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

Complex Analysis in Locally Convex Spaces

1st Edition
Volume 57
January 1, 1981
S. Dineen
English
eBook
9 7 8 0 0 8 0 8 7 1 6 8 4

The Handbook of Artificial Intelligence

1st Edition
May 12, 2014
Avron Barr + 1 more
English
eBook
9 7 8 1 4 8 3 2 1 4 3 7 5

The Handbook of Artificial Intelligence, Volume I focuses on the progress in artificial intelligence (AI) and its increasing applications, including parsing, grammars, and search methods. The book first elaborates on AI, AI handbook and literature, problem representation, search methods, and sample search programs. The text then ponders on representation of knowledge, including survey of representation techniques and representation schemes. The manuscript explores understanding natural languages, as well as machine translation, grammars, parsing, test generation, and natural language processing systems. The book also takes a look at understanding spoken language, including systems architecture and the ARPA SUR projects. The text is a valuable source of information for computer science experts and researchers interested in pursuing further research in artificial intelligence.

I: Functional Analysis

1st Edition
Volume 1
December 28, 1980
Michael Reed + 1 more
English
Hardback
9 7 8 0 1 2 5 8 5 0 5 0 6
eBook
9 7 8 0 0 8 0 5 7 0 4 8 8

This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations.

Martingale Limit Theory and Its Application

1st Edition
July 10, 2014
P. Hall + 1 more
Z. W. Birnbaum + 1 more
English
eBook
9 7 8 1 4 8 3 2 6 3 2 2 9

Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.

Functional Analysis and Linear Control Theory

1st Edition
December 5, 1980
J.R. Leigh
English
eBook
9 7 8 0 0 8 0 9 5 9 9 8 6

Developments in Statistics

1st Edition
Volume 3
June 28, 2014
Paruchuri R. Krishnaiah
English
eBook
9 7 8 1 4 8 3 2 6 4 2 0 2

Development in Statistics, Volume 3 is a collection of papers that deals with asymptotic expansions in parametric statistical theory, orthogonal models for contingency tables, statistical concepts in economic analysis, and an exposition of path analysis. One paper presents an inference model based on a sample of independent identically distributed observations to arrive at a general statistical theory founded on asymptotic methods. Another paper discusses the applicability of statistical concepts to economics and related areas, with emphasis on not-so-obvious applications (known as utility and expected loss). The paper explains information theory concepts for the measurement of income inequality, intergenerational occupational mobility, as well as to first- and second-order moments of univariate and bivariate distributions (such as measurements applied to the cost of living and of real income). One paper notes that the starting point in path analysis is a linear predictor (in the least-squares sense) for one random variable in terms of a number of others. The paper adds that the work of Koopmans and Hood (1953) on econometrics is part of the starting point. Statisticians, economists, mathematicians, students, and professors of calculus or advanced mathematics will surely appreciate the collection.

An Introduction to Nonharmonic Fourier Series

1st Edition
Volume 93
January 9, 1981
Robert M. Young
English
eBook
9 7 8 0 0 8 0 8 7 4 0 9 8

Convexity Theory and its Applications in Functional Analysis

1st Edition
June 28, 2014
L. Asimow
English
eBook
9 7 8 1 4 8 3 2 9 4 6 9 8

Convexity Theory and its Applications in Functional Analysis is a five-chapter text that provides a geometric perspective of the convexity theory and its practical applications. Chapter 1 reviews the functional analytic preliminaries, including the Krein-Smulyan Theorem, the basic Choquet Theory, and the Bishop-Phelps Theorem. Chapter 2 gives the basic duality results, lattice theory and concrete representation theorems for order unit spaces and Banach lattices of type Mand L. Chapters 3 and 4 deal with the real affine function spaces through examining the Choquet simplex and the application of the study of real A(K) spaces to complex-values function spaces by means of a complex state space. Chapter 5 highlights the application of the theory to the study of non-commutative Banach algebras. This book will prove useful to mathematicians, engineers, and physicists.

Applied Stochastic Processes

1st Edition
May 9, 2014
G. Adomian
English
eBook
9 7 8 1 4 8 3 2 5 9 0 8 6

Applied Stochastic Processes is a collection of papers dealing with stochastic processes, stochastic equations, and their applications in many fields of science. One paper discusses stochastic systems involving randomness in the system itself that can be a large dynamical multi-input, multi-output system. Examples of a large system are the national economy of a major country or when an acoustic wave is propagating as in the atmosphere, ocean, or sea. Another paper proves that only the average properties of the molecules of biology can be measured with precision in the test tube; and disputes a "simplistic" model of the cell as defined by a miniature Laplaces' universe. The paper notes that the way existing cells are constructed implies that quantum mechanical principles lead to certain questions (about simple experiments) having only statistical answers. Another paper addresses the detection of distributed, fluctuating targets in a reverberation limited, randomly time, and space varying transmission media. This approach is done by using the concepts of "random Green's functions" and the "stochastic Green's function." The collection will prove useful for cellular researchers, mathematicians, physicist, engineers, and academicians in the field of applied mathematics, statistics, and chemistry.

Fuzzy Sets and Systems

1st Edition
October 28, 1980
Didier J. Dubois
English
Hardback
9 7 8 0 1 2 2 2 2 7 5 0 9
eBook
9 7 8 0 0 8 0 9 1 7 7 2 6

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