**Classroom Resource Materials**

Volume: 20;
2003;
160 pp;
Softcover
**Print ISBN: 978-0-88385-734-2
Product Code: CLRM/20**

List Price: $40.00

AMS Member Price: $30.00

MAA member Price: $30.00

# Exploratory Examples for Real Analysis

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*Joanne E. Snow; Kirk E. Weller*

MAA Press: An Imprint of the American Mathematical Society

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 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 authors were inspired by Ellen
Parker's book, Laboratory Experiences in Group Theory, also published
by the MAA.