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
Understanding Analysis And Its Connections To Secondary Mathematics Teaching
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Author : Nicholas H. Wasserman
language : en
Publisher: Springer Nature
Release Date : 2022-01-03
Understanding Analysis And Its Connections To Secondary Mathematics Teaching written by Nicholas H. Wasserman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-03 with Education categories.
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.
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.
Understanding Regression Analysis
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Author : Michael Patrick Allen
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-23
Understanding Regression Analysis written by Michael Patrick Allen 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 2007-11-23 with Social Science categories.
By assuming it is possible to understand regression analysis without fully comprehending all its underlying proofs and theories, this introduction to the widely used statistical technique is accessible to readers who may have only a rudimentary knowledge of mathematics. Chapters discuss: -descriptive statistics using vector notation and the components of a simple regression model; -the logic of sampling distributions and simple hypothesis testing; -the basic operations of matrix algebra and the properties of the multiple regression model; -testing compound hypotheses and the application of the regression model to the analyses of variance and covariance, and -structural equation models and influence statistics.
Pattern Analysis
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Author : H. Niemann
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Pattern Analysis written by H. Niemann 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 Computers categories.
This book is devoted to pattern analysis, that is, the automatic construc tion of a symbolic description for a complex pattern, like an image or con nected speech. Pattern analysis thus tries to simulate certain capabilities which go without saying in any human central nervous system. The increasing interest and growing efforts at solving the problems related with pattern analysis are motivated by the challenge of the problem and the expected ap plications. Potential applications are numerous and result from the fact that data can be gathered and stored by modern devices in ever increasing extent, thus making the finding of particular interesting facts or events in these hosts of data an ever increasing problem. It was tried to organize the book around one particular view of pattern analysis: the view that pattern analysis requires an appropriate set of modules operating on a common data base which contains interme processing diate results of processing. Although other views are certainly possible, this one was adopted because the author feels that it is a useful idea, be cause the size of this book had to be kept within reasonable bounds, and because it facilitated the composition of fairly self-contained chapters.
Understanding Signals
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Author : Michael Burianyk
language : en
Publisher: SEG Books
Release Date : 2019-05-15
Understanding Signals written by Michael Burianyk and has been published by SEG Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-15 with Science categories.
Written for students as well as professionals who work with and support geophysicists, this book presents a simple and informal discussion of fundamental concepts which underlie the quantitative part of geophysical analysis and interpretation. These general concepts are applicable for an analytical approach to any phenomena that can be measured and recorded. With examples and figures created using Microsoft Excel®, this book is accessible and insightful. Topics covered include: the concept of signals based on the sine function; the summation of sine waves as a more complicated signal; the notion of Fourier series and the spectral representation of signals; digital sampling and discrete representation of signals; the discrete Fourier transform and inverse transform; the concept of filtering in the spectral domain; and the idea of filtering outside of the spectral domain, by convolution, and the relationship between the measurement and spectral domains. This book will be valuable for geologists, junior seismic interpreters, software developers, high school and university students, and geophysical professionals seeking a refresher of the basic concepts.
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.