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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

    • Foundations of Galois Theory

      • 1st Edition
      • July 10, 2014
      • M.M. Postnikov
      • I. N. Sneddon + 2 more
      • English
      • Paperback
        9 7 8 1 4 8 3 1 2 4 0 5 6
      • eBook
        9 7 8 1 4 8 3 1 5 6 4 7 7
      Foundations of Galois Theory is an introduction to group theory, field theory, and the basic concepts of abstract algebra. The text is divided into two parts. Part I presents the elements of Galois Theory, in which chapters are devoted to the presentation of the elements of field theory, facts from the theory of groups, and the applications of Galois Theory. Part II focuses on the development of general Galois Theory and its use in the solution of equations by radicals. Equations that are solvable by radicals; the construction of equations solvable by radicals; and the unsolvability by radicals of the general equation of degree n ? 5 are discussed as well. Mathematicians, physicists, researchers, and students of mathematics will find this book highly useful.

    • Design Problem Solving

      • 1st Edition
      • July 10, 2014
      • David C. Brown + 1 more
      • English
      • Paperback
        9 7 8 0 2 7 3 0 8 7 6 6 3
      • eBook
        9 7 8 1 4 8 3 2 5 8 8 8 1
      Design Problem Solving: Knowledge Structures and Control Strategies describes the application of the generic task methodology to the problem of routine design. This book discusses the generic task methodology and what constitutes the essence of the Al approach to problem solving, including the analysis of design as an information processing activity. The basic design problem solving framework, DSPL language, and AIR-CYL Air cylinder design system are also elaborated. Other topics include the high level languages based on generic tasks, structure of a Class 3 design problem solver, and failure handling in routine design. The conceptual structure for the air cylinder and improvements to DSPL system support are likewise covered in this text. This publication is beneficial to students and specialists concerned with solving design problems.

    • A Course of Higher Mathematics

      • 1st Edition
      • July 10, 2014
      • V. I. Smirnov
      • I. N. Sneddon + 2 more
      • English
      • Paperback
        9 7 8 0 0 8 0 1 3 7 1 9 3
      • eBook
        9 7 8 1 4 8 3 1 3 9 3 7 1
      International Series of Monographs in Pure and Applied Mathematics, Volume 62: A Course of Higher Mathematics, V: Integration and Functional Analysis focuses on the theory of functions. The book first discusses the Stieltjes integral. Concerns include sets and their powers, Darboux sums, improper Stieltjes integral, jump functions, Helly’s theorem, and selection principles. The text then takes a look at set functions and the Lebesgue integral. Operations on sets, measurable sets, properties of closed and open sets, criteria for measurability, and exterior measure and its properties are discussed. The text also examines set functions, absolute continuity, and generalization of the integral. Absolutely continuous set functions; absolutely continuous functions of several variables; supplementary propositions; and the properties of the Hellinger integral are presented. The text also focuses on metric and normed spaces. Separability, compactness, linear functionals, conjugate spaces, and operators in normed spaces are underscored. The book also discusses Hilbert space. Linear functionals, projections, axioms of the space, sequences of operators, and weak convergence are described. The text is a valuable source of information for students and mathematicians interested in studying the theory of functions.

    • Theory of Automata

      • 1st Edition
      • July 10, 2014
      • Arto Salomaa
      • I. N. Sneddon + 2 more
      • English
      • Paperback
        9 7 8 1 4 8 3 1 2 1 9 7 0
      • eBook
        9 7 8 1 4 8 3 1 5 4 3 9 8
      Theory of Automata deals with mathematical aspects of the theory of automata theory, with emphasis on the finite deterministic automaton as the basic model. All other models, such as finite non-deterministic and probabilistic automata as well as pushdown and linear bounded automata, are treated as generalizations of this basic model. The formalism chosen to describe finite deterministic automata is that of regular expressions. A detailed exposition regarding this formalism is presented by considering the algebra of regular expressions. This volume is comprised of four chapters and begins with a discussion on finite deterministic automata, paying particular attention to regular and finite languages; analysis and synthesis theorems; equivalence relations induced by languages; sequential machines; sequential functions and relations; definite languages and non-initial automata; and two-way automata. The next chapter describes finite non-deterministic and probabilistic automata and covers theorems concerning stochastic languages; non-regular stochastic languages; and probabilistic sequential machines. The book then introduces the reader to the algebra of regular expressions before concluding with a chapter on formal languages and generalized automata. Theoretical exercises are included, along with ""problems"" at the end of some sections. This monograph will be a useful resource for beginning graduate or advanced undergraduates of mathematics.

    • Regular Figures

      • 1st Edition
      • July 10, 2014
      • L. Fejes Tóth
      • I. N. Sneddon + 2 more
      • English
      • Paperback
        9 7 8 1 4 8 3 1 1 9 0 1 4
      • eBook
        9 7 8 1 4 8 3 1 5 1 4 3 4
      Regular Figures concerns the systematology and genetics of regular figures. The first part of the book deals with the classical theory of the regular figures. This topic includes description of plane ornaments, spherical arrangements, hyperbolic tessellations, polyhedral, and regular polytopes. The problem of geometry of the sphere and the two-dimensional hyperbolic space are considered. Classical theory is explained as describing all possible symmetrical groupings in different spaces of constant curvature. The second part deals with the genetics of the regular figures and the inequalities found in polygons; also presented as examples are the packing and covering problems of a given circle using the most or least number of discs. The problem of distributing n points on the sphere for these points to be placed as far as possible from each other is also discussed. The theories and problems discussed are then applied to pollen-grains, which are transported by animals or the wind. A closer look into the exterior composition of the grain shows many characteristics of uniform distribution of orifices, as well as irregular distribution. A formula that calculates such packing density is then explained. More advanced problems such as the genetics of the protean regular figures of higher spaces are also discussed. The book is ideal for physicists, mathematicians, architects, and students and professors in geometry.

    • An Introduction to Mathematical Analysis

      • 1st Edition
      • July 10, 2014
      • Robert A. Rankin
      • English
      • Paperback
        9 7 8 1 4 8 3 1 6 9 2 2 4
      • eBook
        9 7 8 1 4 8 3 1 8 5 0 3 3
      International Series of Monographs on Pure and Applied Mathematics, Volume 43: An Introduction to Mathematical Analysis discusses the various topics involved in the analysis of functions of a single real variable. The title first covers the fundamental idea and assumptions in analysis, and then proceeds to tackling the various areas in analysis, such as limits, continuity, differentiability, integration, convergence of infinite series, double series, and infinite products. The book will be most useful to undergraduate students of mathematical analysis.

    • Multidimensional Singular Integrals and Integral Equations

      • 1st Edition
      • July 10, 2014
      • S. G. Mikhlin
      • I. N. Sneddon + 2 more
      • English
      • Paperback
        9 7 8 1 4 8 3 1 3 2 0 7 5
      • eBook
        9 7 8 1 4 8 3 1 6 4 4 9 6
      Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals; properties of the symbol, with particular reference to Fourier transform of a kernel and the symbol of a singular operator; singular integrals in Lp spaces; and singular integral equations. The differentiation of integrals with a weak singularity is also considered, along with the rule for the multiplication of the symbols in the general case. The final chapter describes several applications of multidimensional singular integral equations to boundary problems in mathematical physics. This book will be of interest to mathematicians and students of mathematics.

    • Representations of Commonsense Knowledge

      • 1st Edition
      • July 10, 2014
      • Ernest Davis
      • Ronald J. Brachman
      • English
      • Paperback
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      • eBook
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      Representations of Commonsense Knowledge provides a rich language for expressing commonsense knowledge and inference techniques for carrying out commonsense knowledge. This book provides a survey of the research on commonsense knowledge. Organized into 10 chapters, this book begins with an overview of the basic ideas on artificial intelligence commonsense reasoning. This text then examines the structure of logic, which is roughly analogous to that of a programming language. Other chapters describe how rules of universal validity can be applied to facts known with absolute certainty to deduce other facts known with absolute certainty. This book discusses as well some prominent issues in plausible inference. The final chapter deals with commonsense knowledge about the interrelations and interactions among agents and discusses some issues in human and social interactions that have been studied in the artificial intelligence literature. This book is a valuable resource for students on a graduate course on knowledge representation.

    • Homology Theory on Algebraic Varieties

      • 1st Edition
      • July 10, 2014
      • Andrew H. Wallace
      • I. N. Sneddon
      • English
      • Paperback
        9 7 8 1 4 8 3 1 2 0 1 8 8
      • eBook
        9 7 8 1 4 8 3 1 5 2 6 0 8
      Homology Theory on Algebraic Varieties, Volume 6 deals with the principles of homology theory in algebraic geometry and includes the main theorems first formulated by Lefschetz, one of which is interpreted in terms of relative homology and another concerns the Poincaré formula. The actual details of the proofs of these theorems are introduced by geometrical descriptions, sometimes aided with diagrams. This book is comprised of eight chapters and begins with a discussion on linear sections of an algebraic variety, with emphasis on the fibring of a variety defined over the complex numbers. The next two chapters focus on singular sections and hyperplane sections, focusing on the choice of a pencil in the latter case. The reader is then introduced to Lefschetz's first and second theorems, together with their corresponding proofs. The Poincaré formula and its proof are also presented, with particular reference to clockwise and anti-clockwise isomorphisms. The final chapter is devoted to invariant cycles and relative cycles. This volume will be of interest to students, teachers, and practitioners of pure and applied mathematics.

    • Lie Algebras

      • 1st Edition
      • Volume 104
      • July 10, 2014
      • Zhe-Xian Wan
      • I. N. Sneddon + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 1 7 1 4 9 4
      • eBook
        9 7 8 1 4 8 3 1 8 7 3 0 3
      Lie Algebras is based on lectures given by the author at the Institute of Mathematics, Academia Sinica. This book discusses the fundamentals of the Lie algebras theory formulated by S. Lie. The author explains that Lie algebras are algebraic structures employed when one studies Lie groups. The book also explains Engel's theorem, nilpotent linear Lie algebras, as well as the existence of Cartan subalgebras and their conjugacy. The text also addresses the Cartan decompositions and root systems of semi-simple Lie algebras and the dependence of structure of semi-simple Lie algebras on root systems. The text explains in details the fundamental systems of roots of semi simple Lie algebras and Weyl groups including the properties of the latter. The book addresses the group of automorphisms and the derivation algebra of a Lie algebra and Schur's lemma. The book then shows the characters of irreducible representations of semi simple Lie algebras. This book can be useful for students in advance algebra or who have a background in linear algebra.

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