Igor Lavrov, Larisa Maksimova, Giovanna Corsi

Problems in Set Theory, Mathematical Logic and the Theory of Algorithms

February 2003, ISBN 0-306-47712-2, Hardbound

Book Series: UNIVERSITY SERIES IN MATHEMATICS

Problems in Set Theory, Mathematical Logic and the Theory of Algorithms by I. Lavrov & L. Maksimova is an English translation of the fourth edition of the most popular student problem book in mathematical logic in Russian. It covers major classical topics in proof theory and the semantics of propositional and predicate logic as well as set theory and computation theory. Each chapter begins with 1-2 pages of terminology and definitions that make the book self-contained. Solutions are provided. The book is likely to become an essential part of curricula in logic.

Peter Bossaerts

The Paradox of Asset Pricing

Cloth | 2002 |ISBN: 0-691-09029-7
192 pp. | 6 x 9 | 7 tables. 21 line illus.

Asset pricing theory abounds with elegant mathematical models. The logic is so compelling that the models are widely used in policy, from banking, investments, and corporate finance to government. To what extent, however, can these models predict what actually happens in financial markets? In The Paradox of Asset Pricing, a leading financial researcher argues forcefully that the empirical record is weak at best. Peter Bossaerts undertakes the most thorough, technically sound investigation in many years into the scientific character of the pricing of financial assets. He probes this conundrum by modeling a decidedly volatile phenomenon that, he says, the world of finance has forgotten in its enthusiasm for the efficient markets hypothesis--speculation.

Bossaerts writes that the existing empirical evidence may be tainted by the assumptions needed to make sense of historical field data or by reanalysis of the same data. To address the first problem, he demonstrates that one central assumption--that markets are efficient processors of information, that risk is a knowable quantity, and so on--can be relaxed substantially while retaining core elements of the existing methodology. The new approach brings novel insights to old data. As for the second problem, he proposes that asset pricing theory be studied through experiments in which subjects trade purposely designed assets for real money. This book will be welcomed by finance scholars and all those math- and statistics-minded readers interested in knowing whether there is science beyond the mathematics of finance.

Peter Bossaerts is Professor of Finance and Director of the Laboratory for Experimental Finance at the California Institute of Technology, and Fellow of the Centre for Economic Policy Research in London. He is the coauthor of Lectures on Corporate Finance.

Endorsements:

"This book, whose rousing style drew me in immediately, is remarkable in how well it is able honestly to convey the core of modern finance theory and then to go on to criticize it fairly."--Thomas Sargent, Stanford University, Hoover Institution

"An important and timely book, The Paradox of Asset Pricing offers a fresh look at what the efficient markets hypothesis really implies. Summarizing forty years of asset pricing tests, it compels researchers to think deeply about what they are doing."--Bernt Arne Odegaard, Norwegian School of Management, Central Bank of Norway

Peter Turchin

Complex Population Dynamics:
A Theoretical/Empirical Synthesis

Paper | January | ISBN: 0-691-09021-1
Cloth | January | ISBN: 0-691-09020-3
456 pp. | 5 x 8 | 13 tables. 59 line illus.

Why do organisms become extremely abundant one year and then seem to disappear a few years later? Why do population outbreaks in particular species happen more or less regularly in certain locations, but only irregularly (or never at all) in other locations? Complex population dynamics have fascinated biologists for decades. By bringing together mathematical models, statistical analyses, and field experiments, this book offers a comprehensive new synthesis of the theory of population oscillations.

Peter Turchin first reviews the conceptual tools that ecologists use to investigate population oscillations, introducing population modeling and the statistical analysis of time series data. He then provides an in-depth discussion of several case studies--including the larch budmoth, southern pine beetle, red grouse, voles and lemmings, snowshoe hare, and ungulates--to develop a new analysis of the mechanisms that drive population oscillations in nature. Through such work, the author argues, ecologists can develop general laws of population dynamics that will help turn ecology into a truly quantitative and predictive science.

Complex Population Dynamics integrates theoretical and empirical studies into a major new synthesis of current knowledge about population dynamics. It is also a pioneering work that sets the course for ecology's future as a predictive science.

Peter Turchin is Professor of Ecology and Evolutionary Biology at the University of Connecticut. He is the author of Quantitative Analysis of Movement and more than sixty scientific articles, including several in Nature and Science.

Endorsements:

"This book gives an excellent introduction to our maturing understanding of how ideas about nonlinear dynamical systems can shed light on the complex behavior of real populations. Turchin first presents the theoretical concepts, next the data, and finally brings the two together in thoughtfully presented case studies. He splendidly achieves his aim of showing how ecological problems can be illuminated by mathematical models which are--in Einstein's words--'as simple as possible, but not more so.' "--Robert M. May, President, Royal Society

"This book is a true landmark in the study of population ecology. Never before has a lucid synthesis of the basic principles and models of population dynamics been so effectively merged with insightful analyses of some of the best data for populations of insects, birds and mammals. Peter Turchin writes with admirable clarity and authority, always retaining a focus on issues that really matter for population ecology."--Ilkka Hanski, University of Helsinki

"Turchin has done an outstanding job and produced a significant milestone in our understanding of population dynamics. I have long been seeking a book like this. It is readable and accessible while going into a good depth that so many undergraduate texts fail. All people working in the field will use it, and professors will use it in courses on population dynamics. The presentation is superb--the text gallops along."--Peter Hudson, University of Stirling

Series: Monographs in Population Biology

Hromkovic, J., RWTH Aachen, Germany

Algorithmics for Hard Problems

2nd ed. 2003 XIII, 544 p. 71 illus. Hardcover
3-540-44134-4

This book is an introduction to the methods of designing algorithms for hard computing tasks. This area has developed very dynamically in the last years and is one of the kernels of current research in algorithm and complexity theory. The book focuses on approximate, randomized and heuristic algorithms, and on the theoretical and experimental comparison of these approaches according to the requirements of the practice; it systematically explains and compares all main possibilities of attacking hard computing problems. Since the topic is fundamental for academic education and research and essential for the transfer of formal methods to practice, the book bridges this gap by providing both, a textbook for graduate students as well as a handbook for practitioners dealing with hard computing problems. The second edition adds new material to two fundamental algorithm design methods - to the method of relaxation to linear programming and of abundance of witnesses for primality testing.

Keywords: Boolean circuits, Boolean functions, Boolesche Funktionen, Boolesche Schaltkreise, Complexity, Formale Sprachen, Heuristics, Kommunikationskomplexitat, Parallele Berechnungen, Randomized and Approximation Algorithms, VLSI circuits, VLSI-Schaltkreise, communication complexity, formal languages, parallel computations

Series: Texts in Theoretical Computer Science. An EATCS Series.


Robdera, M. A., Al Akhawayn University, Morocco

A Concise Approach to Mathematical Analysis

2003 XII, 362 p. 47 illus. Softcover
1-85233-552-1

A Concise Approach to Mathematical Analysis introduces the undergraduate student to the more abstract concepts of advanced calculus. The main aim of the book is to smooth the transition from the problem-solving approach of standard calculus to the more rigorous approach of proof-writing and a deeper understanding of mathematical analysis. The first half of the textbook deals with the basic foundation of analysis on the real line; the second half introduces more abstract notions in mathematical analysis. Each topic begins with a brief introduction followed by detailed examples. A selection of exercises, ranging from the routine to the more challenging, then gives students the opportunity to practise writing proofs. The book is designed to be accessible to students with appropriate backgrounds from standard calculus courses but with limited or no previous experience in rigorous proofs. It is written primarily for advanced students of mathematics - in the 3rd or 4th year of their degree - who wish to specialise in pure and applied mathematics, but it will also prove useful to students of physics, engineering and computer science who also use advanced mathematical techniques.

Keywords: Advanced calculus, Mathematical analysis


Contents: Numbers and Functions.- Sequences.- Series.- Limits and Continuity.- Differentiation.- Elements of Integration.- Sequences and Series of Functions.- Local Structure on the Real Line.- Continuous Functions.- Introduction to Lebesgue Integral.- Elements of Fourier Analysis.-Appendix.- Hints for Selected Exercises.- Bibliography.- Index

Capasso, V., University of Milano, Italy; Merzbach, E., Bar-Ilan University, Ramat-Gan, Israel; Ivanoff, B. G., University of Ottawa, Ottawa, Canada; Dozzi, M., University Henry Poincare Nancy 1, France; Dalang, R., EPFL, Lausanne, Switzerland; Mountford, T., University of California, Los Angeles, USA

Topics in Spatial Stochastic Processes
Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, July 1-8, 2001

2003 VII, 253 p. Softcover
3-540-00295-2

The theory of stochastic processes indexed by a partially ordered set has been the subject of much research over the past twenty years. The objective of this CIME International Summer School was to bring to a large audience of young probabilists the general theory of spatial processes, including the theory of set-indexed martingales and to present the different branches of applications of this theory, including stochastic geometry, spatial statistics, empirical processes, spatial estimators and survival analysis. This theory has a broad variety of applications in environmental sciences, social sciences, structure of material and image analysis. In this volume, the reader will find different approaches which foster the development of tools to modelling the spatial aspects of stochastic problems.

Contents:

Preface.- Capasso V., Micheletti A.: Stochastic Geometry of Spatially Structured Birth and Growth Processes. Application to Crystallization Processes.- Merzbach, E.: An Introduction to the General Theory of Set-Indexed Martingales.- Ivanoff, B.G.: Set-Indexed Processes: Distributions and Weak Convergence.- Dozzi, M.: Occupation Density and Sample Path Properties of N-Parameter Processes.- Dalang, R.C.: Level Sets and Excursions of the Brownian Sheet.- Mountford, T.S.: Critical Reversible Attractive Nearest Particle Systems.

Series: Lecture Notes in Mathematics. Volume. 1802