ISBN: 978-0-470-61796-0
Hardcover
336 pages
July 2010
The needed foundation and theory is complimented with tangible applications in physics and other disciplines. Since many practical applications are non-linear, numerical solution techniques are required. Consequently, the book introduces this topic in a general way before providing the necessary details. As for an introduction to a specific method, the finite difference method is the natural place to begin. With this approach, readers more clearly understand the notations of order and convergence as well as explicit and implicit methodologies.
Later, readers are introduced to the finite element method in such a way that it is seen as essentially a sub-space approximation technique. Finally, the finite analytic method is introduced, where readers are presented with the application of the Fourier Series methodology to linearized versions of non-linear PDEs. In terms of theory, material on linear PDEs reinforces the important concept of inner product spaces introduced in a linear algebra course, especially those of infinite dimension. Further, it introduces the concept of completeness, thereby introducing readers to Hilbert Spaces. Past experience with ordinary differential equations is called upon to understand the solution process for Sturm-Liouville boundary value ODE problems, which leads to an infinite-dimensional basis for an inner product space, and ultimately, a Fourier Series representation of the solution of an initial boundary value problems. Computer algebra resources such as Maple, Mathematica, and MATLAB can be used to aid in understanding and applying the solution techniques to interesting problems. This can begin as soon as the theoretical work is in Sturm-Liouville problems and Fourier series is covered.
Later on, it is used to apply numerical solution methods to various applications.
ISBN: 978-0-470-47565-2
Hardcover
344 pages
July 2010
The new data challenges associated with online auctions motivate the need for clever statistical ideas and new statistical innovation in order to gain knowledge about bidders, sellers, prices, and a host of other questions of interest.
In this book, the authors draw upon their experience of working with online auction data and introduce the reader to state-of-the-art statistical methodology for extracting new knowledge from online auction data.
Rather than approach the topic from the traditional game-theoretic route, the authors treat the online auction mechanism as a new type of data generator, as well as use statistical and data mining methods to collect, explore, model, and forecast data that arises from online auction databases.
Every effort is made to embellish cross-disciplinary fertilization between statistics, data mining, marketing, information systems, and economics and related fields.
ISBN: 978-0-470-74826-8
Hardcover
376 pages
September 2010
This book provides comprehensive coverage of simulation of complex systems using Monte Carlo methods.
Developing algorithms that are immune to the local trap problem has long been considered as the most important topic in MCMC research. Various advanced MCMC algorithms which address this problem have been developed include, the modified Gibbs sampler, the methods based on auxiliary variables and the methods making use of past samples. The focus of this book is on the algorithms that make use of past samples.
This book includes the multicanonical algorithm, dynamic weighting, dynamically weighted importance sampling, the Wang-Landau algorithm, equal energy sampler, stochastic approximation Monte Carlo, adaptive MCMC algorithms, conjugate gradient Monte Carlo, adaptive direction sampling, the sampling Metropolis-Hasting algorithm and the multiplica sampler
Synthesis Lectures on Digital Circuits and Systems
2009, 153 pages, (doi:10.2200/S00243ED1V01Y200912DCS026)
This book brings together five topics on the application of Boolean functions. They are
1. Equivalence classes of Boolean functions: The number of n-variable functions is large, even for values as small as n = 6, and there has been much research on classifying functions. There are many classifications, each with their own distinct merit.
2. Boolean functions for cryptography: The process of encrypting/decrypting plaintext messages often depends on Boolean functions with specific properties. For example, highly nonlinear functions are valued because they are less susceptible to linear attacks.
3. Boolean differential calculus: An operation analogous to taking the derivative of a real-valued function offers important insight into the properties of Boolean functions. One can determine tests or susceptibility to hazards.
4. Reversible logic: Most logic functions are irreversible; it is impossible to reconstruct the input, given the output. However, Boolean functions that are reversible are necessary for quantum computing, and hold significant promise for low-power computing.
5. Data mining: The process of extracting subtle patterns from enormous amounts of data has benefited from the use of a graph-based representation of Boolean functions. This has use in surveillance, fraud detection, scientific discovery including bio-informatics, genetics, medicine, and education.
Written by experts, these chapters present a tutorial view of new and emerging technologies in Boolean functions.
Equivalence Classes of Boolean Functions / Boolean Functions for Cryptography / Boolean Differential Calculus / Synthesis of Boolean Functions in Reversible Logic / Data Mining Using Binary Decision Diagrams
272 pages | 234x156mm
978-0-19-954149-2 | Hardback | September 2010
Long-awaited book from a widely respected philosopher of mathematics
Weir sets out an original philosophy of mathematics
Will be accessible to all with basic logic training
Truth Through Proof defends an anti-platonist philosophy of mathematics derived from game formalism. Classic formalists claimed implausibly that mathematical utterances are truth-valueless moves in a game. Alan Weir aims to develop a more satisfactory successor to game formalism utilising a widely accepted, broadly neo-Fregean framework, in which the proposition expressed by an utterance is a function of both sense and background circumstance. This framework allows for sentences whose truth-conditions are not representational, which are made true or false by conditions residing in the circumstances of utterances but not transparently in the sense.
Applications to projectivism and fiction pave the way for the claim that mathematical utterances are made true or false by the existence of concrete proofs or refutations, though these truth-making conditions form no part of their sense or informational content.
The position is compared with rivals, an account of the applicability of mathematics developed, and a new account of the nature of idealisation proffered in which it is argued that the finitistic limitations Godel placed on proofs are without rational justification. Finally a non-classical logical system is provided in which excluded middle fails, yet enough logical power remains to recapture the results of standard mathematics.
Readership: Scholars and advanced students of philosophy of mathematics and logic
Introduction
1: Metaphysics
2: Ontological Reduction
3: Neo-formalism
4: Objections and Comparisons
5: Applying Mathematics
6: Proof Set in Concrete
7: Idealisation Naturalised
8: Logic
Conclusion
Appendix