Series: Springer Monographs in Mathematics
2008, XX, 239 p. 28 illus. Also available online., Hardcover
ISBN: 978-3-540-77398-6
Due: February 20, 2008
About this book
One of the beautiful results in the representation theory of the finite groups is McKay's theorem on a correspondence between representations of the binary polyhedral group of SU(2) and vertices of an extended simply-laced Dynkin diagram.
The Coxeter transformation is the main tool in the proof of the McKay correspondence, and is closely interrelated with the Cartan matrix and Poincare series. The Coxeter functors constructed by Bernstein, Gelfand and Ponomarev plays a distinguished role in the representation theory of quivers.
On these pages, the ideas and formulas due to J. N. Bernstein, I. M. Gelfand and V. A. Ponomarev, H.S.M. Coxeter, V. Dlab and C.M. Ringel, V. Kac, J. McKay, T.A. Springer, B. Kostant, P. Slodowy, R. Steinberg, W. Ebeling and several other authors, as well as the author and his colleagues from Subbotin's seminar, are presented in detail. Several proofs seem to be new.
Table of contents
Introduction.- Preliminaries.- The Jordan normal form of the Coxeter transformation.- Eigenvalues, splitting formulas and diagrams Tp,q r .- R. Steinberg's theorem, B. Kostant's construction. - The affine Coxeter transformation.- A. The McKay correspondence and the Slodowy correspondence.- B. Regularity conditions for representations of quivers.- C. Miscellanea.- References.- Index.
Series: Modern Birkhauser Classics
Originally published as a monograph
1st ed. 2001. 2nd printing, 2008, Approx. 285 p. 255 illus., Softcover
ISBN: 978-0-8176-4782-7
Due: February 2008
About this textbook
Provides a non-technical introduction to geometry
Gives an entertaining history of an important subject in modern mathematics
Discusses questions about the very nature of mathematics
How unique and definitive is Euclidean geometry in describing the "real" space in which we live?
Richard Trudeau confronts the fundamental question of truth and its representation through mathematical models in The Non-Euclidean Revolution. First, the author analyzes geometry in its historical and philosophical setting; second, he examines a revolution every bit as significant as the Copernican revolution in astronomy and the Darwinian revolution in biology; third, on the most speculative level, he questions the possibility of absolute knowledge of the world.
Trudeau writes in a lively, entertaining, and highly accessible style. His book provides one of the most stimulating and personal presentations of a struggle with the nature of truth in mathematics and the physical world. A portion of the book won the Polya Prize, a distinguished award from the Mathematical Association of America.
Table of contents
Preface.- Introduction.- First Things.- Euclidean Geometry.- Geometry and the Diamond Theory of Truth.- The Problem with Postulate 5.- The Possibility of Non-Euclidean Geometry.- Hyperbolic Geometry.- Consistency.- Geometry and the Story Theory of Truth.- Bibliography.- Index.
Orignial French edition published by Lavoisier 2006.
2008, Approx. 110 p., Hardcover
ISBN: 978-3-540-75258-5
Due: February 27, 2008
About this book
Considering the stupendous gain in importance, in the banking and insurance industries since the early 1990’s, of mathematical methodology, especially probabilistic methodology, it was a very natural idea for the French "Academie des Sciences" to propose a series of public lectures, accessible to an educated audience, to promote a wider understanding for some of the fundamental ideas, techniques and new tools of the financial industries.
These lectures were given at the "Academie des Sciences" in Paris by internationally renowned experts in mathematical finance, and later written up for this volume which develops, in simple yet rigorous terms, some challenging topics such as risk measures, the notion of arbitrage, dynamic models involving fundamental stochastic processes like Brownian motion and Levy processes.
The Ariadne’s thread leads the reader from Louis Bachelier’s thesis 1900 to the famous Black-Scholes formula of 1973 and to most recent work close to Malliavin’s stochastic calculus of variations. The book also features a description of the trainings of French financial analysts which will help them to become experts in these fast evolving mathematical techniques.
The authors are: P. Barrieu, N. El Karoui, H. Follmer, H. Geman, E. Gobet, G. Pages, W. Schachermayer and M. Yor.
Table of contents
Introduction: Some Aspects of Mathematical Finance (Marc Yor). -Financial Uncertainty, Risk Measures and Strong Preferences (Hans Follmer). -The Notion of Arbitrage and Free Lunch in Mathematical Finance (Walter Schachermayer). -Dynamic Financial Risk Management (Pauline Barrieu and Nicole El Karoui). -Stochastic Clock and Financial Markets (Helyette Geman). -Options and Partial Differential Equations (Damien Lamberton). -Mathematics and Finance (Emmanuel Gobet, Gilles Pages, Marc Yor).
Series: Studies in Universal Logic
2008, Approx. 360 p., Softcover
ISBN: 978-3-7643-8707-5
Due: March 2008
About this book
This book develops model theory independently of any concrete logical system or structure, within the abstract category-theoretic framework of the so called ‘institution theory’. The concept of institution provides a model theory oriented mathematical formulation for the intuitive concept of logical system and had arisen within computing science as a response to the population explosion of specification logics. Our development includes most of the important methods and concepts of conventional concrete model theory at the abstract institution-independent level. Consequently it is easily applicable to a rather large diverse collection of logics from the mathematical and computer science practice, many of them not having a proper model theory prior to this work. Moreover the novel top-down methodology proposed leads to an understanding of model theoretic phenomena which is guided by structurally clean causality. This facilitates the access to deep results and even the discovery of new ones in well worked areas of conventional concrete model theories. The book contains also some applications to computing science.
Table of contents
1. Introduction.- 2. Categories.- 3. Institutions.- 4. Theories and Models.- 5. Internal Logic.- 6. Model Ultraproducts.- 7. Saturated Models.- 8. Preservation and Axiomatizability.- 9. Interpolation.- 10. Definability.- 11. Possible Worlds.- 12. Grothendieck Institutions.- 13. Institutions with Proofs.- 14. Specification.- 15. Logic Programming.
Series: Undergraduate Texts in Mathematics
Subseries: Readings in Mathematics
2008, Approx. 390 p. 192 illus., Softcover
ISBN: 978-0-387-77031-4
Due: March 2008
About this textbook
Aims at presenting stimulating and enjoyable coverage of the topics
Presents topics in the historical order it was developed in, showing how the ideas inspired further development of each topic
Many quotations are included to give the flavor of the history
The authors have published other successful titles with Springer
This book presents first-year calculus roughly in the order in which it first was discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.
Table of contents
Preface.- Introduction to Analysis of the Infinite.- Differential and Integral Calculus.- Foundations of Classical Analysis.- Calculus in Several Variables.- Appendix.- References.- Symbol Index.- Index.