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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

    • Handbook of Algebra

      • 1st Edition
      • Volume 1
      • December 18, 1995
      • English
      • eBook
        9 7 8 0 0 8 0 5 3 2 9 5 0
      Handbook of Algebra defines algebra as consisting of many different ideas, concepts and results. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. Each chapter of the book combines some of the features of both a graduate-level textbook and a research-level survey. This book is divided into eight sections. Section 1A focuses on linear algebra and discusses such concepts as matrix functions and equations and random matrices. Section 1B cover linear dependence and discusses matroids. Section 1D focuses on fields, Galois Theory, and algebraic number theory. Section 1F tackles generalizations of fields and related objects. Section 2A focuses on category theory, including the topos theory and categorical structures. Section 2B discusses homological algebra, cohomology, and cohomological methods in algebra. Section 3A focuses on commutative rings and algebras. Finally, Section 3B focuses on associative rings and algebras. This book will be of interest to mathematicians, logicians, and computer scientists.

    • Linear Algebra

      • 1st Edition
      • June 12, 1995
      • Richard Bronson
      • English
      • Paperback
        9 7 8 0 1 2 1 3 5 2 4 5 5
      • eBook
        9 7 8 0 0 8 0 5 7 1 9 0 4
      In this appealing and well-written text, Richard Bronson gives readers a substructure for a firm understanding of the abstract concepts of linear algebra and its applications. The author starts with the concrete andcomputational (a 3 x 5 matrix describing a stores inventory) and leads the reader to a choice of major applications (Markov chains, least squares approximation, and solution of differential equations using Jordan normal form). The first three chapters address the basics: matrices, vector spaces, and linear transformations. The next three cover eigenvalues, Euclidean inner products, and Jordan canonical forms, offering possibilities that can be tailored to the instructors taste and to the length of the course. Bronsons approach to computation is modern and algorithmic, and his theory is clean and straightforward. Throughout, the views of the theory presented are broad and balanced. Key material is highlighted in the text and summarized at end of each chapter. The book also includes ample exercises with answers and hints. With its inclusion of all the needed pedagogical features, this text will be a pleasure for teachers and students alike.

    • Solution of Continuous Nonlinear PDEs through Order Completion

      • 1st Edition
      • Volume 181
      • July 14, 1994
      • M.B. Oberguggenberger + 1 more
      • English
      • eBook
        9 7 8 0 0 8 0 8 7 2 9 2 6
      This work inaugurates a new and general solution method for arbitrary continuous nonlinear PDEs. The solution method is based on Dedekind order completion of usual spaces of smooth functions defined on domains in Euclidean spaces. However, the nonlinear PDEs dealt with need not satisfy any kind of monotonicity properties. Moreover, the solution method is completely type independent. In other words, it does not assume anything about the nonlinear PDEs, except for the continuity of their left hand term, which includes the unkown function. Furthermore the right hand term of such nonlinear PDEs can in fact be given any discontinuous and measurable function.

    • Computability, Complexity, and Languages

      • 2nd Edition
      • February 3, 1994
      • Martin Davis + 2 more
      • English
      • Hardback
        9 7 8 1 4 9 3 3 0 0 3 4 1
      • Paperback
        9 7 8 0 1 2 2 0 6 3 8 2 4
      • eBook
        9 7 8 0 0 8 0 5 0 2 4 6 5
      Computability, Complexity, and Languages is an introductory text that covers the key areas of computer science, including recursive function theory, formal languages, and automata. It assumes a minimal background in formal mathematics. The book is divided into five parts: Computability, Grammars and Automata, Logic, Complexity, and Unsolvability.

    • Groups - Modular Mathematics Series

      • 1st Edition
      • July 1, 1994
      • Camilla Jordan + 1 more
      • English
      • Paperback
        9 7 8 0 3 4 0 6 1 0 4 5 9
      • eBook
        9 7 8 0 0 8 0 5 7 1 6 5 2
      This text provides an introduction to group theory with an emphasis on clear examples. The authors present groups as naturally occurring structures arising from symmetry in geometrical figures and other mathematical objects. Written in a 'user-friendly' style, where new ideas are always motivated before being fully introduced, the text will help readers to gain confidence and skill in handling group theory notation before progressing on to applying it in complex situations. An ideal companion to any first or second year course on the topic.

    • Noncommutative Geometry

      • 1st Edition
      • November 22, 1994
      • Alain Connes
      • English
      • Hardback
        9 7 8 0 1 2 1 8 5 8 6 0 5
      • eBook
        9 7 8 0 0 8 0 5 7 1 7 5 1
      This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.

    • Handbook of Econometrics

      • 1st Edition
      • Volume 4
      • December 13, 1994
      • Robert Engle + 1 more
      • English
      • Hardback
        9 7 8 0 4 4 4 8 8 7 6 6 5
      • eBook
        9 7 8 0 0 8 0 9 3 4 1 1 2

    • The Quantum Brain

      • 1st Edition
      • March 3, 1994
      • A. Stern
      • English
      • Paperback
        9 7 8 0 4 4 4 5 6 8 6 8 7
      • eBook
        9 7 8 0 0 8 0 5 7 1 5 9 1
      While for the majority of physicists the problem of the deciphering of the brain code, the intelligence code, is a matter for future generations, the author boldly and forcefully disagrees. Breaking with the dogma of classical logic he develops in the form of the conversion postulate a concrete working hypothesis for the actual thought mechanism.The reader is invited on a fascinating mathematical journey to the very edges of modern scientific knowledge. From lepton and quark to mind, from cognition to a logic analogue of the Schrödinger equation, from Fibonacci numbers to logic quantum numbers, from imaginary logic to a quantum computer, from coding theory to atomic physics - the breadth and scope of this work is overwhelming. Combining quantum physics, fundamental logic and coding theory this unique work sets the stage for future physics and is bound to titillate and challenge the imagination of physicists, biophysicists and computer designers. Growing from the author's matrix operator formalization of logic, this work pursues a synthesis of physics and logic methods, leading to the development of the concept of infophysics.The experimental verification of the proposed quantum hypothesis of the brain is presently in preparation in cooperation with the Cavendish Laboratory, Cambridge, UK, and, if proved positive, would have major theoretical implications. Even more significant should be the practical applications in such fields as molecular electronics and computer science, biophysics and neuroscience, medicine and education. The new possiblities that could be opened up by quantum level computing could be truly revolutionary.The book aims at researchers and engineers in technical sciences as well as in biophysics and biosciences in general. It should have great appeal for physicists, mathematicians, logicians and for philosophers with a mathematical bent.

    • Topological Theory of Dynamical Systems

      • 1st Edition
      • Volume 52
      • June 3, 1994
      • N. Aoki + 1 more
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 8 5 6 5
      • eBook
        9 7 8 0 0 8 0 8 8 7 2 1 0
      This monograph aims to provide an advanced account of some aspects of dynamical systems in the framework of general topology, and is intended for use by interested graduate students and working mathematicians. Although some of the topics discussed are relatively new, others are not: this book is not a collection of research papers, but a textbook to present recent developments of the theory that could be the foundations for future developments.This book contains a new theory developed by the authors to deal with problems occurring in diffentiable dynamics that are within the scope of general topology. To follow it, the book provides an adequate foundation for topological theory of dynamical systems, and contains tools which are sufficiently powerful throughout the book.Graduate students (and some undergraduates) with sufficient knowledge of basic general topology, basic topological dynamics, and basic algebraic topology will find little difficulty in reading this book.

    • Numbers, Sequences and Series

      • 1st Edition
      • December 8, 1994
      • Keith Hirst
      • English
      • Paperback
        9 7 8 0 3 4 0 6 1 0 4 3 5
      • eBook
        9 7 8 0 0 8 0 9 2 8 5 8 6
      Number and geometry are the foundations upon which mathematics has been built over some 3000 years. This book is concerned with the logical foundations of number systems from integers to complex numbers. The author has chosen to develop the ideas by illustrating the techniques used throughout mathematics rather than using a self-contained logical treatise. The idea of proof has been emphasised, as has the illustration of concepts from a graphical, numerical and algebraic point of view. Having laid the foundations of the number system, the author has then turned to the analysis of infinite processes involving sequences and series of numbers, including power series. The book also has worked examples throughout and includes some suggestions for self-study projects. In addition there are tutorial problems aimed at stimulating group work and discussion.

Related subjects

Mathematics and applied mathematics

Statistics and probability