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

Advances in Computers

1st Edition
Volume 56
August 5, 2002
Marvin Zelkowitz
English
eBook
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Advances in Computers remains at the forefront in presenting the new developments in the ever-changing field of information technology. Since 1960, Advances in Computers has chronicled the constantly shifting theories and methods of this technology that greatly shape our lives today. Volume 56 presents eight chapters that describe how the software, hardware and applications of computers are changing the use of computers during the early part of the 21st century: Software Evolution and the Staged Model of the Software Lifecycle; Embedded Software; Empirical Studies of Quality Models in Object-Oriented Systems; Software Fault Prevention by Language Choice; Quantum computing and communication; Exception Handling; Breaking the Robustness Barrier: Recent Progress on the Design of Robust Multimodal Systems; Using Data Mining to Discover the Preferences of Computer Criminals. As the longest-running continuous serial on computers, Advances in Computers presents technologies that will affect the industry in the years to come, covering hot topics from fundamentals to applications. Additionally, readers benefit from contributions of both academic and industry professionals of the highest caliber.

Pyramid Algorithms

1st Edition
July 10, 2002
Ron Goldman
English
Hardback
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eBook
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Pyramid Algorithms presents a unique approach to understanding, analyzing, and computing the most common polynomial and spline curve and surface schemes used in computer-aided geometric design, employing a dynamic programming method based on recursive pyramids.The recursive pyramid approach offers the distinct advantage of revealing the entire structure of algorithms, as well as relationships between them, at a glance. This book-the only one built around this approach-is certain to change the way you think about CAGD and the way you perform it, and all it requires is a basic background in calculus and linear algebra, and simple programming skills.

Database and Data Communication Network Systems, Three-Volume Set

1st Edition
July 2, 2002
Cornelius T. Leondes
English
eBook
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Database and Data Communication Network Systems examines the utilization of the Internet and Local Area/Wide Area Networks in all areas of human endeavor. This three-volume set covers, among other topics, database systems, data compression, database architecture, data acquisition, asynchronous transfer mode (ATM) and the practical application of these technologies. The international collection of contributors was culled from exhaustive research of over 100,000 related archival and technical journals. This reference will be indispensable to engineering and computer science libraries, research libraries, and telecommunications, networking, and computer companies. It covers a diverse array of topics, including:* Techniques in emerging database system architectures* Techniques and applications in data mining* Object-oriented database systems* Data acquisition on the WWW during heavy client/server traffic periods* Information exploration on the WWW* Education and training in multimedia database systems* Data structure techniques in rapid prototyping and manufacturing* Wireless ATM in data networks for mobile systems* Applications in corporate finance* Scientific data visualization* Data compression and information retrieval* Techniques in medical systems, intensive care units

Relation Algebras by Games

1st Edition
Volume 147
July 1, 2002
Robin Hirsch + 1 more
English
eBook
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Relation algebras are algebras arising from the study of binary relations.They form a part of the field of algebraic logic, and have applications in proof theory, modal logic, and computer science. This research text uses combinatorial games to study the fundamental notion of representations of relation algebras. Games allow an intuitive and appealing approach to the subject, and permit substantial advances to be made. The book contains many new results and proofs not published elsewhere. It should be invaluable to graduate students and researchers interested in relation algebras and games.After an introduction describing the authors' perspective on the material, the text proper has six parts. The lengthy first part is devoted to background material, including the formal definitions of relation algebras, cylindric algebras, their basic properties, and some connections between them. Examples are given. Part 1 ends with a short survey of other work beyond the scope of the book. In part 2, games are introduced, and used to axiomatise various classes of algebras. Part 3 discusses approximations to representability, using bases, relation algebra reducts, and relativised representations. Part 4 presents some constructions of relation algebras, including Monk algebras and the 'rainbow construction', and uses them to show that various classes of representable algebras are non-finitely axiomatisable or even non-elementary. Part 5 shows that the representability problem for finite relation algebras is undecidable, and then in contrast proves some finite base property results. Part 6 contains a condensed summary of the book, and a list of problems. There are more than 400 exercises.The book is generally self-contained on relation algebras and on games, and introductory text is scattered throughout. Some familiarity with elementary aspects of first-order logic and set theory is assumed, though many of the definitions are given. Chapter 2 introduces the necessary universal algebra and model theory, and more specific model-theoretic ideas are explained as they arise.

Nonlinear Partial Differential Equations and Their Applications

1st Edition
Volume 31
June 21, 2002
Doina Cioranescu + 1 more
English
eBook
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This book contains the written versions of lectures delivered since 1997 in the well-known weekly seminar on Applied Mathematics at the Collège de France in Paris, directed by Jacques-Louis Lions. It is the 14th and last of the series, due to the recent and untimely death of Professor Lions. The texts in this volume deal mostly with various aspects of the theory of nonlinear partial differential equations. They present both theoretical and applied results in many fields of growing importance such as Calculus of variations and optimal control, optimization, system theory and control, operations research, fluids and continuum mechanics, nonlinear dynamics, meteorology and climate, homogenization and material science, numerical analysis and scientific computations The book is of interest to everyone from postgraduate, who wishes to follow the most recent progress in these fields.

Complex Numbers in n Dimensions

1st Edition
Volume 190
June 20, 2002
S. Olariu
English
eBook
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Two distinct systems of hypercomplex numbers in n dimensions are introduced in this book, for which the multiplication is associative and commutative, and which are rich enough in properties such that exponential and trigonometric forms exist and the concepts of analytic n-complex function, contour integration and residue can be defined.The first type of hypercomplex numbers, called polar hypercomplex numbers, is characterized by the presence in an even number of dimensions greater or equal to 4 of two polar axes, and by the presence in an odd number of dimensions of one polar axis. The other type of hypercomplex numbers exists as a distinct entity only when the number of dimensions n of the space is even, and since the position of a point is specified with the aid of n/2-1 planar angles, these numbers have been called planar hypercomplex numbers.The development of the concept of analytic functions of hypercomplex variables was rendered possible by the existence of an exponential form of the n-complex numbers. Azimuthal angles, which are cyclic variables, appear in these forms at the exponent, and lead to the concept of n-dimensional hypercomplex residue. Expressions are given for the elementary functions of n-complex variable. In particular, the exponential function of an n-complex number is expanded in terms of functions called in this book n-dimensional cosexponential functionsof the polar and respectively planar type, which are generalizations to n dimensions of the sine, cosine and exponential functions.In the case of polar complex numbers, a polynomial can be written as a product of linear or quadratic factors, although it is interesting that several factorizations are in general possible. In the case of planar hypercomplex numbers, a polynomial can always be written as a product of linear factors, although, again, several factorizations are in general possible.The book presents a detailed analysis of the hypercomplex numbers in 2, 3 and 4 dimensions, then presents the properties of hypercomplex numbers in 5 and 6 dimensions, and it continues with a detailed analysis of polar and planar hypercomplex numbers in n dimensions. The essence of this book is the interplay between the algebraic, the geometric and the analytic facets of the relations.

Almost Free Modules

1st Edition
Volume 65
April 29, 2002
P.C. Eklof + 1 more
English
eBook
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This book provides a comprehensive exposition of the use of set-theoretic methods in abelian group theory, module theory, and homological algebra, including applications to Whitehead's Problem, the structure of Ext and the existence of almost-free modules over non-perfect rings. This second edition is completely revised and udated to include major developments in the decade since the first edition. Among these are applications to cotorsion theories and covers, including a proof of the Flat Cover Conjecture, as well as the use of Shelah's pcf theory to constuct almost free groups. As with the first edition, the book is largely self-contained, and designed to be accessible to both graduate students and researchers in both algebra and logic. They will find there an introduction to powerful techniques which they may find useful in their own work.

Mathematics

2nd Edition
April 1, 2002
S. Page + 2 more
English
Paperback
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eBook
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Provides less mathematically minded students with a gentle introduction to basic mathematics and some more advanced topics. Covering algebra, trigonometry, calculus and statistics, it manages to combine clarity of presentation with liveliness of style and sympathy for students’ needs. It is straightforward, pragmatic and packed full of illustrative examples, exercises and self-test questions. The essentials of formal mathematics are lucidly explained, with terms such as ‘integral’ or ‘differential equation’ fully clarified.

Mathematics Teaching Practice

1st Edition
March 1, 2002
J H Mason
English
eBook
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Mathematics; Clarifying the distinction between mathematical research and mathematics education, this book offers hundreds of suggestions for making small and medium sized changes for lectures, tutorials, task design, or problem solving. Here is guidance and inspiration for effective mathematics teaching in a modern technological environment, directed to teachers who are unhappy with results or experience, or those now in teacher training or new to the profession. Commencing with a range of student behaviours and attitudes that have struck and amazed tutors and lecturers, Professor Mason offers a wealth of partial diagnoses, followed by specific advice and suggestions for remedial actions.

Manifold Theory

1st Edition
March 1, 2002
D. Martin
English
eBook
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This account of basic manifold theory and global analysis, based on senior undergraduate and post-graduate courses at Glasgow University for students and researchers in theoretical physics, has been proven over many years. The treatment is rigorous yet less condensed than in books written primarily for pure mathematicians. Prerequisites include knowledge of basic linear algebra and topology. Topology is included in two appendices because many courses on mathematics for physics students do not include this subject.

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