps the book’s greatest strength is the "In fewer than 150 pages Vilenkin has author’s zeal and skill for helping students packed a whole course on infinity: its history, write mathematics better. Careful guidance philosophy, and mathematical theory. Abe is given throughout the book. Basic issues Shenitzer's translation is very smooth and like not abusing equal signs are treated natural... When fractals have gone out of explicitly. Attention is given to even relatively style, and chaos is no longer the flavor of the small issues, like not placing a mathematical month, some kind of 'geometric set theory' or 'set-theoretic geometry' may very well symbol directly after a punctuation mark. remain, and In Search of Infinity may still be Throughout the book, theorems are often the best introduction to it." followed first by informative ‘scratch work’ American Mathematical Monthly and only then by proofs. Thus students can see many examples of what they should SßJV+DUGFRYHU EUR 38.– / CHF 48.– / ISBN 978-0-8176-3819-1 think, what they should write, and how these are usually not the same." MAA Online Ordered Sets 2000. XXI, 424 p. Hardcover EUR 48.– / CHF 78.– / ISBN 978-0-8176-4111-5 An Introduction Schröder, B. Set Theory "This book is a most successful introduction Centre de Recerca Matemàtica to the theory of ordered sets. The range of Barcelona, 2003-2004 topics covered is wide yet the exposition is Bagaria, J. / Todorcevic, S. (Eds) self-contained … The focus on open problems TM – Trends in Mathematics makes for enthusiastic writing and provides continuity among the diverse topics that 2006. VI, 406 p. Hardcover are discussed … in each chapter the author EUR 98.– / CHF 158.– / ISBN 978-3-7643-7691-8 6 proves a solid collection of basic results, Combinatorics 2nd ed. A Beginner's Guide to Walks on Ordinals and Their Graph Theory Characteristics Wallis, W.D., Southern Illinois University, Todorcevic, S., Université Paris VII - CNRS, Carbondale, IL, USA France and University of Toronto, Canada Graph theory continues to be one of PM – Progress in Mathematics, Vol. 263 the fastest growing areas of modern Due in September 2007 mathematics because of its wide applicability in such diverse disciplines as computer The walks on ordinals and analysis of their science, engineering, chemistry, management characteristics is a subject matter started science, social science, and resource by the author some twenty years ago in planning. Graphs arise as mathematical order to disprove a particular extension of models in these fields, and the theory of the Ramsey theorem. A further analysis graphs provides a spectrum of methods of has shown however that the resulting proof.