Some Random Series of Functions
Some Random Series of Functions

Author: Jean-Pierre Kahane

Publisher: Cambridge University Press

Published: 1985

Total Pages: 324

ISBN-13: 9780521456029

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The subject matter of Some Random Series of Functions is important and has wide application in mathematics, statistics, engineering, and physics.

Lectures on Modules and Rings
Lectures on Modules and Rings

Author: Tsit-Yuen Lam

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 577

ISBN-13: 1461205255

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This new book can be read independently from the first volume and may be used for lecturing, seminar- and self-study, or for general reference. It focuses more on specific topics in order to introduce readers to a wealth of basic and useful ideas without the hindrance of heavy machinery or undue abstractions. User-friendly with its abundance of examples illustrating the theory at virtually every step, the volume contains a large number of carefully chosen exercises to provide newcomers with practice, while offering a rich additional source of information to experts. A direct approach is used in order to present the material in an efficient and economic way, thereby introducing readers to a considerable amount of interesting ring theory without being dragged through endless preparatory material.

An Introduction to Dynamical Systems
An Introduction to Dynamical Systems

Author: D. K. Arrowsmith

Publisher: Cambridge University Press

Published: 1990-07-27

Total Pages: 436

ISBN-13: 9780521316507

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In recent years there has been an explosion of research centred on the appearance of so-called 'chaotic behaviour'. This book provides a largely self contained introduction to the mathematical structures underlying models of systems whose state changes with time, and which therefore may exhibit this sort of behaviour. The early part of this book is based on lectures given at the University of London and covers the background to dynamical systems, the fundamental properties of such systems, the local bifurcation theory of flows and diffeomorphisms, Anosov automorphism, the horseshoe diffeomorphism and the logistic map and area preserving planar maps . The authors then go on to consider current research in this field such as the perturbation of area-preserving maps of the plane and the cylinder. This book, which has a great number of worked examples and exercises, many with hints, and over 200 figures, will be a valuable first textbook to both senior undergraduates and postgraduate students in mathematics, physics, engineering, and other areas in which the notions of qualitative dynamics are employed.

Mathematical Logic with Special Reference to the Natural Numbers
Mathematical Logic with Special Reference to the Natural Numbers

Author: S. W. P. Steen

Publisher: Cambridge University Press

Published: 1972

Total Pages: 0

ISBN-13: 0521080533

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This book presents a comprehensive treatment of basic mathematical logic. The author's aim is to make exact the vague, intuitive notions of natural number, preciseness, and correctness, and to invent a method whereby these notions can be communicated to others and stored in the memory. He adopts a symbolic language in which ideas about natural numbers can be stated precisely and meaningfully, and then investigates the properties and limitations of this language. The treatment of mathematical concepts in the main body of the text is rigorous, but, a section of 'historical remarks' traces the evolution of the ideas presented in each chapter. Sources of the original accounts of these developments are listed in the bibliography.

Introduction to Set Theory and Topology
Introduction to Set Theory and Topology

Author: Kazimierz Kuratowski

Publisher: Elsevier

Published: 2014-07-10

Total Pages: 353

ISBN-13: 1483151638

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Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered. This volume consists of 21 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its application to propositions each having one of two logical values, 0 and 1. Operations on sets which are analogous to arithmetic operations are also discussed. The chapters that follow focus on the mapping concept, the power of a set, operations on cardinal numbers, order relations, and well ordering. The section on topology explores metric and topological spaces, continuous mappings, cartesian products, and other spaces such as spaces with a countable base, complete spaces, compact spaces, and connected spaces. The concept of dimension, simplexes and their properties, and cuttings of the plane are also analyzed. This book is intended for students and teachers of mathematics.