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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.

  • Ring Theory

    Proceedings of a Conference on Ring Theory Held in Park City, Utah, March 2–6, 1971
    • 1st Edition
    • Robert Gordon
    • English
    Ring Theory provides information pertinent to the fundamental aspects of ring theory. This book covers a variety of topics related to ring theory, including restricted semi-primary rings, finite free resolutions, generalized rational identities, quotient rings, idealizer rings, identities of Azumaya algebras, endomorphism rings, and some remarks on rings with solvable units. Organized into 24 chapters, this book begins with an overview of the characterization of restricted semi-primary rings. This text then examines the case where K is a Hensel ring and A is a separable algebra. Other chapters consider establishing the basic properties of the four classes of projective modules, with emphasis on the finitely generated case. This book discusses as well the non-finitely generated cases and studies infinitely generated projective modules. The final chapter deals with abelian groups G that are injective when viewed as modules over their endomorphism rings E(G). This book is a valuable resource for mathematicians.

  • Computational Probability

    The Proceedings of the Actuarial Research Conference on Computational Probability Held at Brown University, Providence, Rhode Island, on August 28-30, 1975
    • 1st Edition
    • P. M. Kahn
    • English
    Computational Probability is a collection of papers presented at the Actuarial Research Conference on Computational Probability and related topics, held at Brown University on August 28-30, 1975. This 19-chapter book explores the development of computational techniques in probability and statistics and their application to problems in insurance. It covers six general topics, including computational probability, computational statistics, computational risk theory, analysis of algorithms, numerical methods, and notation and computation. Applications covered both life and nonlife insurance. This book will prove useful to applied mathematicians, statisticians, and computer scientists.

  • Theoretical Studies in Computer Science

    • 1st Edition
    • Jeffrey D. Ullman
    • English
    Theoretical Studies in Computer Science focuses on the field of theoretical computer science. This book discusses the context-free multi-languages, non-membership in certain families of context-free languages, and single tree grammars. The complexity of structural containment and equivalence, interface between language theory and database theory, and automata theory for database theoreticians are also deliberated. This text likewise covers the datalog linearization of chain queries, expressive power of query languages, and object identity and query equivalences. Other topics include the unified approach to data and meta-data modification for data/knowledge bases, polygon clipping algorithms, and convex polygon generator. This publication is intended for computer scientists and researchers interested in theoretical computer science.

  • Table of Integrals, Series, and Products

    • 1st Edition
    • I. S. Gradshteyn + 1 more
    • English
    Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.

  • Large Problems, Small Machines

    Transforming Your Programs with Advanced Algorithms
    • 1st Edition
    • Steve Heller
    • English
    Large Problems, Small Machines: Transforming Your Programs with Advanced Algorithms describes a practical, real-world approach to program optimization based on advanced algorithms. Topics covered range from how to save storage using a restricted character set and how to speed up access to records by employing hash coding (or "scatter storage") and caching. A selective mailing list system is used to illustrate rapid access to and rearrangement of information selected by criteria specified at run-time. Comprised of six chapters, this book begins by discussing factors to consider when deciding whether a program needs optimization. In the next chapter, a supermarket price lookup system is used to illustrate how to save storage by using a restricted character set and how to speed up access to records with the aid of hash coding and caching. Attention is paid to rapid retrieval of prices. A selective mailing list system is then used to illustrate rapid access to and rearrangement of information selected by criteria specified at run-time. The book also considers the Huffman coding and arithmetic coding methods of data compression before concluding with a review of the characteristics of the algorithms encountered in previous chapters, as well as the future of the art of optimization. This monograph will be a useful resource for practicing computer programmers and those who intend to be working programmers.

  • Set-Theoretic Topology

    • 1st Edition
    • George M. Reed
    • English
    Set-Theoretic Topology deals with results concerning set theoretic topology and indicates directions for further investigations. Topics covered include normality and conditions in abstract spaces, compactifications, cardinal invariance, mapping theory, product spaces, and metrization. Comprised of 29 chapters, this volume begins with an example concerning the preservation of the Lindelöf property in product spaces, followed by a discussion on closed-completeness in spaces with a quasi-G? diagonal and with weak covering properties. The reader is then introduced to countably compact extensions of normal locally compact M-spaces; continuously semi-metrizable spaces; and closed discrete collections of singular cardinality. Subsequent chapters focus on open mapping theory; a selection-theoretic approach to certain extension theorems; semicompletable Moore spaces; and non-normal spaces. The book also considers complete mappings in base of countable order theory before concluding with an analysis of locally separable Moore spaces. This monograph should be of value to students, researchers, and specialists in the field of mathematics.

  • Data Structures, Computer Graphics, and Pattern Recognition

    • 1st Edition
    • A. Klinger + 2 more
    • English
    Data Structures, Computer Graphics, and Pattern Recognition focuses on the computer graphics and pattern recognition applications of data structures methodology. This book presents design related principles and research aspects of the computer graphics, system design, data management, and pattern recognition tasks. The topics include the data structure design, concise structuring of geometric data for computer aided design, and data structures for pattern recognition algorithms. The survey of data structures for computer graphics systems, application of relational data structures in computer graphics, and observations on linguistics for scene analysis are also elaborated. This text likewise covers the design of satellite graphics systems, interactive image segmentation, surface representation for computer aided design, and error-correcting parsing for syntactic pattern recognition. This publication is valuable to practitioners in data structures, particularly those who are applying real computer systems to problems involving image, speech, and medical data.

  • Statistical Decision Theory and Related Topics

    Proceedings of a Symposium Held at Purdue University, May 17-19, 1976
    • 1st Edition
    • Shanti S. Gupta + 1 more
    • English
    Statistical Decision Theory and Related Topics II is a compendium of papers presented at an international symposium on Statistical Decision Theory and Related Topics held at Purdue University in May, 1976. The researchers invited to participate, and to author papers for this volume, are among the leaders in the field of Statistical Decision Theory. This collection features works on general decision theory, multiple decision theory, optimal experimental design, and robustness. Mathematicians and statisticians will find the book highly insightful and informative.

  • International Conference on Differential Equations

    • 1st Edition
    • H.A. Antosiewicz
    • English
    International Conference on Differential Equations contains the proceedings of an International Conference on Differential Equations held at the University of Southern California, on September 3-7, 1974. The papers review advances in the qualitative-analytic theory of differential equations and highlight three broad areas: analytic theory (singular perturbations), qualitative theory (boundary value problems), and mathematical control theory (variational methods). Comprised of 82 chapters, this book begins with a discussion on continuous extensions, their construction, and their application in the theory of differential equations. The reader is then introduced to an approach to boundary control of partial differential equations based on the theory of semigroups of operators; lower closure and existence theorems in optimal control; and a nonlinear oscillation theorem. Subsequent chapters focus on matrices of rational functions; asymptotic integration of linear differential systems; solutions near bifurcated steady states; and geometric views in existence theory. This monograph will be of interest to students and instructors of mathematics.

  • Interval Mathematics 1980

    • 1st Edition
    • Karl L. E. Nickel
    • English
    Interval Mathematics 1980 contains the proceedings of an International Symposium on Interval Mathematics held in Germany on May 27-31, 1980. The book introduces the reader to some of the most important work done in the field of interval mathematics and its application to computing. Topics covered range from purely theoretical to computational methods and computer architecture. Comprised of 41 chapters, this book begins with an overview of set functions and their applications, followed by a discussion on global constrained optimization using interval analysis. A model for the propagation of rounding error in floating arithmetic is then presented, and the importance of 3-valued notions for interval mathematics is highlighted. Subsequent chapters focus on the transformation of interval programs into convergent interval programs; specifications for interval programming languages; interval contractions for the solution of integral equations; and mean convergence enclosing of solutions of operator equations with convex and inverse monotonic operators. This monograph will be of value to both students and specialists in the fields of mathematics and computer science.

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