A Sequential Introduction To Real Analysis
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A Sequential Introduction To Real Analysis
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Author : J Martin Speight
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-10-29
A Sequential Introduction To Real Analysis written by J Martin Speight and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-29 with Mathematics categories.
Real analysis provides the fundamental underpinnings for calculus, arguably the most useful and influential mathematical idea ever invented. It is a core subject in any mathematics degree, and also one which many students find challenging. A Sequential Introduction to Real Analysis gives a fresh take on real analysis by formulating all the underlying concepts in terms of convergence of sequences. The result is a coherent, mathematically rigorous, but conceptually simple development of the standard theory of differential and integral calculus ideally suited to undergraduate students learning real analysis for the first time.This book can be used as the basis of an undergraduate real analysis course, or used as further reading material to give an alternative perspective within a conventional real analysis course.
Introduction To Real Analysis
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Author : Manfred Stoll
language : en
Publisher: CRC Press
Release Date : 2021-03-09
Introduction To Real Analysis written by Manfred Stoll and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-09 with Mathematics categories.
This classic textbook has been used successfully by instructors and students for nearly three decades. This timely new edition offers minimal yet notable changes while retaining all the elements, presentation, and accessible exposition of previous editions. A list of updates is found in the Preface to this edition. This text is based on the author’s experience in teaching graduate courses and the minimal requirements for successful graduate study. The text is understandable to the typical student enrolled in the course, taking into consideration the variations in abilities, background, and motivation. Chapters one through six have been written to be accessible to the average student, w hile at the same time challenging the more talented student through the exercises. Chapters seven through ten assume the students have achieved some level of expertise in the subject. In these chapters, the theorems, examples, and exercises require greater sophistication and mathematical maturity for full understanding. In addition to the standard topics the text includes topics that are not always included in comparable texts. Chapter 6 contains a section on the Riemann-Stieltjes integral and a proof of Lebesgue’s t heorem providing necessary and sufficient conditions for Riemann integrability. Chapter 7 also includes a section on square summable sequences and a brief introduction to normed linear spaces. C hapter 8 contains a proof of the Weierstrass approximation theorem using the method of aapproximate identities. The inclusion of Fourier series in the text allows the student to gain some exposure to this important subject. The final chapter includes a detailed treatment of Lebesgue measure and the Lebesgue integral, using inner and outer measure. The exercises at the end of each section reinforce the concepts. Notes provide historical comments or discuss additional topics.
An Introduction To Real Analysis
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Author : Ravi P. Agarwal
language : en
Publisher: CRC Press
Release Date : 2018-02-28
An Introduction To Real Analysis written by Ravi P. Agarwal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-28 with Mathematics categories.
This book provides a compact, but thorough, introduction to the subject of Real Analysis. It is intended for a senior undergraduate and for a beginning graduate one-semester course.
Introduction To Real Analysis
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Author : Michael J. Schramm
language : en
Publisher: Courier Corporation
Release Date : 2012-05-11
Introduction To Real Analysis written by Michael J. Schramm and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-11 with Mathematics categories.
This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition.
A Concrete Introduction To Real Analysis
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Author : Robert Carlson
language : en
Publisher: CRC Press
Release Date : 2017-11-28
A Concrete Introduction To Real Analysis written by Robert Carlson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-28 with Mathematics categories.
A Concrete Introduction to Analysis, Second Edition offers a major reorganization of the previous edition with the goal of making it a much more comprehensive and accessible for students. The standard, austere approach to teaching modern mathematics with its emphasis on formal proofs can be challenging and discouraging for many students. To remedy this situation, the new edition is more rewarding and inviting. Students benefit from the text by gaining a solid foundational knowledge of analysis, which they can use in their fields of study and chosen professions. The new edition capitalizes on the trend to combine topics from a traditional transition to proofs course with a first course on analysis. Like the first edition, the text is appropriate for a one- or two-semester introductory analysis or real analysis course. The choice of topics and level of coverage is suitable for mathematics majors, future teachers, and students studying engineering or other fields requiring a solid, working knowledge of undergraduate mathematics. Key highlights: Offers integration of transition topics to assist with the necessary background for analysis Can be used for either a one- or a two-semester course Explores how ideas of analysis appear in a broader context Provides as major reorganization of the first edition Includes solutions at the end of the book
Real Analysis An Introduction
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Author : Michael Cullinane
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-08-18
Real Analysis An Introduction written by Michael Cullinane and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-18 with Mathematics categories.
Designed for a broad spectrum of mathematics majors, not only those pursuing graduate school, this book also provides a thorough explanation of undergraduate Real Analysis. Through a developmentally appropriate narrative that integrates informal discussion, motivation, and basic proof writing approaches with mathematical rigor and clarity, the aim is to assist all students in learning more about the real number system and calculus theory.
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.
Introduction To Number Theory
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Author : Richard Michael Hill
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017-12-04
Introduction To Number Theory written by Richard Michael Hill and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-04 with Mathematics categories.
'Probably its most significant distinguishing feature is that this book is more algebraically oriented than most undergraduate number theory texts.'MAA ReviewsIntroduction to Number Theory is dedicated to concrete questions about integers, to place an emphasis on problem solving by students. When undertaking a first course in number theory, students enjoy actively engaging with the properties and relationships of numbers.The book begins with introductory material, including uniqueness of factorization of integers and polynomials. Subsequent topics explore quadratic reciprocity, Hensel's Lemma, p-adic powers series such as exp(px) and log(1+px), the Euclidean property of some quadratic rings, representation of integers as norms from quadratic rings, and Pell's equation via continued fractions.Throughout the five chapters and more than 100 exercises and solutions, readers gain the advantage of a number theory book that focuses on doing calculations. This textbook is a valuable resource for undergraduates or those with a background in university level mathematics.
Analysis In Euclidean Space
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Author : Joaquim Bruna
language : en
Publisher: World Scientific
Release Date : 2022-10-04
Analysis In Euclidean Space written by Joaquim Bruna and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-04 with Mathematics categories.
Based on notes written during the author's many years of teaching, Analysis in Euclidean Space mainly covers Differentiation and Integration theory in several real variables, but also an array of closely related areas including measure theory, differential geometry, classical theory of curves, geometric measure theory, integral geometry, and others.With several original results, new approaches and an emphasis on concepts and rigorous proofs, the book is suitable for undergraduate students, particularly in mathematics and physics, who are interested in acquiring a solid footing in analysis and expanding their background. There are many examples and exercises inserted in the text for the student to work through independently.Analysis in Euclidean Space comprises 21 chapters, each with an introduction summarizing its contents, and an additional chapter containing miscellaneous exercises. Lecturers may use the varied chapters of this book for different undergraduate courses in analysis. The only prerequisites are a basic course in linear algebra and a standard first-year calculus course in differentiation and integration. As the book progresses, the difficulty increases such that some of the later sections may be appropriate for graduate study.
A First Course In Algebraic Geometry And Algebraic Varieties
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Author : Flaminio Flamini
language : en
Publisher: World Scientific
Release Date : 2023-02-13
A First Course In Algebraic Geometry And Algebraic Varieties written by Flaminio Flamini and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-13 with Mathematics categories.
This book provides a gentle introduction to the foundations of Algebraic Geometry, starting from computational topics (ideals and homogeneous ideals, zero loci of ideals) up to increasingly intrinsic and abstract arguments, such as 'Algebraic Varieties', whose natural continuation is a more advanced course on the theory of schemes, vector bundles, and sheaf-cohomology.Valuable to students studying Algebraic Geometry and Geometry, this title contains around 60 exercises (with solutions) to help students thoroughly understand the theories introduced in the book. Proofs of the results are carried out in full detail. Many examples are discussed in order to reinforce the understanding of both the theoretical elements and their consequences, as well as the possible applications of the material.