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

Topological Algebras

1st Edition
Volume 24
October 10, 2011
Edward Beckenstein + 2 more
English
eBook
9 7 8 0 0 8 0 8 7 1 3 5 6

This book discusses general topological algebras; space C(T,F) of continuous functions mapping T into F as an algebra only (with pointwise operations); and C(T,F) endowed with compact-open topology as a topological algebra C(T,F,c). It characterizes the maximal ideals and homomorphisms closed maximal ideals and continuous homomorphisms of topological algebras in general and C(T,F,c) in particular. A considerable inroad is made into the properties of C(T,F,c) as a topological vector space. Many of the results about C(T,F,c) serve to illustrate and motivate results about general topological algebras. Attention is restricted to the algebra C(T,R) of real-valued continuous functions and to the pursuit of the maximal ideals and real-valued homomorphisms of such algebras. The chapter presents the correlation of algebraic properties of C(T,F) with purely topological properties of T. The Stone–Čech compactification and the Wallman compactification play an important role in characterizing the maximal ideals of certain topological algebras.

Contributions to Universal Algebra

1st Edition
May 15, 2014
B. Csákány + 1 more
English
eBook
9 7 8 1 4 8 3 1 0 3 0 2 0

Contributions to Universal Algebra focuses on the study of algebra. The compilation first discusses the congruence lattice of pseudo-simple algebras; elementary properties of limit reduced powers with applications to Boolean powers; and congruent lattices of 2-valued algebras. The book further looks at duality for algebras; weak homomorphisms of stone algebras; varieties of modular lattices not generated by their finite dimensional members; and remarks on algebraic operations of stone algebras. The text describes polynomial normal forms and the embedding of polynomial algebras; coverings in the lattice of varieties; embedding semigroups in semigroups generated by idempotents; and endomorphism semigroups and subgroupoid lattices. The book also discusses a report on sublattices of a free lattice, and then presents the cycles in finite semi-distributive lattices; cycles in S-lattices; and summary of results. The text also describes primitive subsets of algebras, ideals, normal sets, and congruences, as well as Jacobson’s density theorem. The book is a good source for readers wanting to study algebra.

Non-Classical Logics, Model Theory, And Computability

1st Edition
Volume 89
April 1, 2000
Lev D. Beklemishev
English
eBook
9 7 8 0 0 8 0 9 5 4 9 8 1

Studies in Integer Programming

1st Edition
Volume 1
October 10, 2011
Peter L. Hammer
English
eBook
9 7 8 0 0 8 0 8 6 7 6 4 9

Construction Of Integration Formulas For Initial Value Problems

1st Edition
December 2, 2012
P.J. Van Der Houwen
English
eBook
9 7 8 0 4 4 4 6 0 1 8 9 6

Construction of Integration Formulas for Initial Value Problems provides practice-oriented insights into the numerical integration of initial value problems for ordinary differential equations. It describes a number of integration techniques, including single-step methods such as Taylor methods, Runge-Kutta methods, and generalized Runge-Kutta methods. It also looks at multistep methods and stability polynomials. Comprised of four chapters, this volume begins with an overview of definitions of important concepts and theorems that are relevant to the construction of numerical integration methods for initial value problems. It then turns to a discussion of how to convert two-point and initial boundary value problems for partial differential equations into initial value problems for ordinary differential equations. The reader is also introduced to stiff differential equations, partial differential equations, matrix theory and functional analysis, and non-linear equations. The order of approximation of the single-step methods to the differential equation is considered, along with the convergence of a consistent single-step method. There is an explanation on how to construct integration formulas with adaptive stability functions and how to derive the most important stability polynomials. Finally, the book examines the consistency, convergence, and stability conditions for multistep methods. This book is a valuable resource for anyone who is acquainted with introductory calculus, linear algebra, and functional analysis.

Mathematical Problems in Elasticity and Homogenization

1st Edition
Volume 2
June 15, 2009
O.A. Oleinik + 2 more
English
eBook
9 7 8 0 0 8 0 8 7 5 2 3 1

This monograph is based on research undertaken by the authors during the last ten years. The main part of the work deals with homogenization problems in elasticity as well as some mathematical problems related to composite and perforated elastic materials. This study of processes in strongly non-homogeneous media brings forth a large number of purely mathematical problems which are very important for applications. Although the methods suggested deal with stationary problems, some of them can be extended to non-stationary equations. With the exception of some well-known facts from functional analysis and the theory of partial differential equations, all results in this book are given detailed mathematical proof.It is expected that the results and methods presented in this book will promote further investigation of mathematical models for processes in composite and perforated media, heat-transfer, energy transfer by radiation, processes of diffusion and filtration in porous media, and that they will stimulate research in other problems of mathematical physics and the theory of partial differential equations.

A Course in Mathematical Logic

1st Edition
January 1, 1977
J.L. Bell + 1 more
English
Hardback
9 7 8 0 7 2 0 4 2 8 4 4 5

A comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included.

Mathematical Tools for Applied Multivariate Analysis

1st Edition
May 10, 2014
Paul E. Green
English
eBook
9 7 8 1 4 8 3 2 1 4 0 4 7

Mathematical Tools for Applied Multivariate Analysis provides information pertinent to the aspects of transformational geometry, matrix algebra, and the calculus that are most relevant for the study of multivariate analysis. This book discusses the mathematical foundations of applied multivariate analysis. Organized into six chapters, this book begins with an overview of the three problems in multiple regression, principal components analysis, and multiple discriminant analysis. This text then presents a standard treatment of the mechanics of matrix algebra, including definitions and operations on matrices, vectors, and determinants. Other chapters consider the topics of eigenstructures and linear transformations that are important to the understanding of multivariate techniques. This book discusses as well the eigenstructures and quadratic forms. The final chapter deals with the geometric aspects of linear transformations. This book is a valuable resource for students.

Introduction to the Theory of Infiniteseimals

1st Edition
Volume 72
January 13, 1977
K.D. Stroyan + 1 more
English
eBook
9 7 8 0 0 8 0 8 7 3 8 8 6

Ergodic Theory and Topological Dynamics

1st Edition
Volume 70
November 15, 1976
James R. Brown
English
eBook
9 7 8 0 0 8 0 8 7 3 8 6 2

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