Understanding Analysis
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Understanding Analysis
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Author : Stephen Abbott
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Understanding Analysis written by Stephen Abbott 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 2012-12-06 with Mathematics categories.
Understanding Analysis outlines an elementary, one-semester course designed to expose students to the rich rewards inherent in taking a mathematically rigorous approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on the questions that give analysis its inherent fascination. Does the Cantor set contain any irrational numbers? Can the set of points where a function is discontinuous be arbitrary? Are derivatives continuous? Are derivatives integrable? Is an infinitely differentiable function necessarily the limit of its Taylor series? In giving these topics center stage, the hard work of a rigorous study is justified by the fact that they are inaccessible without it.
Understanding Analysis
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Author : Stephen Abbott
language : en
Publisher: Springer
Release Date : 2015-05-19
Understanding Analysis written by Stephen Abbott and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-19 with Mathematics categories.
This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one. Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler’s computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the book’s cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis.
Understanding Real Analysis
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Author : Paul Zorn
language : en
Publisher: CRC Press
Release Date : 2017-11-22
Understanding Real Analysis written by Paul Zorn and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
Understanding Real Analysis, Second Edition offers substantial coverage of foundational material and expands on the ideas of elementary calculus to develop a better understanding of crucial mathematical ideas. The text meets students at their current level and helps them develop a foundation in real analysis. The author brings definitions, proofs, examples and other mathematical tools together to show how they work to create unified theory. These helps students grasp the linguistic conventions of mathematics early in the text. The text allows the instructor to pace the course for students of different mathematical backgrounds. Key Features: Meets and aligns with various student backgrounds Pays explicit attention to basic formalities and technical language Contains varied problems and exercises Drives the narrative through questions
Higher English Reading For Understanding Analysis And Evaluation
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Author : Ann Bridges
language : en
Publisher: Hachette UK
Release Date : 2015-04-24
Higher English Reading For Understanding Analysis And Evaluation written by Ann Bridges and has been published by Hachette UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-24 with Study Aids categories.
Exam Board: SQA Level: Higher Subject: English First Teaching: September 2014 First Exam: June 2015 A brand new edition of the former Higher English Close Reading, completely rewritten for the new Higher element - worth 30% of marks in the final exam. Written by two highly experienced authors, this book shows you how to practise for the Reading for Understanding, Analysis and Evaluation section of the CfE Higher English exam. It introduces the terms and concepts that lie behind success and offers guidance on the interpretation of questions and targeting answers. - Acquire and improve the skills needed for success in this area of CfE Higher - Includes questions and passages to reflect the style of assessments in this section of the paper - Revise for the exam using the practice papers and accompanying book of suggested answers
Higher English Reading For Understanding Analysis And Evaluation Answers And Marking Schemes
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Author : Ann Bridges
language : en
Publisher: Hachette UK
Release Date : 2015-05-15
Higher English Reading For Understanding Analysis And Evaluation Answers And Marking Schemes written by Ann Bridges and has been published by Hachette UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-15 with Study Aids categories.
Exam Board: SQA Level: Higher Subject: English First Teaching: September 2014 First Exam: June 2015 This book (which is photocopiable within the purchasing institution) provides detailed suggested marking instructions to use alongside the student book of the same name, which offers practice in the Higher element of Reading for Understanding, Analysis and Evaluation - worth 30% of marks in the final exam. Written by two highly experienced authors, the student book introduces the terms and concepts that lie behind success and offers guidance on the interpretation of questions and targeting answers. - Acquire and improve the skills needed for success in this area of CfE Higher - Detailed marking instructions to reflect the style of assessments in this section of the paper - Revise for the exam using the practice papers in the accompanying student book
Analysis A Gateway To Understanding Mathematics
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Author : Sean Dineen
language : en
Publisher: World Scientific Publishing Company
Release Date : 2012-05-04
Analysis A Gateway To Understanding Mathematics written by Sean Dineen 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 2012-05-04 with Mathematics categories.
This book shows that it is possible to provide a fully rigorous treatment of calculus for those planning a career in an area that uses mathematics regularly (e.g., statistics, mathematics, economics, finance, engineering, etc.). It reveals to students on the ways to approach and understand mathematics. It covers efficiently and rigorously the differential and integral calculus, and its foundations in mathematical analysis. It also aims at a comprehensive, efficient, and rigorous treatment by introducing all the concepts succinctly. Experience has shown that this approach, which treats understanding on par with technical ability, has long term benefits for students.
A Book Of Abstract Algebra
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Author : Charles C Pinter
language : en
Publisher: Courier Corporation
Release Date : 2010-01-14
A Book Of Abstract Algebra written by Charles C Pinter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-14 with Mathematics categories.
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Real Analysis
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Author : Jay Cummings
language : en
Publisher:
Release Date : 2019-07-15
Real Analysis written by Jay Cummings and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-15 with categories.
This textbook is designed for students. Rather than the typical definition-theorem-proof-repeat style, this text includes much more commentary, motivation and explanation. The proofs are not terse, and aim for understanding over economy. Furthermore, dozens of proofs are preceded by "scratch work" or a proof sketch to give students a big-picture view and an explanation of how they would come up with it on their own. Examples often drive the narrative and challenge the intuition of the reader. The text also aims to make the ideas visible, and contains over 200 illustrations. The writing is relaxed and includes interesting historical notes, periodic attempts at humor, and occasional diversions into other interesting areas of mathematics. The text covers the real numbers, cardinality, sequences, series, the topology of the reals, continuity, differentiation, integration, and sequences and series of functions. Each chapter ends with exercises, and nearly all include some open questions. The first appendix contains a construction the reals, and the second is a collection of additional peculiar and pathological examples from analysis. The author believes most textbooks are extremely overpriced and endeavors to help change this.Hints and solutions to select exercises can be found at LongFormMath.com.
Understanding Regression Analysis
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Author : Larry D. Schroeder
language : en
Publisher: SAGE Publications
Release Date : 2016-11-08
Understanding Regression Analysis written by Larry D. Schroeder and has been published by SAGE Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-08 with Social Science categories.
Understanding Regression Analysis: An Introductory Guide by Larry D. Schroeder, David L. Sjoquist, and Paula E. Stephan presents the fundamentals of regression analysis, from its meaning to uses, in a concise, easy-to-read, and non-technical style. It illustrates how regression coefficients are estimated, interpreted, and used in a variety of settings within the social sciences, business, law, and public policy. Packed with applied examples and using few equations, the book walks readers through elementary material using a verbal, intuitive interpretation of regression coefficients, associated statistics, and hypothesis tests. The Second Edition features updated examples and new references to modern software output.
Analysis I
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Author : Terence Tao
language : en
Publisher: Springer
Release Date : 2016-08-29
Analysis I written by Terence Tao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-29 with Mathematics categories.
This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.