Stochastic systems, Volume 169 (Mathematics in Science and Engineering)

Stochastic systems, Volume 169 (Mathematics in Science and Engineering)
Adomian | 1983-06-11 00:00:00 | Academic Press | 331 | Information Theory

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Toeplitz and Circulant Matrices: A review (Foundations and Trends in Communications and Information The)

Toeplitz and Circulant Matrices: A review (Foundations and Trends in Communications and Information The)
Robert M. Gray | 2006-01-02 00:00:00 | Now Publishers Inc | 104 | Information Theory
Toeplitz and Circulant Matrices: A review derives in a tutorial manner the fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes. Toeplitz and Circulant Matrices: A review is written for students and practicing engineers in an accessible manner bringing this important topic to a wider audience.
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This is an excellent review article published in the top journal Foundations and Trends in Communications and Information Theory. This journal only publishes one article once and also publishes as a book version.
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The 'book' gives no insight into anything. A better title for the book is: An incomplete proof of Szego's theorem with some vague references to its application.

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Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers, Vol. 1 (Studies in Logic and the Foundations of Mathematics, Vol. 125)

Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers, Vol. 1 (Studies in Logic and the Foundations of Mathematics, Vol. 125)
Piergiorgio Odifreddi | 1992-02-18 00:00:00 | North Holland | 660 | Information Theory
1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first principles.

Among the subjects covered are: various equivalent approaches to effective computability and their relations with computers and programming languages; a discussion of Church's thesis; a modern solution to Post's problem; global properties of Turing degrees; and a complete algebraic characterization of many-one degrees. Included are a number of applications to logic (in particular Gödel's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation.


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I agree with much of what another reviewer has said (July 11, 2005 ). But I don't think that Odifreddi has exaggerated when he claims that the prerequisites of reading his book will be roughly freshman math. Having said that, I admit that since many students in their sophomore year still don't possess a working knowledge of, say proof by mathematical induction, the book is certainly too heavy for those readers. Further aggravating the difficulty for beginners is the book's admittedly less-than-ideal organization and presentation of some portion of the enormously many topics it treats. This will be frustrating for readers who are not enthusiasts of the book's multifarious viewpoints and prefer a quick introduction to the subject instead. I recommend N.Cutland's "Computability" to newcomers. Nevertheless, for those who plan a future career in mathematical logic, especially recursion theory, Odifreddi's book will prove to be a treasure trove of unusual and stimulating insights not easily encountered elsewhere - even though one might not always agree with his ideas. For the future logicians I also recommend R.Soare's "Recursively enumerable sets and degrees" for a deeper treatment of r.e. sets.
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The stated goal of the book is to have no prerequisites other than freshman math, but you really need at least undergrad logic and set theory. It is a thick book and covers a lot of interesting stuff, but there can be a frustrating lack of order and detail. He is an engaging writer, but sloppy in that he gives only part of the information you need to understand something, forgetting that he didn't give it or you don't know it. Sections are often either too sketchy or wordy and unfocused. Sometimes, though, he comes through with an elegant explanation of something. He is at his best when relating recursion theory to science, philosophy, and other branches of math. These discussions tend to be rather handwavy, but he gives references to the literature. The book as a whole is not very unified and it doesn't clearly indentify and relate the central ideas of recursion theory, so it wouldn't make a good introductory text. But it is a good reference for those with a moderate background.

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Linear and quasilinear elliptic equations, Volume 46 (Mathematics in Science and Engineering)

Linear and quasilinear elliptic equations, Volume 46 (Mathematics in Science and Engineering)
Ladyzhenskaya | 1968-02-11 00:00:00 | Academic Press | 496 | Information Theory

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Combinatorial Optimization and Applications: Third International Conference, COCOA 2009, Huangshan, China, June 10-12, 2009, Proceedings (Lecture Notes ... Computer Science and General Issues)

Combinatorial Optimization and Applications: Third International Conference, COCOA 2009, Huangshan, China, June 10-12, 2009, Proceedings (Lecture Notes ... Computer Science and General Issues)
Ding-Zhu Du,Xiaodong Hu,Panos M. Pardalos | 2009-06-30 00:00:00 | Springer | 542 | Information Theory

This book constitutes the refereed proceedings of the Third International Conference on Combinatorial Optimization and Applications, COCOA 2009, held in Huangshan, China, in June 2009.

The 50 revised full papers were carefully reviewed and selected from 103 submissions. The papers feature original research in the areas of combinatorial optimization - both theoretical issues and and applications motivated by real-world problems thus showing convincingly the usefulness and efficiency of the algorithms discussed in a practical setting.

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Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial (Foundations and Trends(R) in Communications and Information Theory)

Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial (Foundations and Trends(R) in Communications and Information Theory)
Igal Sason,Shlomo Shamai | 2006-06-20 00:00:00 | Now Publishers Inc | 236 | Information Theory
Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial focuses on the performance evaluation of linear codes under optimal maximum-likelihood (ML) decoding. Though the ML decoding algorithm is prohibitively complex for most practical codes, their performance analysis under ML decoding allows to predict their performance without resorting to computer simulations. Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial is a comprehensive introduction to this important topic for students, practitioners and researchers working in communications and information theory.

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