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.

Books Journals

Pure Mathematics

1st Edition
Volume 2
January 30, 1992
J.L. Britton
English
Hardback
9 7 8 0 4 4 4 8 8 0 5 9 8

The collected works of Turing, including a substantial amount of unpublished material, will comprise four volumes: Mechanical Intelligence, Pure Mathematics, Morphogenesis and Mathematical Logic. Alan Mathison Turing (1912-1954) was a brilliant man who made major contributions in several areas of science. Today his name is mentioned frequently in philosophical discussions about the nature of Artificial Intelligence. Actually, he was a pioneer researcher in computer architecture and software engineering; his work in pure mathematics and mathematical logic extended considerably further and his last work, on morphogenesis in plants, is also acknowledged as being of the greatest originality and of permanent importance. He was one of the leading figures in Twentieth-century science, a fact which would have been known to the general public sooner but for the British Official Secrets Act, which prevented discussion of his wartime work. What is maybe surprising about these papers is that although they were written decades ago, they address major issues which concern researchers today.

Continuous Linear Representations

1st Edition
Volume 168
January 30, 1992
Z. Magyar
English
eBook
9 7 8 0 0 8 0 8 7 2 7 9 7

This monograph gives access to the theory of continuous linear representations of general real Lie groups to readers who are already familiar with the rudiments of functional analysis and Lie groups. The first half of the book is centered around the relation between a continuous linear representation (of a Lie group over a Banach space or even a more general space) and its tangent; the latter is a Lie algebra representation in a sense. Starting with the Hille-Yosida theory, quite recent results are reached. The second half is more standard unitary theory with applications concerning the Galilean and Poincaré groups. Appendices help readers with diverse backgrounds to find the precise descriptions of the concepts needed from earlier literature.Each chapter includes exercises.

Mathematica by Example

1st Edition
January 28, 1992
Martha L Abell + 1 more
English
eBook
9 7 8 1 4 8 3 2 5 9 2 8 4

Mathematica by Example presents the commands and applications of Mathematica, a system for doing mathematics on a computer. This text serves as a guide to beginning users of Mathematica and users who do not intend to take advantage of the more specialized applications of Mathematica. The book combines symbolic manipulation, numerical mathematics, outstanding graphics, and a sophisticated programming language. It is comprised of 10 chapters. Chapter 1 gives a brief background of the software and how to install it in the computer. Chapter 2 introduces the essential commands of Mathematica. Basic operations on numbers, expressions, and functions are introduced and discussed. Chapter 3 provides Mathematica's built-in calculus commands. The fourth chapter presents elementary operations on lists and tables. This chapter is a prerequisite for Chapter 5 which discusses nested lists and tables in detail. The purpose of Chapter 6 is to illustrate various computations Mathematica can perform when solving differential equations. Chapters 7, 8, and 9 introduce Mathematica Packages that are not found in most Mathematica reference book. The final chapter covers the Mathematica Help feature. Engineers, computer scientists, physical scientists, mathematicians, business professionals, and students will find the book useful.

Handbook of Differential Equations

2nd Edition
January 28, 1992
Daniel Zwillinger
English
eBook
9 7 8 1 4 8 3 2 6 3 9 6 0

Handbook of Differential Equations, Second Edition is a handy reference to many popular techniques for solving and approximating differential equations, including numerical methods and exact and approximate analytical methods. Topics covered range from transformations and constant coefficient linear equations to Picard iteration, along with conformal mappings and inverse scattering. Comprised of 192 chapters, this book begins with an introduction to transformations as well as general ideas about differential equations and how they are solved, together with the techniques needed to determine if a partial differential equation is well-posed or what the "natural" boundary conditions are. Subsequent sections focus on exact and approximate analytical solution techniques for differential equations, along with numerical methods for ordinary and partial differential equations. This monograph is intended for students taking courses in differential equations at either the undergraduate or graduate level, and should also be useful for practicing engineers or scientists who solve differential equations on an occasional basis.

Lectures on Homotopy Theory

1st Edition
Volume 171
January 21, 1992
R.A. Piccinini
English
eBook
9 7 8 0 0 8 0 8 7 2 8 2 7

The central idea of the lecture course which gave birth to this book was to define the homotopy groups of a space and then give all the machinery needed to prove in detail that the nth homotopy group of the sphere Sn, for n greater than or equal to 1 is isomorphic to the group of the integers, that the lower homotopy groups of Sn are trivial and that the third homotopy group of S2 is also isomorphic to the group of the integers. All this was achieved by discussing H-spaces and CoH-spaces, fibrations and cofibrations (rather thoroughly), simplicial structures and the homotopy groups of maps.Later, the book was expanded to introduce CW-complexes and their homotopy groups, to construct a special class of CW-complexes (the Eilenberg-Mac Lane spaces) and to include a chapter devoted to the study of the action of the fundamental group on the higher homotopy groups and the study of fibrations in the context of a category in which the fibres are forced to live; the final material of that chapter is a comparison of various kinds of universal fibrations. Completing the book are two appendices on compactly generated spaces and the theory of colimits. The book does not require any prior knowledge of Algebraic Topology and only rudimentary concepts of Category Theory are necessary; however, the student is supposed to be well at ease with the main general theorems of Topology and have a reasonable mathematical maturity.

Wavelets

1st Edition
Volume 2
January 17, 1992
Bozzano G Luisa
English
eBook
9 7 8 0 3 2 3 1 3 9 7 4 8

Wavelets: A Tutorial in Theory and Applications is the second volume in the new series WAVELET ANALYSIS AND ITS APPLICATIONS. As a companion to the first volume in this series, this volume covers several of the most important areas in wavelets, ranging from the development of the basic theory such as construction and analysis of wavelet bases to an introduction of some of the key applications, including Mallat's local wavelet maxima technique in second generation image coding. A fairly extensive bibliography is also included in this volume.

Progress in Functional Analysis

1st Edition
Volume 170
January 10, 1992
K.D. Bierstedt + 3 more
English
eBook
9 7 8 0 0 8 0 8 7 2 8 1 0

This volume includes a collection of research articles inFunctional Analysis, celebrating the occasion of Manuel Valdivia'ssixtieth birthday. The papers included in the volume are basedon the main lectures presented during the internationalfunctional analysis meeting held in Peñíscola(Valencia, Spain) in October 1990.During his career, Valdiviahas made contributions to a wide variety of areas of FunctionalAnalysis and his work has had a profound impact. A thoroughappreciation of Valdivia's work is presented in J.Horváth's article. In honor of Valdivia's achievements, this volume presents more than twenty-five papers on topics related to his research(Banach spaces, operator ideals, tensor products, Fréchet,(DF) and (LF) spaces, distribution theory, infinite holomorphyetc.). While the majority of papers are research articles, survey articles are also included. The book covers a broad spectrum of interests in today's Functional Analysis and presents new results by leading specialists in the field.

Probability and Random Processes

1st Edition
January 3, 1992
Scott Miller + 1 more
English
Hardback
9 7 8 0 1 2 1 7 2 6 5 1 5
eBook
9 7 8 0 0 8 0 4 7 0 4 2 9

Probability and Random Processes provides a clear presentation of foundational concepts with specific applications to signal processing and communications, clearly the two areas of most interest to students and instructors in this course. It includes unique chapters on narrowband random processes and simulation techniques. It also includes applications in digital communications, information theory, coding theory, image processing, speech analysis, synthesis and recognition, and other fields. The appendices provide a refresher in such areas as linear algebra, set theory, random variables, and more. Exceptional exposition and numerous worked out problems make the book extremely readable and accessible. It is meant for practicing engineers as well as graduate students.

An Introduction to Wavelets

1st Edition
Volume 1
January 3, 1992
Charles K. Chui
English
Hardback
9 7 8 0 1 2 1 7 4 5 8 4 4
eBook
9 7 8 0 0 8 0 4 9 9 0 6 2

An Introduction to Wavelets is the first volume in a new series, WAVELET ANALYSIS AND ITS APPLICATIONS. This is an introductory treatise on wavelet analysis, with an emphasis on spline wavelets and time-frequency analysis. Among the basic topics covered in this book are time-frequency localization, integral wavelet transforms, dyadic wavelets, frames, spline-wavelets, orthonormal wavelet bases, and wavelet packets. In addition, the author presents a unified treatment of nonorthogonal, semiorthogonal, and orthogonal wavelets. This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis. It is suitable as a textbook for a beginning course on wavelet analysis and is directed toward both mathematicians and engineers who wish to learn about the subject. Specialists may use this volume as a valuable supplementary reading to the vast literature that has already emerged in this field.

Operational Expert System Applications in Europe

1st Edition
January 1, 1992
Gian Piero Zarri
English
eBook
9 7 8 1 4 8 3 1 4 4 9 1 7

Operational Expert System Applications in Europe describes the representative case studies of the operational expert systems (ESs) that are used in Europe. This compilation provides examples of operational ES that are realized in 10 different European countries, including countries not usually examined in the standard reviews of the field. This book discusses the decision support system using several artificial intelligence tools; expert systems for fault diagnosis on computerized numerical control (CNC) machines; and expert consultation system for personal portfolio management. The failure probability based troubleshooting expert system for the Airbus A-310; automatic diagnosis of rotating machinery faults; and expert system for naval resource allocation are also covered. This publication is suitable for researchers and specialists interested in the operational expert system applications in Europe.

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