This collection of articles grew out of an expository and tutorial conference on public-key cryptography held at the Joint mathematics Meetings (Baltimore). The book provides an introduction and survey on public-key ...
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ISBN:
(纸本)9780821833650
This collection of articles grew out of an expository and tutorial conference on public-key cryptography held at the Joint mathematics Meetings (Baltimore). The book provides an introduction and survey on public-key cryptography for those with considerable mathematical maturity and general mathematical knowledge. Its goal is to bring visibility to the cryptographic issues that fall outside the scope of standard mathematics. These mathematical expositions are intended for experienced mathematicians who are not well acquainted with the subject. The book is suitable for graduate students, researchers, and engineers interested in mathematical aspects and applications of public-key cryptography.
Symbolic dynamics originated as a tool for analyzing dynamical systems and flows by discretizing space as well as time. The development of information theory gave impetus to the study of symbol sequences as objects in...
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ISBN:
(纸本)9780821831571
Symbolic dynamics originated as a tool for analyzing dynamical systems and flows by discretizing space as well as time. The development of information theory gave impetus to the study of symbol sequences as objects in their own right. Today, symbolic dynamics has expanded to encompass multi-dimensional arrays of symbols and has found diverse applications both within and beyond mathematics. This volume is based on the AMS Short Course on Symbolic Dynamics and its Applications. It contains introductory articles on the fundamental ideas of the field and on some of its applications. Topics include the use of symbolic dynamics techniques in coding theory and in complex dynamics, the relation between the theory of multi-dimensional systems and the dynamics of tilings, and strong shift equivalence theory. Contributors to the volume are experts in the field and are clear expositors. The book is suitable for graduate students and research mathematicians interested in symbolic dynamics and its applications.
This volume presents proceedings from the AMS short course, Trends in Optimization 2004, held at the Joint mathematics Meetings in Phoenix (AZ). It focuses on seven exciting areas of discrete optimization. In particu...
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ISBN:
(纸本)9780821835845
This volume presents proceedings from the AMS short course, Trends in Optimization 2004, held at the Joint mathematics Meetings in Phoenix (AZ). It focuses on seven exciting areas of discrete optimization. In particular, Karen Aardal describes Lovasz's fundamental algorithm for producing a short vector in a lattice by basis reduction and H.W. Lenstra's use of this idea in the early 1980s in his polynomial-time algorithm for integer programming in fixed dimension. Aardal's article, "Lattice basis reduction in optimization: Selected Topics", is one of the most lucid presentations of the material. It also contains practical developments using computational tools. Bernd Sturmfels' article, "Algebraic recipes for integer programming", discusses how methods of commutative algebra and algebraic combinatorics can be used successfully to attack integer programming problems. Specifically, Gröbner bases play a central role in algorithmic theory and practice. Moreover, it is shown that techniques based on short rational functions are bringing new insights, such as in computing the integer programming gap. Overall, these articles, together with five other contributions, make this volume an impressive compilation on the state-of-the-art of optimization. It is suitable for graduate students and researchers interested in discrete optimization.
From the Publisher: About the Author Michael W. Berry is an Associate Professor of Computer Science at the University of Tennessee. His current research interests include information retrieval, scientific computing, c...
ISBN:
(纸本)9780898715002
From the Publisher: About the Author Michael W. Berry is an Associate Professor of Computer Science at the University of Tennessee. His current research interests include information retrieval, scientific computing, computational science, numerical linear algebra, and parallel computation.
To understand multiscale phenomena, it is essential to employ asymptotic methods to construct approximate solutions and to design effective computational algorithms. This volume consists of articles based on the AMS S...
To understand multiscale phenomena, it is essential to employ asymptotic methods to construct approximate solutions and to design effective computational algorithms. This volume consists of articles based on the AMS Short Course in Singular Perturbations held at the annual Joint mathematics Meetings in Baltimore (MD). Leading experts discussed the following topics which they expand upon in the book: boundary layer theory, matched expansions, multiple scales, geometric theory, computational techniques, and applications in physiology and dynamic metastability. Readers will find that this text offers an up-to-date survey of this important field with numerous references to the current literature, both pure and applied.
Event trees, and more generally, event spaces, can be used to provide a foundation for mathematical probability that includes a systematic understanding of causality. This foundation justifies the use of statistics in...
ISBN:
(纸本)0821806114
Event trees, and more generally, event spaces, can be used to provide a foundation for mathematical probability that includes a systematic understanding of causality. This foundation justifies the use of statistics in causal investigation and provides a rigorous semantics for causal reasoning.
In this paper, we present the mathematical foundations of constraint programming. A program is a set of constraints, i.e. a mathematical formula. A set of constraints is viewed as an implicit representation of the set...
ISBN:
(纸本)0821806114
In this paper, we present the mathematical foundations of constraint programming. A program is a set of constraints, i.e. a mathematical formula. A set of constraints is viewed as an implicit representation of the set of all constraints that it entails. There is a query system such that an answer to a query is a relationship that is satisfied if and only if the query is entailed by the system. And most importantly there exists a SINGLE algorithm to answer all queries (an oracle). In the case of logic programming, the constraint domain is Horn clauses and the algorithm is resolution. The soundness and completeness of resolution guarantees a well-defined programming system. In the domain of arithmetic constraints, the algorithm is quantifier elimination, and Tarski's theorem provides the counterpart to the soundness and completeness of resolution. As the cost of implementation in the general case is prohibitive, we restrict ourselves to the linear case. A program is a conjunction of linear constraints which represents a polyhedral set. Fourier's algorithm, the counterpart of Tarski's for the linear case, provides the parametric query answering mechanism. Interestingly, in this framework, classic linear programming results are interpreted in a new light. In particular, duality is given a quantifier elimination interpretation rather than the usual economic one, and a link between the simplex algorithm and the ubiquitous Helly's theorem is shown. Note that proofs are not included in the following presentation. The interested reader is referred to the literature.
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