(Eds.) Bonilla, M., University of Valencia, Spain
Casasus, T., University of Valencia, Spain
Sala, R., University of Valencia, SpainFinancial Modelling
2000. XIV, 427 pp. 79 figs., 74 tabs.
3-7908-1282-X
The book presents 27 selected contributions from the 24th EURO Working Group on Financial Modelling
Meeting. The papers deal with financial theory, financial time series, risk analysis, portfolio analysis, financial
institutions, microstructures market and corporate finance, methods in finance, and models in finance and
derivatives. They present new developments in the fields of the optimization and the analysis of financial time
series behaviour.
Keywords: Finance, Financial Modelling, Financial Time Series, Financial Management
Series: Contributions to Management Science.
Fields: Finance; Econometrics; Mathematical Finance
Written for: Researchers
Book category: Proceedings
Publication language: English
Publication date: March 2000
Dullerud, G.E., University of Illinois, Urbana, IL, USA
Paganini, F., University of California, Los Angeles, CA, USAA Course in Robust Control Theory
A Convex Approach
2000. Approx. 400 pp. 36 figs.
0-387-98945-5
During the 90 robust control theory has seen major advances and achieved a new maturity, centered around the notion of convexity. The goal of this book is to give a graduate-level course on this theory that emphasizes these new developments, but at the same time conveys the main principles and ubiquitous tools at the heart of the subject. Its pedagogical objectives are to introduce a coherent and unified framework for studying the theory, to provide students with the control-theoretic background required to read and contribute to the research literature, and to present the main ideas and demonstrations of the major results. The book will be of value to mathematical researchers and computer scientists, graduate students planning to do research in the area, and engineering practitioners requiring advanced control techniques.
Contents: Introduction.- Preliminaries in Finite Dimensional Space.- State Space System Theory.- Linear
Analysis.- Model Realizations and Reduction.- Stabilizing Controllers.- H2 Optimal Control.- H_Synthesis.-
Uncertain Systems.- Feedback Control of Uncertain Systems.- Further Topics: Analysis.- Further Topics:
Synthesis.- Some Basic Measure Theory.- Proofs of Strict Separation.- u-Simple Structures.- References.
Series: Texts in Applied Mathematics.VOL. 36
Fields: Optimization and Optimal Control; Functional Analysis,Operator Theory
Written for: Graduate students, researchers
Book category: Graduate Textbook
Publication language: English
Publication date: March 2000
Euler, L.
Foundations of Differential Calculus
2000. Approx. 300 pp.
0-387-98534-4
Preliminary Promotion Text: Do Not Use. The positive response to the publication of Blanton's English
translations of Euler's "Introduction to Analysis of the Infinite" confirmed the relevance of this 240 year old work and encouraged Blanton to translate Euler's "Foundations of Differential Calculus" as well. The current book constitutes just the first 9 out of 27 chapters. The remaining chapters will be published at a later time. With this new translation, Euler's thoughts will not only be more accessible but more widely enjoyed by the mathematical community.
Contents: Preface.- Translator's Introduction.- On Finite Differences.- On the Use of Differences in the
Theory of Series.- On the Infinite and the Infinitely Small.- On the Nature of Differential of Each Order.- On the Differentiation of Algebraic Functions of One Variable.- On the Differentiation of Transcendental Functions.- On the Differentiation of Functions of Two or More Variables.- On the Higher Differentiation of Functions of Differential Formulas.- On Differential Equations.
Fields: Real Functions,Measure and Integration; Differential,Difference and Integral Equations
Written for: Math historians, math teachers, mathematicians
Book category: Monograph
Publication language: English
Publication date: April 2000
Lemmermeyer, F., Max-Planck-Institut f?r Mathematik, Bonn, Germany
Reciprocity Laws
From Euler to Eisenstein
2000. XIX, 487 pp.
3-540-66957-4
This book is about the development of reciprocity laws, starting from conjectures of Euler and discussing the
contributions of Legendre, Gauss, Dirichlet, Jacobi, and Eisenstein. Readers knowledgeable in basic algebraic
number theory and Galois theory will find detailed discussions of the reciprocity laws for quadratic, cubic, quartic, sextic and octic residues, rational reciprocity laws, and Eisenstein's reciprocity law. An extensive bibliography will be of interest to readers interested in the history of reciprocity laws or in the current research in this area.
Keywords: Reciprocity Laws, Number Theory, Elliptic functions, Zeta functions
Contents: 1. The Genesis of Quadratic Reciprocity.- 2. Quadratic Number Fields.- 3. Cyclotomic Number
Fields.- 4. Power Residues and Gauss Sums.- 5. Rational Reciprocity Laws.- 6. Quartic Reciprocity.- 7. Cubic
Reciprocity.- 8. Eisenstein's Analytic Proofs.- 9. Octic Reciprocity.- 10. Gauss's Last Entry.- 11. Eisenstein
Reciprocity.- Appendix.- A. Dramatis Personae.- B. Chronology of Proofs.
Series: Springer Monographs in Mathematics.
Fields: Number Theory
Written for: Researchers and graduate students
Book category: Monograph
Publication language: English
Publication date: April 2000
Shorack, G.R., University of Washington, Seattle, WA, USA
Probability for Statisticians
2000. Approx. 640 pp. 15 figs.
0-387-98953-6
The choice of examples used in this text clearly illustrate its use for a one-year graduate course. The material to be presented in the classroom constitutes a little more than half the text, while the rest of the text provides background, offers different routes that could be pursued in the classroom, as well as additional material that is appropriate for self-study. Of particular interest is a presentation of the major central limit theorems via Stein method either prior to or alternative to a characteristic function presentation. Additionally, there is considerable emphasis placed on the quantile function as well as the distribution function, with both the bootstrap and trimming presented. The section on martingales covers censored data martingales.
Contents: Measures.- Measurable Functions and Convergence.- Integration.- Derivatives Via Signed
Measures.- Measures and Processes on Products.- General Topology and Hilbert Space.- Distribution and
Quantile Functions.- Independence and Conditional Distributions.- Special Distributions.- WLLN, SLLN, LIL and Series.- Convergence in Distribution.- Brownian Motion, Embedding and Empirical Processes.- Characteristic Functions.- CLT's Via Characteristic Functions.- Infinitely Divisible and Stable Distributions.- Asymptotics Via Empirical Processes.- Asymptotics Via Stein's Approach.- Martingales.- Convergence on Metric Spaces.
Series: Springer Texts in Statistics.
Fields: Statistics, general; Probability and its Applications
Written for: Graduate students
Book category: Graduate Textbook
Publication language: English
Publication date: April 2000
Naber, G.L., California State University, Chico, CA, USA
Topology, Geometry and Gauge Fields
Interactions
2000. Approx. 455 pp. 9 figs.
0-387-98947-1
A study of topology and geometry, beginning with a comprehensible account of the extraordinary and rather
mysterious impact of mathematical physics, and especially gauge theory, on the study of the geometry and
topology of manifolds. The focus of the book is the Yang-Mills-Higgs field and some considerable effort is
expended to make clear its origin and significance in physics. Much of the mathematics developed here to study these fields is standard, but the treatment always keeps one eye on the physics and sacrifices generality in favor of clarity. The author brings readers up the level of physics and mathematics needed to conclude with a brief discussion of the Seiberg-Witten invariants. A large number of exercises are included to encourage active participation on the part of the reader.
"It is unusual to find a book so carefully tailored to the needs of this interdisciplinary area of mathematical
physics...Naber combines a knowledge of his subject with an excellent informal writing style." NZMS
NEWSLETTER
Contents: Preface.- Acknowledgements.- Geometrical Background.- Physical Motivation.- Frame Bundles and Spacetime.- Differential Forms and Integration Introduction.- de Rham Cohomology Introduction.- Characteristic Classes.- Appendix.- References.- Symbols.- Index.
Series: Applied Mathematical Sciences.VOL. 141
Fields: Combinatorial Mathematics/Graph Theory and Discrete Mathematics; Geometry
Written for: Researchers and graduate students
Book category: Graduate Textbook
Publication language: English
Publication date: April 2000