REAL VARIABLES WITH BASIC METRIC SPACE TOPOLOGY DOVER BOOKS ON MATHEMATICS

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Real Variables With Basic Metric Space Topology

Author : Robert B. Ash
ISBN : 9780486151496
Genre : Mathematics
File Size : 28.65 MB
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Designed for a first course in real variables, this text encourages intuitive thinking and features detailed solutions to problems. Topics include complex variables, measure theory, differential equations, functional analysis, probability. 1993 edition.
Category: Mathematics

Real Variables With Basic Metric Space Topology

Author : Robert B. Ash
ISBN : 9780486151496
Genre : Mathematics
File Size : 25.29 MB
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Designed for a first course in real variables, this text encourages intuitive thinking and features detailed solutions to problems. Topics include complex variables, measure theory, differential equations, functional analysis, probability. 1993 edition.
Category: Mathematics

Basic Abstract Algebra

Author : Robert B. Ash
ISBN : 9780486318110
Genre : Mathematics
File Size : 20.35 MB
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Relations between groups and sets, results and methods of abstract algebra in terms of number theory and geometry, and noncommutative and homological algebra. Solutions. 2006 edition.
Category: Mathematics

Basic Methods Of Linear Functional Analysis

Author : John D. Pryce
ISBN : 9780486173634
Genre : Mathematics
File Size : 66.47 MB
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Introduction to the themes of mathematical analysis, geared toward advanced undergraduate and graduate students. Topics include operators, function spaces, Hilbert spaces, and elementary Fourier analysis. Numerous exercises and worked examples.1973 edition.
Category: Mathematics

Introduction To Analysis

Author : Maxwell Rosenlicht
ISBN : 9780486134680
Genre : Mathematics
File Size : 21.64 MB
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Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.
Category: Mathematics

Counterexamples In Analysis

Author : Bernard R. Gelbaum
ISBN : 9780486134918
Genre : Mathematics
File Size : 42.98 MB
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These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.
Category: Mathematics

Invitation To Geometry

Author : Z. A. Melzak
ISBN : 9780486789484
Genre : Mathematics
File Size : 61.38 MB
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Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. Only a slight acquaintance with mathematics beyond the high-school level is necessary, including some familiarity with calculus and linear algebra. This text's introductions to several branches of geometry feature topics and treatments based on memorability and relevance. The author emphasizes connections with calculus and simple mechanics, focusing on developing students' grasp of spatial relationships. Subjects include classical Euclidean material, polygonal and circle isoperimetry, conics and Pascal's theorem, geometrical optimization, geometry and trigonometry on a sphere, graphs, convexity, and elements of differential geometry of curves. Additional material may be conveniently introduced in several places, and each chapter concludes with exercises of varying degrees of difficulty.
Category: Mathematics

Statistical Inference

Author : Robert B. Ash
ISBN : 9780486481586
Genre : Mathematics
File Size : 81.31 MB
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This book offers a brief course in statistical inference that requires only a basic familiarity with probability and matrix and linear algebra. Ninety problems with solutions make it an ideal choice for self-study as well as a helpful review of a wide-ranging topic with important uses to professionals in business, government, public administration, and other fields. 2011 edition.
Category: Mathematics

Complex Variables

Author : Robert B. Ash
ISBN : 9781483216195
Genre : Mathematics
File Size : 51.55 MB
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Complex Variables deals with complex variables and covers topics ranging from Cauchy's theorem to entire functions, families of analytic functions, and the prime number theorem. Major applications of the basic principles, such as residue theory, the Poisson integral, and analytic continuation are given. Comprised of seven chapters, this book begins with an introduction to the basic definitions and concepts in complex variables such as the extended plane, analytic and elementary functions, and Cauchy-Riemann equations. The first chapter defines the integral of a complex function on a path in the complex plane and develops the machinery to prove an elementary version of Cauchy's theorem. Some applications, including the basic properties of power series, are then presented. Subsequent chapters focus on the general Cauchy theorem and its applications; entire functions; families of analytic functions; and the prime number theorem. The geometric intuition underlying the concept of winding number is emphasized. The linear space viewpoint is also discussed, along with analytic number theory, residue theory, and the Poisson integral. This book is intended primarily for students who are just beginning their professional training in mathematics.
Category: Mathematics

Real Analysis And Probability

Author : Robert B. Ash
ISBN : 9781483191423
Genre : Mathematics
File Size : 54.26 MB
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Real Analysis and Probability provides the background in real analysis needed for the study of probability. Topics covered range from measure and integration theory to functional analysis and basic concepts of probability. The interplay between measure theory and topology is also discussed, along with conditional probability and expectation, the central limit theorem, and strong laws of large numbers with respect to martingale theory. Comprised of eight chapters, this volume begins with an overview of the basic concepts of the theory of measure and integration, followed by a presentation of various applications of the basic integration theory. The reader is then introduced to functional analysis, with emphasis on structures that can be defined on vector spaces. Subsequent chapters focus on the connection between measure theory and topology; basic concepts of probability; and conditional probability and expectation. Strong laws of large numbers are also examined, first from the classical viewpoint, and then via martingale theory. The final chapter is devoted to the one-dimensional central limit problem, paying particular attention to the fundamental role of Prokhorov's weak compactness theorem. This book is intended primarily for students taking a graduate course in probability.
Category: Mathematics