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Understanding Analysis

Author: Stephen Abbott

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 269

ISBN-13: 0387215069

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This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.

Book Synopsis Understanding Analysis by : Stephen Abbott

Download or read book Understanding Analysis written by Stephen Abbott and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.

Understanding Real Analysis

Author: Paul Zorn

Publisher: CRC Press

Published: 2017-11-22

Total Pages: 336

ISBN-13: 1315315076

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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

Book Synopsis Understanding Real Analysis by : Paul Zorn

Download or read book Understanding Real Analysis written by Paul Zorn and published by CRC Press. This book was released on 2017-11-22 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Understanding Analysis and its Connections to Secondary Mathematics Teaching

Author: Nicholas H. Wasserman

Publisher: Springer Nature

Published: 2022-01-03

Total Pages: 226

ISBN-13: 3030891984

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Getting certified to teach high school mathematics typically requires completing a course in real analysis. Yet most teachers point out real analysis content bears little resemblance to secondary mathematics and report it does not influence their teaching in any significant way. This textbook is our attempt to change the narrative. It is our belief that analysis can be a meaningful part of a teacher's mathematical education and preparation for teaching. This book is a companion text. It is intended to be a supplemental resource, used in conjunction with a more traditional real analysis book. The textbook is based on our efforts to identify ways that studying real analysis can provide future teachers with genuine opportunities to think about teaching secondary mathematics. It focuses on how mathematical ideas are connected to the practice of teaching secondary mathematics–and not just the content of secondary mathematics itself. Discussions around pedagogy are premised on the belief that the way mathematicians do mathematics can be useful for how we think about teaching mathematics. The book uses particular situations in teaching to make explicit ways that the content of real analysis might be important for teaching secondary mathematics, and how mathematical practices prevalent in the study of real analysis can be incorporated as practices for teaching. This textbook will be of particular interest to mathematics instructors–and mathematics teacher educators–thinking about how the mathematics of real analysis might be applicable to secondary teaching, as well as to any prospective (or current) teacher who has wondered about what the purpose of taking such courses could be.

Book Synopsis Understanding Analysis and its Connections to Secondary Mathematics Teaching by : Nicholas H. Wasserman

Download or read book Understanding Analysis and its Connections to Secondary Mathematics Teaching written by Nicholas H. Wasserman and published by Springer Nature. This book was released on 2022-01-03 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Getting certified to teach high school mathematics typically requires completing a course in real analysis. Yet most teachers point out real analysis content bears little resemblance to secondary mathematics and report it does not influence their teaching in any significant way. This textbook is our attempt to change the narrative. It is our belief that analysis can be a meaningful part of a teacher's mathematical education and preparation for teaching. This book is a companion text. It is intended to be a supplemental resource, used in conjunction with a more traditional real analysis book. The textbook is based on our efforts to identify ways that studying real analysis can provide future teachers with genuine opportunities to think about teaching secondary mathematics. It focuses on how mathematical ideas are connected to the practice of teaching secondary mathematics–and not just the content of secondary mathematics itself. Discussions around pedagogy are premised on the belief that the way mathematicians do mathematics can be useful for how we think about teaching mathematics. The book uses particular situations in teaching to make explicit ways that the content of real analysis might be important for teaching secondary mathematics, and how mathematical practices prevalent in the study of real analysis can be incorporated as practices for teaching. This textbook will be of particular interest to mathematics instructors–and mathematics teacher educators–thinking about how the mathematics of real analysis might be applicable to secondary teaching, as well as to any prospective (or current) teacher who has wondered about what the purpose of taking such courses could be.

A Radical Approach to Real Analysis

Author: David Bressoud

Publisher: American Mathematical Society

Published: 2022-02-22

Total Pages: 339

ISBN-13: 1470469049

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In this second edition of the MAA classic, exploration continues to be an essential component. More than 60 new exercises have been added, and the chapters on Infinite Summations, Differentiability and Continuity, and Convergence of Infinite Series have been reorganized to make it easier to identify the key ideas. A Radical Approach to Real Analysis is an introduction to real analysis, rooted in and informed by the historical issues that shaped its development. It can be used as a textbook, as a resource for the instructor who prefers to teach a traditional course, or as a resource for the student who has been through a traditional course yet still does not understand what real analysis is about and why it was created. The book begins with Fourier's introduction of trigonometric series and the problems they created for the mathematicians of the early 19th century. It follows Cauchy's attempts to establish a firm foundation for calculus and considers his failures as well as his successes. It culminates with Dirichlet's proof of the validity of the Fourier series expansion and explores some of the counterintuitive results Riemann and Weierstrass were led to as a result of Dirichlet's proof.

Book Synopsis A Radical Approach to Real Analysis by : David Bressoud

Download or read book A Radical Approach to Real Analysis written by David Bressoud and published by American Mathematical Society. This book was released on 2022-02-22 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this second edition of the MAA classic, exploration continues to be an essential component. More than 60 new exercises have been added, and the chapters on Infinite Summations, Differentiability and Continuity, and Convergence of Infinite Series have been reorganized to make it easier to identify the key ideas. A Radical Approach to Real Analysis is an introduction to real analysis, rooted in and informed by the historical issues that shaped its development. It can be used as a textbook, as a resource for the instructor who prefers to teach a traditional course, or as a resource for the student who has been through a traditional course yet still does not understand what real analysis is about and why it was created. The book begins with Fourier's introduction of trigonometric series and the problems they created for the mathematicians of the early 19th century. It follows Cauchy's attempts to establish a firm foundation for calculus and considers his failures as well as his successes. It culminates with Dirichlet's proof of the validity of the Fourier series expansion and explores some of the counterintuitive results Riemann and Weierstrass were led to as a result of Dirichlet's proof.

Elementary Analysis

Author: Kenneth A. Ross

Publisher: CUP Archive

Published: 2014-01-15

Total Pages: 192

ISBN-13:

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Book Synopsis Elementary Analysis by : Kenneth A. Ross

Download or read book Elementary Analysis written by Kenneth A. Ross and published by CUP Archive. This book was released on 2014-01-15 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analysis: A Gateway To Understanding Mathematics

Author: Dineen Sean

Publisher: World Scientific Publishing Company

Published: 2012-05-04

Total Pages: 320

ISBN-13: 9814401404

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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.

Book Synopsis Analysis: A Gateway To Understanding Mathematics by : Dineen Sean

Download or read book Analysis: A Gateway To Understanding Mathematics written by Dineen Sean and published by World Scientific Publishing Company. This book was released on 2012-05-04 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Real Mathematical Analysis

Author: Charles Chapman Pugh

Publisher: Springer Science & Business Media

Published: 2013-03-19

Total Pages: 445

ISBN-13: 0387216847

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Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.

Book Synopsis Real Mathematical Analysis by : Charles Chapman Pugh

Download or read book Real Mathematical Analysis written by Charles Chapman Pugh and published by Springer Science & Business Media. This book was released on 2013-03-19 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.

Understanding Statistical Analysis and Modeling

Author: Robert Bruhl

Publisher: SAGE Publications

Published: 2017-11-15

Total Pages: 320

ISBN-13: 1506317375

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Understanding Statistical Analysis and Modeling is a text for graduate and advanced undergraduate students in the social, behavioral, or managerial sciences seeking to understand the logic of statistical analysis. Robert Bruhl covers all the basic methods of descriptive and inferential statistics in an accessible manner by way of asking and answering research questions. Concepts are discussed in the context of a specific research project and the book includes probability theory as the basis for understanding statistical inference. Instructions on using SPSS® are included so that readers focus on interpreting statistical analysis rather than calculations. Tables are used, rather than formulas, to describe the various calculations involved with statistical analysis and the exercises in the book are intended to encourage students to formulate and execute their own empirical investigations.

Book Synopsis Understanding Statistical Analysis and Modeling by : Robert Bruhl

Download or read book Understanding Statistical Analysis and Modeling written by Robert Bruhl and published by SAGE Publications. This book was released on 2017-11-15 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding Statistical Analysis and Modeling is a text for graduate and advanced undergraduate students in the social, behavioral, or managerial sciences seeking to understand the logic of statistical analysis. Robert Bruhl covers all the basic methods of descriptive and inferential statistics in an accessible manner by way of asking and answering research questions. Concepts are discussed in the context of a specific research project and the book includes probability theory as the basis for understanding statistical inference. Instructions on using SPSS® are included so that readers focus on interpreting statistical analysis rather than calculations. Tables are used, rather than formulas, to describe the various calculations involved with statistical analysis and the exercises in the book are intended to encourage students to formulate and execute their own empirical investigations.

Elementary Classical Analysis

Author: Jerrold E. Marsden

Publisher: Macmillan

Published: 1993-03-15

Total Pages: 760

ISBN-13: 9780716721055

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Designed for courses in advanced calculus and introductory real analysis, Elementary Classical Analysis strikes a careful balance between pure and applied mathematics with an emphasis on specific techniques important to classical analysis without vector calculus or complex analysis. Intended for students of engineering and physical science as well as of pure mathematics.

Book Synopsis Elementary Classical Analysis by : Jerrold E. Marsden

Download or read book Elementary Classical Analysis written by Jerrold E. Marsden and published by Macmillan. This book was released on 1993-03-15 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for courses in advanced calculus and introductory real analysis, Elementary Classical Analysis strikes a careful balance between pure and applied mathematics with an emphasis on specific techniques important to classical analysis without vector calculus or complex analysis. Intended for students of engineering and physical science as well as of pure mathematics.