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Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

BooksJournals

    • Topological Fields

      • 1st Edition
      • Volume 157
      • June 1, 1989
      • S. Warner
      • English
      • eBook
        9 7 8 0 0 8 0 8 7 2 6 8 1
      Aimed at those acquainted with basic point-set topology and algebra, this text goes up to the frontiers of current research in topological fields (more precisely, topological rings that algebraically are fields).The reader is given enough background to tackle the current literature without undue additional preparation. Many results not in the text (and many illustrations by example of theorems in the text) are included among the exercises. Sufficient hints for the solution of the exercises are offered so that solving them does not become a major research effort for the reader. A comprehensive bibliography completes the volume.

    • Graph Colouring and Variations

      • 1st Edition
      • Volume 39
      • January 1, 1989
      • D. de Werra + 1 more
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 7 1 3 1
      • Hardback
        9 7 8 0 4 4 4 7 0 5 3 3 4
      • eBook
        9 7 8 0 0 8 0 8 6 7 7 9 3

    • Logic-Based Decision Support

      • 1st Edition
      • Volume 40
      • February 1, 1989
      • R.G. Jeroslow
      • English
      • eBook
        9 7 8 0 0 8 0 8 6 7 8 0 9
      This monograph is based on a series of lectures given by the author at the first Advanced Research Institute on Discrete Applied Mathematics, held at Rutgers University. It emphasizes connections between the representational aspects of mixed integer programming and applied logic, as well as discussing logic-based approaches to decision support which help to create more `intelligent' systems. Dividing naturally into two parts, the first four chapters are an overview of mixed-integer programming representability techniques. This is followed by five chapters on applied logic, expert systems, logic and databases, and complexity theory. It concludes with a summary of open research issues and an attempt to extrapolate trends in this rapidly developing area.

    • Graph Theory and Combinatorics 1988

      • 1st Edition
      • Volume 43
      • July 1, 1989
      • B. Bollobás
      • English
      • eBook
        9 7 8 0 0 8 0 8 6 7 8 3 0
      Combinatorics has not been an established branch of mathematics for very long: the last quarter of a century has seen an explosive growth in the subject. This growth has been largely due to the doyen of combinatorialists, Paul Erdős, whose penetrating insight and insatiable curiosity has provided a huge stimulus for workers in the field. There is hardly any branch of combinatorics that has not been greatly enriched by his ideas.This volume is dedicated to Paul Erdős on the occasion of his seventy-fifth birthday.

    • Computability, Complexity, Logic

      • 1st Edition
      • Volume 128
      • July 1, 1989
      • E. Börger
      • English
      • eBook
        9 7 8 0 0 8 0 8 8 7 0 4 3
      The theme of this book is formed by a pair of concepts: the concept of formal language as carrier of the precise expression of meaning, facts and problems, and the concept of algorithm or calculus, i.e. a formally operating procedure for the solution of precisely described questions and problems.The book is a unified introduction to the modern theory of these concepts, to the way in which they developed first in mathematical logic and computability theory and later in automata theory, and to the theory of formal languages and complexity theory. Apart from considering the fundamental themes and classical aspects of these areas, the subject matter has been selected to give priority throughout to the new aspects of traditional questions, results and methods which have developed from the needs or knowledge of computer science and particularly of complexity theory.It is both a textbook for introductory courses in the above-mentioned disciplines as well as a monograph in which further results of new research are systematically presented and where an attempt is made to make explicit the connections and analogies between a variety of concepts and constructions.

    • Vertex Operator Algebras and the Monster

      • 1st Edition
      • Volume 134
      • March 28, 1989
      • Igor Frenkel + 2 more
      • English
      • Hardback
        9 7 8 0 1 2 2 6 7 0 6 5 7
      • Paperback
        9 7 8 0 1 2 3 9 9 4 5 4 7
      • eBook
        9 7 8 0 0 8 0 8 7 4 5 4 8
      This work is motivated by and develops connections between several branches of mathematics and physics--the theories of Lie algebras, finite groups and modular functions in mathematics, and string theory in physics. The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of two-dimensional holomorphic conformal quantum field theory. The remaining part constructs the Monster finite simple group as the automorphism group of a very special vertex operator algebra, called the "moonshine module" because of its relevance to "monstrous moonshine."

    • Planar Graphs

      • 1st Edition
      • Volume 32
      • April 1, 1988
      • T. Nishizeki + 1 more
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 6 9 3 6
      • eBook
        9 7 8 0 0 8 0 8 6 7 7 4 8
      Collected in this volume are most of the important theorems and algorithms currently known for planar graphs, together with constructive proofs for the theorems. Many of the algorithms are written in Pidgin PASCAL, and are the best-known ones; the complexities are linear or 0(nlogn). The first two chapters provide the foundations of graph theoretic notions and algorithmic techniques. The remaining chapters discuss the topics of planarity testing, embedding, drawing, vertex- or edge-coloring, maximum independence set, subgraph listing, planar separator theorem, Hamiltonian cycles, and single- or multicommodity flows. Suitable for a course on algorithms, graph theory, or planar graphs, the volume will also be useful for computer scientists and graph theorists at the research level. An extensive reference section is included.

    • Real Reductive Groups I

      • 1st Edition
      • Volume 132
      • February 28, 1988
      • Nolan R. Wallach
      • English
      • Paperback
        9 7 8 0 1 2 3 9 9 4 5 9 2
      • eBook
        9 7 8 0 0 8 0 8 7 4 5 1 7
      Real Reductive Groups I is an introduction to the representation theory of real reductive groups. It is based on courses that the author has given at Rutgers for the past 15 years. It also had its genesis in an attempt of the author to complete a manuscript of the lectures that he gave at the CBMS regional conference at The University of North Carolina at Chapel Hill in June of 1981. This book comprises 10 chapters and begins with some background material as an introduction. The following chapters then discuss elementary representation theory; real reductive groups; the basic theory of (g, K)-modules; the asymptotic behavior of matrix coefficients; The Langlands Classification; a construction of the fundamental series; cusp forms on G; character theory; and unitary representations and (g, K)-cohomology. This book will be of interest to mathematicians and statisticians.

    • Extreme Value Theory in Engineering

      • 1st Edition
      • August 28, 1988
      • Enrique Castillo
      • English
      • Paperback
        9 7 8 0 1 2 3 9 5 9 4 4 7
      • Hardback
        9 7 8 0 1 2 1 6 3 4 7 5 9
      • eBook
        9 7 8 0 0 8 0 9 1 7 2 5 2
      This book is a comprehensive guide to extreme value theory in engineering. Written for the end user with intermediate and advanced statistical knowledge, it covers classical methods as well as recent advances. A collection of 150 examples illustrates the theoretical results and takes the reader from simple applications through complex cases of dependence.

    • Infinite-Dimensional Topology

      • 1st Edition
      • Volume 43
      • December 1, 1988
      • J. van Mill
      • English
      • Paperback
        9 7 8 0 4 4 4 8 7 1 3 4 3
      • Hardback
        9 7 8 0 4 4 4 8 7 1 3 3 6
      • eBook
        9 7 8 0 0 8 0 9 3 3 6 8 9
      The first part of this book is a text for graduate courses in topology. In chapters 1 - 5, part of the basic material of plane topology, combinatorial topology, dimension theory and ANR theory is presented. For a student who will go on in geometric or algebraic topology this material is a prerequisite for later work. Chapter 6 is an introduction to infinite-dimensional topology; it uses for the most part geometric methods, and gets to spectacular results fairly quickly. The second part of this book, chapters 7 & 8, is part of geometric topology and is meant for the more advanced mathematician interested in manifolds. The text is self-contained for readers with a modest knowledge of general topology and linear algebra; the necessary background material is collected in chapter 1, or developed as needed.One can look upon this book as a complete and self-contained proof of Toruńczyk's Hilbert cube manifold characterization theorem: a compact ANR X is a manifold modeled on the Hilbert cube if and only if X satisfies the disjoint-cells property. In the process of proving this result several interesting and useful detours are made.

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