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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

    • An Introduction to Complex Analysis in Several Variables

      • 3rd Edition
      • Volume 7
      • January 2, 1990
      • L. Hormander
      • English
      • Hardback
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      • eBook
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      A number of monographs of various aspects of complex analysis in several variables have appeared since the first version of this book was published, but none of them uses the analytic techniques based on the solution of the Neumann Problem as the main tool. The additions made in this third, revised edition place additional stress on results where these methods are particularly important. Thus, a section has been added presenting Ehrenpreis' ``fundamental principle'' in full. The local arguments in this section are closely related to the proof of the coherence of the sheaf of germs of functions vanishing on an analytic set. Also added is a discussion of the theorem of Siu on the Lelong numbers of plurisubharmonic functions. Since the L2 techniques are essential in the proof and plurisubharmonic functions play such an important role in this book, it seems natural to discuss their main singularities.

    • Unitary Representations and Harmonic Analysis

      • 2nd Edition
      • Volume 44
      • March 1, 1990
      • M. Sugiura
      • English
      • eBook
        9 7 8 0 0 8 0 8 8 7 5 9 3
      The principal aim of this book is to give an introduction to harmonic analysis and the theory of unitary representations of Lie groups. The second edition has been brought up to date with a number of textual changes in each of the five chapters, a new appendix on Fatou's theorem has been added in connection with the limits of discrete series, and the bibliography has been tripled in length.

    • Induced Modules over Group Algebras

      • 1st Edition
      • Volume 161
      • March 1, 1990
      • G. Karpilovsky
      • English
      • Paperback
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      • eBook
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      In 1898 Frobenius discovered a construction which, in present terminology, associates with every module of a subgroup the induced module of a group. This construction proved to be of fundamental importance and is one of the basic tools in the entire theory of group representations.This monograph is designed for research mathematicians and advanced graduate students and gives a picture of the general theory of induced modules as it exists at present. Much of the material has until now been available only in research articles. The approach is not intended to be encyclopedic, rather each topic is considered in sufficient depth that the reader may obtain a clear idea of the major results in the area.After establishing algebraic preliminaries, the general facts about induced modules are provided, as well as some of their formal properties, annihilators and applications. The remaining chapters include detailed information on the process of induction from normal subgroups, projective summands of induced modules, some basic results of the Green theory with refinements and extensions, simple induction and restriction pairs and permutation modules. The final chapter is based exclusively on the work of Weiss, presenting a number of applications to the isomorphism problem for group rings.

    • Model Theory

      • 3rd Edition
      • Volume 73
      • June 12, 1990
      • C.C. Chang + 1 more
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 8 3 1 2
      • eBook
        9 7 8 0 0 8 0 8 8 0 0 7 5
      Since the second edition of this book (1977), Model Theory has changed radically, and is now concerned with fields such as classification (or stability) theory, nonstandard analysis, model-theoretic algebra, recursive model theory, abstract model theory, and model theories for a host of nonfirst order logics. Model theoretic methods have also had a major impact on set theory, recursion theory, and proof theory.This new edition has been updated to take account of these changes, while preserving its usefulness as a first textbook in model theory. Whole new sections have been added, as well as new exercises and references. A number of updates, improvements and corrections have been made to the main text.

    • Almost Free Modules

      • 1st Edition
      • Volume 46
      • April 23, 1990
      • P.C. Eklof + 1 more
      • English
      • eBook
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      This is an extended treatment of the set-theoretic techniques which have transformed the study of abelian group and module theory over the last 15 years. Part of the book is new work which does not appear elsewhere in any form. In addition, a large body of material which has appeared previously (in scattered and sometimes inaccessible journal articles) has been extensively reworked and in many cases given new and improved proofs. The set theory required is carefully developed with algebraists in mind, and the independence results are derived from explicitly stated axioms. The book contains exercises and a guide to the literature and is suitable for use in graduate courses or seminars, as well as being of interest to researchers in algebra and logic.

    • Classification Theory

      • 2nd Edition
      • Volume 92
      • December 6, 1990
      • S. Shelah
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 6 9 8 1
      • eBook
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      In this research monograph, the author's work on classification and related topics are presented. This revised edition brings the book up to date with the addition of four new chapters as well as various corrections to the 1978 text.The additional chapters X - XIII present the solution to countable first order T of what the author sees as the main test of the theory. In Chapter X the Dimensional Order Property is introduced and it is shown to be a meaningful dividing line for superstable theories. In Chapter XI there is a proof of the decomposition theorems. Chapter XII is the crux of the matter: there is proof that the negation of the assumption used in Chapter XI implies that in models of T a relation can be defined which orders a large subset of m

    • C*-Algebras and Operator Theory

      • 1st Edition
      • August 28, 1990
      • Gerald J. Murphy
      • English
      • Hardback
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      • Paperback
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      • eBook
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      This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.

    • Uniform Fréchet Algebras

      • 1st Edition
      • Volume 162
      • April 17, 1990
      • H. Goldmann
      • English
      • eBook
        9 7 8 0 0 8 0 8 7 2 7 3 5
      The first part of this monograph is an elementary introduction to the theory of Fréchet algebras. Important examples of Fréchet algebras, which are among those considered, are the algebra of all holomorphic functions on a (hemicompact) reduced complex space, and the algebra of all continuous functions on a suitable topological space.The problem of finding analytic structure in the spectrum of a Fréchet algebra is the subject of the second part of the book. In particular, the author pays attention to function algebraic characterizations of certain Stein algebras (= algebras of holomorphic functions on Stein spaces) within the class of Fréchet algebras.

    • Handbook of Convex Geometry

      • 1st Edition
      • October 7, 1990
      • Bozzano G Luisa
      • English
      • Paperback
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      • Hardback
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      • eBook
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      Handbook of Convex Geometry, Volume A offers a survey of convex geometry and its many ramifications and relations with other areas of mathematics, including convexity, geometric inequalities, and convex sets. The selection first offers information on the history of convexity, characterizations of convex sets, and mixed volumes. Topics include elementary convexity, equality in the Aleksandrov-Fenchel inequality, mixed surface area measures, characteristic properties of convex sets in analysis and differential geometry, and extensions of the notion of a convex set. The text then reviews the standard isoperimetric theorem and stability of geometric inequalities. The manuscript takes a look at selected affine isoperimetric inequalities, extremum problems for convex discs and polyhedra, and rigidity. Discussions focus on include infinitesimal and static rigidity related to surfaces, isoperimetric problem for convex polyhedral, bounds for the volume of a convex polyhedron, curvature image inequality, Busemann intersection inequality and its relatives, and Petty projection inequality. The book then tackles geometric algorithms, convexity and discrete optimization, mathematical programming and convex geometry, and the combinatorial aspects of convex polytopes. The selection is a valuable source of data for mathematicians and researchers interested in convex geometry.

    • Matrix Perturbation Theory

      • 1st Edition
      • June 28, 1990
      • G. W. Stewart + 1 more
      • English
      • Paperback
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      • Hardback
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      • eBook
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      This book is a comprehensive survey of matrix perturbation theory, a topic of interest to numerical analysts, statisticians, physical scientists, and engineers. In particular, the authors cover perturbation theory of linear systems and least square problems, the eignevalue problem, and the generalized eignevalue problem as wellas a complete treatment of vector and matrix norms, including the theory of unitary invariant norms.

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