Exploratory Examples for Real Analysis (Classroom Resource Materials) (Paperback)

~ Joanne Snow (Author), Kirk Weller (Author) "In this lab, we examine some properties dealing with boundedness: upper bound, lower bound, supremum, infimum, maximum, and minimum..." (more)
Key Phrases: epsilon band, indexing set, plotting package, Example Set, Critical Thinking Questions, Using Examples (more...)

Editorial Reviews

Product Description

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 authors 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 authors 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 the 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, Report Guides for a lab session approach, and solutions to all 12 exercises, are provided online.

In designing the exercises, the authors were inspired by Ellen Parker’s book, Laboratory Experiences in Group Theory, also published by the MAA.

Book Description

Supplementary exercises and projects designed to facilitate students' understanding of the fundamental concepts in real analysis. They can be used to motivate a lecture; as a basis for in-class activities; in lab sessions. Programs in Maple are supplied with further ancillary material available from http://www.saintmarys.edu/~jsnow/maplets.html.

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Product Details

• Paperback: 158 pages
• Publisher: The Mathematical Association of America (October 14, 2004)
• Language: English
• ISBN-10: 0883857340
• ISBN-13: 978-0883857342
• Product Dimensions: 10.3 x 7.3 x 0.4 inches
• Shipping Weight: 11.2 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon.com Sales Rank: #1,121,859 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

1 of 1 people found the following review helpful:

4.0 out of 5 stars Good exercises demonstrating epsilon-delta concepts, February 18, 2004

By	Charles Ashbacher "([e-mail])" (Marion, Iowa United States([e-mail])) - See all my reviews (TOP 50 REVIEWER)

If there is a single concept that separates the successful math major from the math student, it is the ability to understand epsilon-delta proofs. First encountered in calculus, I have received more negative student feedback about what they mean than any other topic and it only gets worse when students move on to real analysis. Therefore, math teachers are always on the lookout for good exercises that can be used to clarify the meaning of those elusive epsilons and deltas.
The authors present twelve exercises that illustrate fundamental concepts of real analysis. The topics covered are boundedness, supremum/infimum, sequences, continuity, limits, limit suprema/infima and pointwise and uniform convergence. Numeric computations using Maple are frequently used with small values for å to demonstrate the trends of the expressions, as visual guide exercises for eight of the labs are included at the end. These labs are very helpful in giving the students visual demonstrations of the behavior of the formulas.
Many of the exercises involve computations designed to be performed on a calculator. There are also many tables where the students are expected to fill in the remaining entries. I found this workbook style to be a very sound approach to the teaching of real analysis and couldn't help but try a few of the problems.
Designed to be a supplement for a first course in real analysis, this book presents a set of problem solving strategies and problems to try them on that will help teach students what real analysis is all about. I definitely recommend that all teachers of calculus and real analysis look it over thoroughly before they teach these subjects the next time.

Published in the recreational mathematics e-mail newsletter, reprinted with permission.