John P. Burgess

Fixing Frege

Cloth | 2005 | ISBN: 0-691-12231-8
272 pp. | 5 1/2 x 8 1/2 | 12 tables.

The great logician Gottlob Frege attempted to provide a purely logical foundation for mathematics. His system collapsed when Bertrand Russell discovered a contradiction in it. Thereafter, mathematicians and logicians, beginning with Russell himself, turned in other directions to look for a framework for modern abstract mathematics. Over the past couple of decades, however, logicians and philosophers have discovered that much more is salvageable from the rubble of Frege's system than had previously been assumed. A variety of repaired systems have been proposed, each a consistent theory permitting the development of a significant portion of mathematics.

This book surveys the assortment of methods put forth for fixing Frege's system, in an attempt to determine just how much of mathematics can be reconstructed in each. John Burgess considers every proposed fix, each with its distinctive philosophical advantages and drawbacks. These systems range from those barely able to reconstruct the rudiments of arithmetic to those that go well beyond the generally accepted axioms of set theory into the speculative realm of large cardinals. For the most part, Burgess finds that attempts to fix Frege do less than advertised to revive his system. This book will be the benchmark against which future analyses of the revival of Frege will be measured.

John P. Burgess is Professor of Philosophy at Princeton University. He is the author of numerous articles on mathematical and philosophical logic and philosophy of mathematics and coauthor of A Subject with No Object.

Reviews:

"This book is without match. I suspect that it will be used both as a general introduction to the subject and as a source on particular topics for years to come."--Kit Fine, New York University

"I suspect that this will become a must-read among those working in the philosophy of mathematics and the foundations of mathematics. It will most certainly be a significant contribution to the field."--Stewart Shapiro, Ohio State University

Wassim M. Haddad, VijaySekhar Chellaboina, & Sergey G. Nersesov

Thermodynamics:
A Dynamical Systems Approach

Cloth | August 2005 | ISBN: 0-691-12327-6
200 pp. | 6 x 9

This book places thermodynamics on a system-theoretic foundation so as to harmonize it with classical mechanics. Using the highest standards of exposition and rigor, the authors develop a novel formulation of thermodynamics that can be viewed as a moderate-sized system theory as compared to statistical thermodynamics. This middle-ground theory involves deterministic large-scale dynamical system models that bridge the gap between classical and statistical thermodynamics.

The authors' theory is motivated by the fact that a discipline as cardinal as thermodynamics--entrusted with some of the most perplexing secrets of our universe--demands far more than physical mathematics as its underpinning. Even though many great physicists, such as Archimedes, Newton, and Lagrange, have humbled us with their mathematically seamless eurekas over the centuries, this book suggests that a great many physicists and engineers who have developed the theory of thermodynamics seem to have forgotten that mathematics, when used rigorously, is the irrefutable pathway to truth.

This book uses system theoretic ideas to bring coherence, clarity, and precision to an extremely important and poorly understood classical area of science.

Wassim M. Haddad is Professor of Aerospace Engineering at the Georgia Institute of Technology. VijaySekhar Chellaboina is Associate Professor in the Department of Mechanical, Aerospace, and Biomedical Engineering at the University of Tennessee, Knoxville. Sergey G. Nersesov is a Ph.D. student in aerospace engineering at Georgia Institute of Technology.

Endorsements:

"This is an original contribution to the important, but very diverse, field of thermodynamics. The book's self-contained system-theoretic approach makes it accessible to a wide audience of readers."--Jan Willems, University of Gronigen

"This is a truly original and fundamental contribution to the field of thermodynamics. It will make a lasting contribution to the literature."--Naira Hovakimyan, Virginia Polytechnic Institute and State University

Pal, Nikhil; Jain, Lakhmi C. (Eds.)

Advanced Techniques in Knowledge Discovery and Data Mining

Series: Advanced Information and Knowledge Processing
2005, 272 p. 101 illus., Hardcover
ISBN: 1-85233-867-9

About this book

This book presents research on some of the most recent advances in data mining and knowledge discovery, providing theory as well as its applications on practical real world applications. The methodologies discussed encompass tools like Bayesian networks, and major facets of computational intelligence paradigms.

Table of contents

Trends in Data Mining and Knowledge Discovery Advanced Methods for the Analysis of Semiconductor Manufacturing Process Data Clustering and visualization of Retail Market Baskets Segmentation Of Continuous Data Streams Based on a Change Detection Methodology Instance Selection Using Evolutionary Algorithms: An Experimental Study Using Cooperative Coevolution for Data Mining of Bayesian Networks Knowledge Discovery and Data Mining in Medicine Satellite Image Classification Using Cascaded Architecture of Neural Fuzzy Network Discovery of Positive and Negative Rules from Medical Databases based on Rough Sets

Ramsay, J., Silverman, B. W.

Functional Data Analysis, 2nd ed.

Series: Springer Series in Statistics
2005, XXII, 434 p. 151 illus., Hardcover
ISBN: 0-387-40080-X

About this book

Scientists today collect samples of curves and other functional observations. This monograph presents many ideas and techniques for such data. Included are expressions in the functional domain of such classics as linear regression, principal components analysis, linear modelling, and canonical correlation analysis, as well as specifically functional techniques such as curve registration and principal differential analysis. Data arising in real applications are used throughout for both motivation and illustration, showing how functional approaches allow us to see new things, especially by exploiting the smoothness of the processes generating the data. The data sets exemplify the wide scope of functional data analysis; they are drwan from growth analysis, meterology, biomechanics, equine science, economics, and medicine. The book presents novel statistical technology while keeping the mathematical level widely accessible. It is designed to appeal to students, to applied data analysts, and to experienced researchers; it will have value both within statistics and across a broad spectrum of other fields. Much of the material is based on the authors' own work, some of which appears here for the first time. Jim Ramsay is Professor of Psychology at McGill University and is an international authority on many aspects of multivariate analysis. He draws on his collaboration with researchers in speech articulation, motor control, meteorology, psychology, and human physiology to illustrate his technical contributions to functional data analysis in a wide range of statistical and application journals. Bernard Silverman, author of the highly regarded "Density Estimation for Statistics and Data Analysis," and coauthor of "Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach," is Professor of Statistics at Bristol University. His published work on smoothing methods and other aspects of applied, computational, and theoretical statistics has been recognized by the Presidents' Award of the Committee of Presidents of Statistical Societies, and the award of two Guy Medals by the Royal Statistical Society.

Table of contents

Introduction * Notation and Techniques * Representing Functional Data as Smooth Functions * The Roughness Penalty Approach * The Registration and Display of Functional Data * Principal Components Analysis for Functional Data * Regularized Principal Components Analysis * Principal Components Analysis of Mixed Data * Functional Linear Models * Functional Linear Models for Scalar Responses * Functional Linear Modesl for Functional Responses * Canonical Correlation and Discriminant Analysis * Differential Operators in Functional Data Analysis * Principal Differential Analysis * More General Roughness Penalties * Some Perspectives on FDA

Amos, Martyn

Theoretical and Experimental DNA Computation

Series: Natural Computing Series
2005, XIII, 173 p., Hardcover
ISBN: 3-540-65773-8

About this book

This book provides a broad overview of the entire field of DNA computation, tracing its history and development. It contains detailed descriptions of all major theoretical models and experimental results to date, which are lacking in existing texts, and discusses potential future developments. It also provides a useful reference source for researchers and students, and an accessible introduction for people new to the field.

The field of DNA computation has flourished since the publication of Adleman's seminal article, in which he demonstrated for the first time how a computation may be performed at a molecular level by performing standard operations on a tube of DNA strands. This monograph provides a detailed survey of the field, before describing recent theoretical and experimental developments. It concludes by outlining the challenges faced by researchers in the field and suggests possible future directions.

Table of contents