Exploratory Examples For Real Analysis

Download Exploratory Examples For Real Analysis full books in PDF, epub, and Kindle. Read online Exploratory Examples For Real Analysis ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Exploratory Examples for Real Analysis

Author : Joanne E. Snow
Publisher : American Mathematical Soc.
ISBN 13 : 0883857340
Total Pages : 163 pages
Book Rating : 4.8/5 (838 download)

DOWNLOAD NOW!

Book Synopsis Exploratory Examples for Real Analysis by : Joanne E. Snow

Download or read book Exploratory Examples for Real Analysis written by Joanne E. Snow and published by American Mathematical Soc.. This book was released on 2003-12-31 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Joanne E. Snow
Publisher : Cambridge University Press
ISBN 13 : 9780883857342
Total Pages : 164 pages
Book Rating : 4.8/5 (573 download)

DOWNLOAD NOW!

Book Synopsis Exploratory Examples for Real Analysis by : Joanne E. Snow

Download or read book Exploratory Examples for Real Analysis written by Joanne E. Snow and published by Cambridge University Press. This book was released on 2003 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Nader Vakil
Publisher : Cambridge University Press
ISBN 13 : 1107002028
Total Pages : 587 pages
Book Rating : 4.1/5 (7 download)

DOWNLOAD NOW!

Book Synopsis Real Analysis Through Modern Infinitesimals by : Nader Vakil

Download or read book Real Analysis Through Modern Infinitesimals written by Nader Vakil and published by Cambridge University Press. This book was released on 2011-02-17 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: A coherent, self-contained treatment of the central topics of real analysis employing modern infinitesimals.

Exploratory Multivariate Analysis by Example Using R

Author : Francois Husson
Publisher : CRC Press
ISBN 13 : 1315301865
Total Pages : 263 pages
Book Rating : 4.3/5 (153 download)

DOWNLOAD NOW!

Book Synopsis Exploratory Multivariate Analysis by Example Using R by : Francois Husson

Download or read book Exploratory Multivariate Analysis by Example Using R written by Francois Husson and published by CRC Press. This book was released on 2017-04-25 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Full of real-world case studies and practical advice, Exploratory Multivariate Analysis by Example Using R, Second Edition focuses on four fundamental methods of multivariate exploratory data analysis that are most suitable for applications. It covers principal component analysis (PCA) when variables are quantitative, correspondence analysis (CA) a

Elements of Real Analysis

Author : Charles Denlinger
Publisher : Jones & Bartlett Learning
ISBN 13 : 0763779474
Total Pages : 769 pages
Book Rating : 4.7/5 (637 download)

DOWNLOAD NOW!

Book Synopsis Elements of Real Analysis by : Charles Denlinger

Download or read book Elements of Real Analysis written by Charles Denlinger and published by Jones & Bartlett Learning. This book was released on 2011 with total page 769 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elements of Real Analysis

Author : Charles G. Denlinger
Publisher : Jones & Bartlett Publishers
ISBN 13 : 1449659934
Total Pages : 769 pages
Book Rating : 4.4/5 (496 download)

DOWNLOAD NOW!

Book Synopsis Elements of Real Analysis by : Charles G. Denlinger

Download or read book Elements of Real Analysis written by Charles G. Denlinger and published by Jones & Bartlett Publishers. This book was released on 2010-05-08 with total page 769 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Real Analysis

Author : William C. Bauldry
Publisher : John Wiley & Sons
ISBN 13 : 1118164431
Total Pages : 280 pages
Book Rating : 4.1/5 (181 download)

DOWNLOAD NOW!

Book Synopsis Introduction to Real Analysis by : William C. Bauldry

Download or read book Introduction to Real Analysis written by William C. Bauldry and published by John Wiley & Sons. This book was released on 2011-09-09 with total page 280 pages. Available in PDF, EPUB and Kindle. 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.

A Radical Approach to Real Analysis

Author : David M. Bressoud
Publisher : MAA
ISBN 13 : 9780883857472
Total Pages : 352 pages
Book Rating : 4.8/5 (574 download)

DOWNLOAD NOW!

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

Download or read book A Radical Approach to Real Analysis written by David M. Bressoud and published by MAA. This book was released on 2007-04-12 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second edition of this introduction to real analysis, rooted in the historical issues that shaped its development.

The How and Why of One Variable Calculus

Author : Amol Sasane
Publisher : John Wiley & Sons
ISBN 13 : 1119043395
Total Pages : 520 pages
Book Rating : 4.1/5 (19 download)

DOWNLOAD NOW!

Book Synopsis The How and Why of One Variable Calculus by : Amol Sasane

Download or read book The How and Why of One Variable Calculus written by Amol Sasane and published by John Wiley & Sons. This book was released on 2015-06-11 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: First course calculus texts have traditionally been either“engineering/science-oriented” with too little rigor,or have thrown students in the deep end with a rigorous analysistext. The How and Why of One Variable Calculus closes thisgap in providing a rigorous treatment that takes an original andvaluable approach between calculus and analysis. Logicallyorganized and also very clear and user-friendly, it covers 6 maintopics; real numbers, sequences, continuity, differentiation,integration, and series. It is primarily concerned with developingan understanding of the tools of calculus. The author presentsnumerous examples and exercises that illustrate how the techniquesof calculus have universal application. The How and Why of One Variable Calculus presents anexcellent text for a first course in calculus for students in themathematical sciences, statistics and analytics, as well as a textfor a bridge course between single and multi-variable calculus aswell as between single variable calculus and upper level theorycourses for math majors.

Resources for the Study of Real Analysis

Author : Robert L. Brabenec
Publisher : Cambridge University Press
ISBN 13 : 9780883857373
Total Pages : 256 pages
Book Rating : 4.8/5 (573 download)

DOWNLOAD NOW!

Book Synopsis Resources for the Study of Real Analysis by : Robert L. Brabenec

Download or read book Resources for the Study of Real Analysis written by Robert L. Brabenec and published by Cambridge University Press. This book was released on 2004 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of materials gathered by the author while teaching real analysis over a period of years.

Mathematical Connections

Author : Albert Cuoco
Publisher : Cambridge University Press
ISBN 13 : 9780883857397
Total Pages : 274 pages
Book Rating : 4.8/5 (573 download)

DOWNLOAD NOW!

Book Synopsis Mathematical Connections by : Albert Cuoco

Download or read book Mathematical Connections written by Albert Cuoco and published by Cambridge University Press. This book was released on 2005-08-11 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about some of the topics that form the foundations for high school mathematics. It focuses on a closely-knit collection of ideas that are at the intersection of algebra, arithmetic, combinatorics, geometry, and calculus. Most of the ideas are classical: methods for fitting polynomial functions to data, for summing powers of integers, for visualizing the iterates of a function defined on the complex plane, or for obtaining identities among entries in Pascal's triangle. Some of these ideas, previously considered quite advanced, have become tractable because of advances in computational technology. Others are just beautiful classical mathematics, topics that have fallen out of fashion and that deserve to be resurrected. Most importantly, the book is about some mathematical ways of thinking the author found extremely useful, both in his roles as a mathematician and as a mentor of young people learning to do mathematics.

Real Infinite Series

Author : Daniel D. Bonar
Publisher : American Mathematical Soc.
ISBN 13 : 1470447827
Total Pages : 261 pages
Book Rating : 4.4/5 (74 download)

DOWNLOAD NOW!

Book Synopsis Real Infinite Series by : Daniel D. Bonar

Download or read book Real Infinite Series written by Daniel D. Bonar and published by American Mathematical Soc.. This book was released on 2018-12-12 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a widely accessible introductory treatment of infinite series of real numbers, bringing the reader from basic definitions and tests to advanced results. An up-to-date presentation is given, making infinite series accessible, interesting, and useful to a wide audience, including students, teachers, and researchers. Included are elementary and advanced tests for convergence or divergence, the harmonic series, the alternating harmonic series, and closely related results. One chapter offers 107 concise, crisp, surprising results about infinite series. Another gives problems on infinite series, and solutions, which have appeared on the annual William Lowell Putnam Mathematical Competition. The lighter side of infinite series is treated in the concluding chapter where three puzzles, eighteen visuals, and several fallacious proofs are made available. Three appendices provide a listing of true or false statements, answers to why the harmonic series is so named, and an extensive list of published works on infinite series.

Which Numbers Are Real?

Author : Michael Henle
Publisher : American Mathematical Soc.
ISBN 13 : 1614441073
Total Pages : 219 pages
Book Rating : 4.6/5 (144 download)

DOWNLOAD NOW!

Book Synopsis Which Numbers Are Real? by : Michael Henle

Download or read book Which Numbers Are Real? written by Michael Henle and published by American Mathematical Soc.. This book was released on 2012-12-31 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everyone knows the real numbers, those fundamental quantities that make possible all of mathematics from high school algebra and Euclidean geometry through the Calculus and beyond; and also serve as the basis for measurement in science, industry, and ordinary life. This book surveys alternative real number systems: systems that generalize and extend the real numbers yet stay close to these properties that make the reals central to mathematics. Alternative real numbers include many different kinds of numbers, for example multidimensional numbers (the complex numbers, the quaternions and others), infinitely small and infinitely large numbers (the hyperreal numbers and the surreal numbers), and numbers that represent positions in games (the surreal numbers). Each system has a well-developed theory, including applications to other areas of mathematics and science, such as physics, the theory of games, multi-dimensional geometry, and formal logic. They are all active areas of current mathematical research and each has unique features, in particular, characteristic methods of proof and implications for the philosophy of mathematics, both highlighted in this book. Alternative real number systems illuminate the central, unifying role of the real numbers and include some exciting and eccentric parts of mathematics. Which Numbers Are Real? Will be of interest to anyone with an interest in numbers, but specifically to upper-level undergraduates, graduate students, and professional mathematicians, particularly college mathematics teachers.

Explorations in Complex Analysis

Author : Michael A. Brilleslyper
Publisher : American Mathematical Soc.
ISBN 13 : 0883857782
Total Pages : 393 pages
Book Rating : 4.8/5 (838 download)

DOWNLOAD NOW!

Book Synopsis Explorations in Complex Analysis by : Michael A. Brilleslyper

Download or read book Explorations in Complex Analysis written by Michael A. Brilleslyper and published by American Mathematical Soc.. This book was released on 2012-12-31 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fourier Series

Author : Rajendra Bhatia
Publisher : MAA
ISBN 13 : 9780883857403
Total Pages : 134 pages
Book Rating : 4.8/5 (574 download)

DOWNLOAD NOW!

Book Synopsis Fourier Series by : Rajendra Bhatia

Download or read book Fourier Series written by Rajendra Bhatia and published by MAA. This book was released on 2005-03-03 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a concise introduction to Fourier series covering history, major themes, theorems, examples, and applications. It can be used for self study, or to supplement undergraduate courses on mathematical analysis. Beginning with a brief summary of the rich history of the subject over three centuries, the reader will appreciate how a mathematical theory develops in stages from a practical problem (such as conduction of heat) to an abstract theory dealing with concepts such as sets, functions, infinity, and convergence. The abstract theory then provides unforeseen applications in diverse areas. Exercises of varying difficulty are included throughout to test understanding. A broad range of applications are also covered, and directions for further reading and research are provided, along with a chapter that provides material at a more advanced level suitable for graduate students.

Game Theory through Examples

Author : Erich Prisner
Publisher : American Mathematical Soc.
ISBN 13 : 1614441154
Total Pages : 287 pages
Book Rating : 4.6/5 (144 download)

DOWNLOAD NOW!

Book Synopsis Game Theory through Examples by : Erich Prisner

Download or read book Game Theory through Examples written by Erich Prisner and published by American Mathematical Soc.. This book was released on 2014-12-31 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Keeping It R.E.A.L.

Author : Carla D. Martin
Publisher : American Mathematical Soc.
ISBN 13 : 0883859610
Total Pages : 129 pages
Book Rating : 4.8/5 (838 download)

DOWNLOAD NOW!

Book Synopsis Keeping It R.E.A.L. by : Carla D. Martin

Download or read book Keeping It R.E.A.L. written by Carla D. Martin and published by American Mathematical Soc.. This book was released on 2011-12-31 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keeping it R.E.A.L.: Research Experiences for All Learners is a collection of computational classroom projects carefully designed to inspire critical thinking and mathematical inquiry. This book also contains background subject information for each project, grading rubrics, and directions for further research. Instructors can use these materials inside or outside the classroom to inspire creativity and encourage undergraduate research. R.E.A.L. projects are suitable for a wide-range of college students, from those with minimal computational exposure and precalculus background to upper-level students in a numerical analysis course. Each project is class tested, and most were presented as posters at regional conferences.