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

Residuated Lattices: An Algebraic Glimpse at Substructural Logics

1st Edition
Volume 151
April 25, 2007
Nikolaos Galatos + 3 more
English
eBook
9 7 8 0 0 8 0 4 8 9 6 4 3

The book is meant to serve two purposes. The first and more obvious one is to present state of the art results in algebraic research into residuated structures related to substructural logics. The second, less obvious but equally important, is to provide a reasonably gentle introduction to algebraic logic. At the beginning, the second objective is predominant. Thus, in the first few chapters the reader will find a primer of universal algebra for logicians, a crash course in nonclassical logics for algebraists, an introduction to residuated structures, an outline of Gentzen-style calculi as well as some titbits of proof theory - the celebrated Hauptsatz, or cut elimination theorem, among them. These lead naturally to a discussion of interconnections between logic and algebra, where we try to demonstrate how they form two sides of the same coin. We envisage that the initial chapters could be used as a textbook for a graduate course, perhaps entitled Algebra and Substructural Logics. As the book progresses the first objective gains predominance over the second. Although the precise point of equilibrium would be difficult to specify, it is safe to say that we enter the technical part with the discussion of various completions of residuated structures. These include Dedekind-McNeille completions and canonical extensions. Completions are used later in investigating several finiteness properties such as the finite model property, generation of varieties by their finite members, and finite embeddability. The algebraic analysis of cut elimination that follows, also takes recourse to completions. Decidability of logics, equational and quasi-equational theories comes next, where we show how proof theoretical methods like cut elimination are preferable for small logics/theories, but semantic tools like Rabin's theorem work better for big ones. Then we turn to Glivenko's theorem, which says that a formula is an intuitionistic tautology if and only if its double negation is a classical one. We generalise it to the substructural setting, identifying for each substructural logic its Glivenko equivalence class with smallest and largest element. This is also where we begin investigating lattices of logics and varieties, rather than particular examples. We continue in this vein by presenting a number of results concerning minimal varieties/maximal logics. A typical theorem there says that for some given well-known variety its subvariety lattice has precisely such-and-such number of minimal members (where values for such-and-such include, but are not limited to, continuum, countably many and two). In the last two chapters we focus on the lattice of varieties corresponding to logics without contraction. In one we prove a negative result: that there are no nontrivial splittings in that variety. In the other, we prove a positive one: that semisimple varieties coincide with discriminator ones. Within the second, more technical part of the book another transition process may be traced. Namely, we begin with logically inclined technicalities and end with algebraically inclined ones. Here, perhaps, algebraic rendering of Glivenko theorems marks the equilibrium point, at least in the sense that finiteness properties, decidability and Glivenko theorems are of clear interest to logicians, whereas semisimplicity and discriminator varieties are universal algebra par exellence. It is for the reader to judge whether we succeeded in weaving these threads into a seamless fabric.

Open Problems in Topology II

1st Edition
March 15, 2007
Elliott M. Pearl
English
eBook
9 7 8 0 0 8 0 4 7 5 2 9 5

This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis.

Linear Algebra

2nd Edition
March 5, 2007
Richard Bronson + 1 more
English
eBook
9 7 8 0 0 8 0 5 1 0 2 6 2

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 and computational, 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 instructor's taste and to the length of the course. Bronson's 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 the end of each chapter. The book also includes ample exercises with answers and hints. With its inclusion of all the needed features, this text will be a pleasure for professionals, teachers, and students.

Computational Methods for Modeling of Nonlinear Systems by Anatoli Torokhti and Phil Howlett

1st Edition
Volume 212
March 2, 2007
Anatoli Torokhti + 1 more
English
Hardback
9 7 8 0 4 4 4 5 3 0 4 4 8
eBook
9 7 8 0 0 8 0 4 7 5 3 8 7

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression.

Table of Integrals, Series, and Products

7th Edition
February 23, 2007
Daniel Zwillinger + 1 more
English
eBook
9 7 8 0 0 8 0 4 7 1 1 1 2

The Table of Integrals, Series, and Products is the essential reference for integrals in the English language. Mathematicians, scientists, and engineers, rely on it when identifying and subsequently solving extremely complex problems. Since publication of the first English-language edition in 1965, it has been thoroughly revised and enlarged on a regular basis, with substantial additions and, where necessary, existing entries corrected or revised. The seventh edition includes a fully searchable CD-Rom.

Introduction to Precise Numerical Methods

2nd Edition
February 23, 2007
Oliver Aberth
English
eBook
9 7 8 0 0 8 0 4 7 1 2 0 4

Precise numerical analysis may be defined as the study of computer methods for solving mathematical problems either exactly or to prescribed accuracy. This book explains how precise numerical analysis is constructed. The book also provides exercises which illustrate points from the text and references for the methods presented.

Handbook of Latent Variable and Related Models

1st Edition
Volume 1
February 8, 2007
Sik-Yum Lee
English
eBook
9 7 8 0 0 8 0 4 7 1 2 6 6

This Handbook covers latent variable models, which are a flexible class of models for modeling multivariate data to explore relationships among observed and latent variables.

Equilibrium Models and Variational Inequalities

1st Edition
Volume 210
February 8, 2007
Igor Konnov
English
eBook
9 7 8 0 0 8 0 4 7 1 3 8 9

The concept of equilibrium plays a central role in various applied sciences, such as physics (especially, mechanics), economics, engineering, transportation, sociology, chemistry, biology and other fields. If one can formulate the equilibrium problem in the form of a mathematical model, solutions of the corresponding problem can be used for forecasting the future behavior of very complex systems and, also, for correcting the the current state of the system under control. This book presents a unifying look on different equilibrium concepts in economics, including several models from related sciences.

Leonhard Euler

1st Edition
Volume 5
February 5, 2007
Robert E. Bradley + 1 more
English
eBook
9 7 8 0 0 8 0 4 7 1 2 9 7

The year 2007 marks the 300th anniversary of the birth of one of the Enlightenment’s most important mathematicians and scientists, Leonhard Euler. This volume is a collection of 24 essays by some of the world’s best Eulerian scholars from seven different countries about Euler, his life and his work. Some of the essays are historical, including much previously unknown information about Euler’s life, his activities in the St. Petersburg Academy, the influence of the Russian Princess Dashkova, and Euler’s philosophy. Others describe his influence on the subsequent growth of European mathematics and physics in the 19th century. Still others give technical details of Euler’s innovations in probability, number theory, geometry, analysis, astronomy, mechanics and other fields of mathematics and science.

RFID+ Study Guide and Practice Exams

1st Edition
February 1, 2007
Paul Sanghera
English
Paperback
9 7 8 1 5 9 7 4 9 1 3 4 1
eBook
9 7 8 0 0 8 0 5 1 6 2 9 5

Radio Frequency Identification (RFID) is an automatic identification method, relying on storing and remotely retrieving data using devices called RFID tags (also called transponders). This book is a guide to CompTIA's new RFID+ Security exam and includes the following study elements: Exam objectives covered in a chapter are clearly explained in the beginning of the chapter, Notes and Alerts highlight the crucial points, Exam’s Eye View emphasizes the important points from the exam’s perspective, Key Terms present definitions, Review Questions contain questions modeled after the real exam questions. Answers to these questions are presented with complete explanations in an appendix. Also included is a full practice exam modeled after the real exam. The answers to the exam questions are presented with full explanations.

Related subjects

Mathematics and applied mathematics

Statistics and probability

Life Sciences

Physical Sciences & Engineering

Social Sciences & Humanities

Health