Understanding Real Analysis

eBook Download

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

Product Details :

Genre : Mathematics
Author : Paul Zorn
Publisher : CRC Press
Release : 2017-11-22
File : 384 Pages
ISBN-13 : 9781315315065


Understanding Analysis

eBook Download

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.

Product Details :

Genre : Mathematics
Author : Stephen Abbott
Publisher : Springer Science & Business Media
Release : 2002-07-12
File : 284 Pages
ISBN-13 : 0387950605


Introduction To Real Analysis

eBook Download

BOOK EXCERPT:

An accessible introduction to real analysis and its connectionto elementary calculus Bridging the gap between the development and history of realanalysis, Introduction to Real Analysis: An EducationalApproach presents a comprehensive introduction to real analysiswhile also offering a survey of the field. With its balance ofhistorical background, key calculus methods, and hands-onapplications, this book provides readers with a solid foundationand fundamental understanding of real analysis. The book begins with an outline of basic calculus, including aclose examination of problems illustrating links and potentialdifficulties. Next, a fluid introduction to real analysis ispresented, guiding readers through the basic topology of realnumbers, limits, integration, and a series of functions in naturalprogression. The book moves on to analysis with more rigorousinvestigations, and the topology of the line is presented alongwith a discussion of limits and continuity that includes unusualexamples in order to direct readers' thinking beyond intuitivereasoning and on to more complex understanding. The dichotomy ofpointwise and uniform convergence is then addressed and is followedby differentiation and integration. Riemann-Stieltjes integrals andthe Lebesgue measure are also introduced to broaden the presentedperspective. The book concludes with a collection of advancedtopics that are connected to elementary calculus, such as modelingwith logistic functions, numerical quadrature, Fourier series, andspecial functions. Detailed appendices outline key definitions and theorems inelementary calculus and also present additional proofs, projects,and sets in real analysis. Each chapter references historicalsources on real analysis while also providing proof-orientedexercises and examples that facilitate the development ofcomputational skills. In addition, an extensive bibliographyprovides additional resources on the topic. Introduction to Real Analysis: An Educational Approach isan ideal book for upper- undergraduate and graduate-level realanalysis courses in the areas of mathematics and education. It isalso a valuable reference for educators in the field of appliedmathematics.

Product Details :

Genre : Mathematics
Author : William C. Bauldry
Publisher : John Wiley & Sons
Release : 2011-09-09
File : 280 Pages
ISBN-13 : 9781118164433


Analysis A Gateway To Understanding Mathematics

eBook Download

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.

Product Details :

Genre : Mathematics
Author : Sean Dineen
Publisher : World Scientific Publishing Company
Release : 2012-05-04
File : 320 Pages
ISBN-13 : 9789814401401


Understanding Analysis

eBook Download

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.

Product Details :

Genre : Mathematics
Author : Stephen Abbott
Publisher : Springer Science & Business Media
Release : 2012-12-06
File : 269 Pages
ISBN-13 : 9780387215068


An Essay Concerning Human Understanding To Which Are Added I An Analysis Of Mr Locke S Doctrine Of Ideas C

eBook Download

BOOK EXCERPT:

Product Details :

Genre :
Author : John Locke
Publisher :
Release : 1818
File : 668 Pages
ISBN-13 : OXFORD:601917317


Understanding Analysis And Its Connections To Secondary Mathematics Teaching

eBook Download

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.

Product Details :

Genre : Education
Author : Nicholas H. Wasserman
Publisher : Springer Nature
Release : 2022-01-03
File : 226 Pages
ISBN-13 : 9783030891985


Understanding Regression Analysis

eBook Download

BOOK EXCERPT:

Understanding Regression Analysis unifies diverse regression applications including the classical model, ANOVA models, generalized models including Poisson, Negative binomial, logistic, and survival, neural networks, and decision trees under a common umbrella -- namely, the conditional distribution model. It explains why the conditional distribution model is the correct model, and it also explains (proves) why the assumptions of the classical regression model are wrong. Unlike other regression books, this one from the outset takes a realistic approach that all models are just approximations. Hence, the emphasis is to model Nature’s processes realistically, rather than to assume (incorrectly) that Nature works in particular, constrained ways. Key features of the book include: Numerous worked examples using the R software Key points and self-study questions displayed "just-in-time" within chapters Simple mathematical explanations ("baby proofs") of key concepts Clear explanations and applications of statistical significance (p-values), incorporating the American Statistical Association guidelines Use of "data-generating process" terminology rather than "population" Random-X framework is assumed throughout (the fixed-X case is presented as a special case of the random-X case) Clear explanations of probabilistic modelling, including likelihood-based methods Use of simulations throughout to explain concepts and to perform data analyses This book has a strong orientation towards science in general, as well as chapter-review and self-study questions, so it can be used as a textbook for research-oriented students in the social, biological and medical, and physical and engineering sciences. As well, its mathematical emphasis makes it ideal for a text in mathematics and statistics courses. With its numerous worked examples, it is also ideally suited to be a reference book for all scientists.

Product Details :

Genre : Business & Economics
Author : Peter H. Westfall
Publisher : CRC Press
Release : 2020-06-25
File : 453 Pages
ISBN-13 : 9781000069631


Human Behavior Analysis Sensing And Understanding

eBook Download

BOOK EXCERPT:

Over the last decade, there has been a growing interest in human behavior analysis, motivated by societal needs such as security, natural interfaces, affective computing, and assisted living. However, the accurate and non-invasive detection and recognition of human behavior remain major challenges and the focus of many research efforts. Traditionally, in order to identify human behavior, it is first necessary to continuously collect the readings of physical sensing devices (e.g., camera, GPS, and RFID), which can be worn on human bodies, attached to objects, or deployed in the environment. Afterwards, using recognition algorithms or classification models, the behavior types can be identified so as to facilitate advanced applications. Although such traditional approaches deliver satisfactory performance and are still widely used, most of them are intrusive and require specific sensing devices, raising issues such as privacy and deployment costs. In this book, we will present our latest findings on non-invasive sensing and understanding of human behavior. Specifically, this book differs from existing literature in the following senses. Firstly, we focus on approaches that are based on non-invasive sensing technologies, including both sensor-based and device-free variants. Secondly, while most existing studies examine individual behaviors, we will systematically elaborate on how to understand human behaviors of various granularities, including not only individual-level but also group-level and community-level behaviors. Lastly, we will discuss the most important scientific problems and open issues involved in human behavior analysis.

Product Details :

Genre : Computers
Author : Zhiwen Yu
Publisher : Springer Nature
Release : 2020-02-29
File : 277 Pages
ISBN-13 : 9789811521096


An Essay Concerning Human Understanding To Which Are Now Added I Analysis Of Mr Locke S Doctrine Of Ideas C

eBook Download

BOOK EXCERPT:

Product Details :

Genre :
Author : John Locke
Publisher :
Release : 1824
File : 552 Pages
ISBN-13 : OXFORD:590611102