# 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 :**69. 12 MB

**Format :**PDF, ePub

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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.

## Basic Abstract Algebra

**Author :**Robert B. Ash

**ISBN :**9780486318110

**Genre :**Mathematics

**File Size :**25. 86 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.

## Basic Methods Of Linear Functional Analysis

**Author :**John D. Pryce

**ISBN :**9780486173634

**Genre :**Mathematics

**File Size :**26. 13 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.

## Statistical Inference

**Author :**Robert B. Ash

**ISBN :**9780486481586

**Genre :**Mathematics

**File Size :**84. 84 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.

## Counterexamples In Analysis

**Author :**Bernard R. Gelbaum

**ISBN :**9780486134918

**Genre :**Mathematics

**File Size :**77. 46 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.

## Introduction To Analysis

**Author :**Maxwell Rosenlicht

**ISBN :**9780486134680

**Genre :**Mathematics

**File Size :**81. 83 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.

## Real Analysis And Probability

**Author :**Robert B. Ash

**ISBN :**9781483191423

**Genre :**Mathematics

**File Size :**77. 39 MB

**Format :**PDF

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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.

## Complex Variables

**Author :**Robert B. Ash

**ISBN :**9781483216195

**Genre :**Mathematics

**File Size :**21. 17 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.

## Probabilistic Metric Spaces

**Author :**B. Schweizer

**ISBN :**9780486445144

**Genre :**Mathematics

**File Size :**79. 83 MB

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This distinctly nonclassical treatment focuses on developing aspects that differ from the theory of ordinary metric spaces, working directly with probability distribution functions rather than random variables. The two-part treatment begins with an overview that discusses the theory's historical evolution, followed by a development of related mathematical machinery. The presentation defines all needed concepts, states all necessary results, and provides relevant proofs. The second part opens with definitions of probabilistic metric spaces and proceeds to examinations of special classes of probabilistic metric spaces, topologies, and several related structures, such as probabilistic normed and inner-product spaces. Throughout, the authors focus on developing aspects that differ from the theory of ordinary metric spaces, rather than simply transferring known metric space results to a more general setting.

## Matrices

**Author :**Denis Serre

**ISBN :**1441976833

**Genre :**Mathematics

**File Size :**88. 82 MB

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In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: • Dunford decomposition, • tensor and exterior calculus, polynomial identities, • regularity of eigenvalues for complex matrices, • functional calculus and the Dunford–Taylor formula, • numerical range, • Weyl's and von Neumann’s inequalities, and • Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the École Normale Supérieure de Lyon.