An Invitation To Real Analysis

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An Invitation To Real Analysis

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Author : Luis F. Moreno
language : en
Publisher: The Mathematical Association of America
Release Date : 2015-05-17

An Invitation To Real Analysis written by Luis F. Moreno and has been published by The Mathematical Association of America this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-17 with Mathematics categories.

An Invitation to Real Analysis is written both as a stepping stone to higher calculus and analysis courses, and as foundation for deeper reasoning in applied mathematics. This book also provides a broader foundation in real analysis than is typical for future teachers of secondary mathematics. In connection with this, within the chapters, students are pointed to numerous articles from The College Mathematics Journal and The American Mathematical Monthly. These articles are inviting in their level of exposition and their wide-ranging content. Axioms are presented with an emphasis on the distinguishing characteristics that new ones bring, culminating with the axioms that define the reals. Set theory is another theme found in this book, beginning with what students are familiar with from basic calculus. This theme runs underneath the rigorous development of functions, sequences, and series, and then ends with a chapter on transfinite cardinal numbers and with chapters on basic point-set topology. Differentiation and integration are developed with the standard level of rigor, but always with the goal of forming a firm foundation for the student who desires to pursue deeper study. A historical theme interweaves throughout the book, with many quotes and accounts of interest to all readers. Over 600 exercises and dozens of figures help the learning process. Several topics (continued fractions, for example), are included in the appendices as enrichment material. An annotated bibliography is included.

An Invitation To Real Analysis

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Author : Michael W. Botsko
language : en
Publisher:
Release Date : 1998

An Invitation To Real Analysis written by Michael W. Botsko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Functions of real variables categories.

Invitation To Real Analysis

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Author : César Ernesto Silva
language : en
Publisher: American Mathematical Soc.
Release Date : 2019

Invitation To Real Analysis written by César Ernesto Silva and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Education categories.

Provides a careful introduction to the real numbers with an emphasis on developing proof-writing skills. The book continues with a logical development of the notions of sequences, open and closed sets (including compactness and the Cantor set), continuity, differentiation, integration, and series of numbers and functions.

Real Analysis For The Undergraduate

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Author : Matthew A. Pons
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-25

Real Analysis For The Undergraduate written by Matthew A. Pons and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-25 with Mathematics categories.

This undergraduate textbook introduces students to the basics of real analysis, provides an introduction to more advanced topics including measure theory and Lebesgue integration, and offers an invitation to functional analysis. While these advanced topics are not typically encountered until graduate study, the text is designed for the beginner. The author’s engaging style makes advanced topics approachable without sacrificing rigor. The text also consistently encourages the reader to pick up a pencil and take an active part in the learning process. Key features include: - examples to reinforce theory; - thorough explanations preceding definitions, theorems and formal proofs; - illustrations to support intuition; - over 450 exercises designed to develop connections between the concrete and abstract. This text takes students on a journey through the basics of real analysis and provides those who wish to delve deeper the opportunity to experience mathematical ideas that are beyond the standard undergraduate curriculum.

An Invitation To Operator Theory

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Author : Yuri A. Abramovich
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

An Invitation To Operator Theory written by Yuri A. Abramovich and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Operator theory categories.

This book offers a comprehensive and reader-friendly exposition of the theory of linear operators on Banach spaces and Banach lattices using their topological and order structures and properties. Abramovich and Aliprantis give a unique presentation that includes many new and very recent developments in operator theory and also draws together results which are spread over the vast literature. For instance, invariant subspaces of positive operators and the Daugavet equation arepresented in monograph form for the first time. The authors keep the discussion self-contained and use exercises to achieve this goal. The book contains over 600 exercises to help students master the material developed in the text. The exercises are of varying degrees of difficulty and play an importantand useful role in the exposition. They help to free the proofs of the main results of some technical details but provide students with accurate and complete accounts of how such details ought to be worked out. The exercises also contain a considerable amount of additional material that includes many well-known results whose proofs are not readily available elsewhere. The companion volume, Problems in Operator Theory, also by Abramovich and Aliprantis, is available from the AMS as Volume 51 inthe Graduate Studies in Mathematics series, and it contains complete solutions to all exercises in An Invitation to Operator Theory. The solutions demonstrate explicitly technical details in the proofs of many results in operator theory, providing the reader with rigorous and complete accounts ofsuch details. Finally, the book offers a considerable amount of additional material and further developments. By adding extra material to many exercises, the authors have managed to keep the presentation as self-contained as possible. The best way of learning mathematics is by doing mathematics, and the book Problems in Operator Theory will help achieve this goal. Prerequisites to each book are the standard introductory graduate courses in real analysis, general topology, measure theory, andfunctional analysis. An Invitation to Operator Theory is suitable for graduate or advanced courses in operator theory, real analysis, integration theory, measure theory, function theory, and functional analysis. Problems in Operator Theory is a very useful supplementary text in the above areas. Bothbooks will be of great interest to researchers and students in mathematics, as well as in physics, economics, finance, engineering, and other related areas, and will make an indispensable reference tool.

Invitation To Real Analysis

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Author : César Ernesto Silva
language : en
Publisher: American Mathematical Soc.
Release Date : 2019

Invitation To Real Analysis written by César Ernesto Silva and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Education categories.

Provides a careful introduction to the real numbers with an emphasis on developing proof-writing skills. The book continues with a logical development of the notions of sequences, open and closed sets (including compactness and the Cantor set), continuity, differentiation, integration, and series of numbers and functions.

Real Analysis

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Author : J. Yeh
language : en
Publisher: World Scientific
Release Date : 2006

Real Analysis written by J. Yeh and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

This book presents a unified treatise of the theory of measure and integration. In the setting of a general measure space, every concept is defined precisely and every theorem is presented with a clear and complete proof with all the relevant details. Counter-examples are provided to show that certain conditions in the hypothesis of a theorem cannot be simply dropped.The dependence of a theorem on earlier theorems is explicitly indicated in the proof, not only to facilitate reading but also to delineate the structure of the theory. The precision and clarity of presentation make the book an ideal textbook for a graduate course in real analysis while the wealth of topics treated also make the book a valuable reference work for mathematicians.

Introduction To Real Analysis

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Author : Robert G. Bartle
language : en
Publisher:
Release Date : 1982-03-24

Introduction To Real Analysis written by Robert G. Bartle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-03-24 with Mathematics categories.

An elementary introduction to analysis. Limits the discussion to one variable, and presents detailed explanations and examples, focusing considerable attention on error estimation and other concepts relevant to computer science.

Invitation To Classical Analysis

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Author : Peter Duren
language : en
Publisher: American Mathematical Soc.
Release Date : 2020

Invitation To Classical Analysis written by Peter Duren and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Education categories.

This book gives a rigorous treatment of selected topics in classical analysis, with many applications and examples. The exposition is at the undergraduate level, building on basic principles of advanced calculus without appeal to more sophisticated techniques of complex analysis and Lebesgue integration. Among the topics covered are Fourier series and integrals, approximation theory, Stirling's formula, the gamma function, Bernoulli numbers and polynomials, the Riemann zeta function, Tauberian theorems, elliptic integrals, ramifications of the Cantor set, and a theoretical discussion of differential equations including power series solutions at regular singular points, Bessel functions, hypergeometric functions, and Sturm comparison theory. Preliminary chapters offer rapid reviews of basic principles and further background material such as infinite products and commonly applied inequalities. This book is designed for individual study but can also serve as a text for second-semester courses in advanced calculus. Each chapter concludes with an abundance of exercises. Historical notes discuss the evolution of mathematical ideas and their relevance to physical applications. Special features are capsule scientific biographies of the major players and a gallery of portraits. Although this book is designed for undergraduate students, others may find it an accessible source of information on classical topics that underlie modern developments in pure and applied mathematics.

Concise Introduction To Basic Real Analysis

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Author : Hemen Dutta
language : en
Publisher: CRC Press
Release Date : 2019-08-12

Concise Introduction To Basic Real Analysis written by Hemen Dutta and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-12 with Mathematics categories.

This book provides an introduction to basic topics in Real Analysis and makes the subject easily understandable to all learners. The book is useful for those that are involved with Real Analysis in disciplines such as mathematics, engineering, technology, and other physical sciences. It provides a good balance while dealing with the basic and essential topics that enable the reader to learn the more advanced topics easily. It includes many examples and end of chapter exercises including hints for solutions in several critical cases. The book is ideal for students, instructors, as well as those doing research in areas requiring a basic knowledge of Real Analysis. Those more advanced in the field will also find the book useful to refresh their knowledge of the topic. Features Includes basic and essential topics of real analysis Adopts a reasonable approach to make the subject easier to learn Contains many solved examples and exercise at the end of each chapter Presents a quick review of the fundamentals of set theory Covers the real number system Discusses the basic concepts of metric spaces and complete metric spaces