Exploratory Examples For Real Analysis
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Exploratory Examples For Real Analysis
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Author : Joanne E. Snow
language : en
Publisher: American Mathematical Soc.
Release Date : 2003-12-31
Exploratory Examples For Real Analysis written by Joanne E. Snow and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-31 with Mathematics categories.
This text supplement contains 12 exploratory exercises designed to facilitate students' understanding of the most elemental concepts encountered in a first real analysis course: notions of boundedness, supremum/infimum, sequences, continuity and limits, limit suprema/infima, and pointwise and uniform convergence. In designing the exercises, the [Author];s ask students to formulate definitions, make connections between different concepts, derive conjectures, or complete a sequence of guided tasks designed to facilitate concept acquisition. Each exercise has three basic components: making observations and generating ideas from hands-on work with examples, thinking critically about the examples, and answering additional questions for reflection. The exercises can be used in a variety of ways: to motivate a lecture, to serve as a basis for in-class activities, or to be used for lab sessions, where students work in small groups and submit reports of their investigations. While the exercises have been useful for real analysis students of all ability levels, the [Author];s believe this resource might prove most beneficial in the following scenarios: A two-semester sequence in which the following topics are covered: properties of the real numbers, sequences, continuity, sequences and series of functions, differentiation, and integration. A class of students for whom analysis is their first upper division course. A group of students with a wide range of abilities for whom a cooperative approach focusing upon fundamental concepts could help to close the gap in skill development and concept acquisition. An independent study or private tutorial in which the student receives a minimal level of instruction. A resource for an instructor developing a cooperative, interactive course that does not involve the use of a standard text. Ancillary materials, including Visual Guide Sheets for those exercises that involve the use of technology and Report Guides for a lab session approach are provided online at: http:www.saintmarys.edu/~jsnow. In designing the exercise, the [Author];s were inspired by Ellen Parker's book, Laboratory Experiences in Group Theory, also published by the MAA.
Exploratory Examples For Real Analysis
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Author : Joanne E. Snow
language : en
Publisher: Cambridge University Press
Release Date : 2003
Exploratory Examples For Real Analysis written by Joanne E. Snow and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Every mathematician must make the transition from the calculations of high school to the structural and theoretical approaches of graduate school. Essentials of Mathematics provides the knowledge needed to move onto advanced mathematical work, and a glimpse of what being a mathematician might be like. No other book takes this particular holistic approach to the task. The content is of two types. There is material for a ""transitions"" course at the sophomore level; introductions to logic and set theory, discussions of proof writing and proof discovery, and introductions to the number systems (natural, rational, real, and complex). The material is presented in a fashion suitable for a Moore Method course, although such an approach is not necessary. An accompanying Instructor's Manual provides support for all flavors of teaching styles. In addition to presenting the important results for student proof, each area provides warm-up and follow-up exercises to help students internalize the material. The second type of content is an introduction to the professional culture of mathematics. There are many things that mathematicians know but weren't exactly taught. To give college students a sense of the mathematical universe, the book includes narratives on this kind of information. There are sections on pure and applied mathematics, the philosophy of mathematics, ethics in mathematical work, professional (including student) organizations, famous theorems, famous unsolved problems, famous mathematicians, discussions of the nature of mathematics research, and more. The prerequisites for a course based on this book include the content of high school mathematics and a certain level of mathematical maturity. The student must be willing to think on an abstract level. Two semesters of calculus indicates a readiness for this material.
Real Analysis Through Modern Infinitesimals
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Author : Nader Vakil
language : en
Publisher: Cambridge University Press
Release Date : 2011-02-17
Real Analysis Through Modern Infinitesimals written by Nader Vakil and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-17 with Mathematics categories.
A coherent, self-contained treatment of the central topics of real analysis employing modern infinitesimals.
Introduction To Real Analysis
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Author : William C. Bauldry
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-09
Introduction To Real Analysis written by William C. Bauldry and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-09 with Mathematics categories.
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.
A Radical Approach To Real Analysis
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Author : David M. Bressoud
language : en
Publisher: MAA
Release Date : 2007-04-12
A Radical Approach To Real Analysis written by David M. Bressoud and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-12 with Mathematics categories.
Second edition of this introduction to real analysis, rooted in the historical issues that shaped its development.
Resources For The Study Of Real Analysis
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Author : Robert L. Brabenec
language : en
Publisher: Cambridge University Press
Release Date : 2004
Resources For The Study Of Real Analysis written by Robert L. Brabenec and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
A collection of materials gathered by the author while teaching real analysis over a period of years.
Elements Of Real Analysis
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Author : Charles G. Denlinger
language : en
Publisher: Jones & Bartlett Publishers
Release Date : 2010-05-08
Elements Of Real Analysis written by Charles G. Denlinger and has been published by Jones & Bartlett Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-08 with Mathematics categories.
Elementary Real Analysis is a core course in nearly all mathematics departments throughout the world. It enables students to develop a deep understanding of the key concepts of calculus from a mature perspective. Elements of Real Analysis is a student-friendly guide to learning all the important ideas of elementary real analysis, based on the author's many years of experience teaching the subject to typical undergraduate mathematics majors. It avoids the compact style of professional mathematics writing, in favor of a style that feels more comfortable to students encountering the subject for the first time. It presents topics in ways that are most easily understood, yet does not sacrifice rigor or coverage. In using this book, students discover that real analysis is completely deducible from the axioms of the real number system. They learn the powerful techniques of limits of sequences as the primary entry to the concepts of analysis, and see the ubiquitous role sequences play in virtually all later topics. They become comfortable with topological ideas, and see how these concepts help unify the subject. Students encounter many interesting examples, including "pathological" ones, that motivate the subject and help fix the concepts. They develop a unified understanding of limits, continuity, differentiability, Riemann integrability, and infinite series of numbers and functions.
Elements Of Real Analysis
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Author : Charles Denlinger
language : en
Publisher: Jones & Bartlett Learning
Release Date : 2011
Elements Of Real Analysis written by Charles Denlinger and has been published by Jones & Bartlett Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
A student-friendly guide to learning all the important ideas of elementary real analysis, this resource is based on the author's many years of experience teaching the subject to typical undergraduate mathematics majors.
Game Theory Through Examples
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Author : Erich Prisner
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-31
Game Theory Through Examples written by Erich Prisner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-31 with Mathematics categories.
Game Theory through Examples is a thorough introduction to elementary game theory, covering finite games with complete information. The core philosophy underlying this volume is that abstract concepts are best learned when encountered first (and repeatedly) in concrete settings. Thus, the essential ideas of game theory are here presented in the context of actual games, real games much more complex and rich than the typical toy examples. All the fundamental ideas are here: Nash equilibria, backward induction, elementary probability, imperfect information, extensive and normal form, mixed and behavioral strategies. The active-learning, example-driven approach makes the text suitable for a course taught through problem solving. Students will be thoroughly engaged by the extensive classroom exercises, compelling homework problems, and nearly sixty projects in the text. Also available are approximately eighty Java applets and three dozen Excel spreadsheets in which students can play games and organize information in order to acquire a gut feeling to help in the analysis of the games. Mathematical exploration is a deep form of play; that maxim is embodied in this book. Game Theory through Examples is a lively introduction to this appealing theory. Assuming only high school prerequisites makes the volume especially suitable for a liberal arts or general education spirit-of-mathematics course. It could also serve as the active-learning supplement to a more abstract text in an upper-division game theory course.
Explorations In Complex Analysis
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Author : Michael A. Brilleslyper
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-12-31
Explorations In Complex Analysis written by Michael A. Brilleslyper and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-31 with Mathematics categories.
Research topics in the book include complex dynamics, minimal surfaces, fluid flows, harmonic, conformal, and polygonal mappings, and discrete complex analysis via circle packing. The nature of this book is different from many mathematics texts: the focus is on student-driven and technology-enhanced investigation. Interlaced in the reading for each chapter are examples, exercises, explorations, and projects, nearly all linked explicitly with computer applets for visualization and hands-on manipulation.