Exploratory Examples for Real Analysis

Joanne E. Snow, Kirk E. Weller - Collection Classroom Resource Materials

139 pages, parution le 01/10/2004

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Résumé

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: www.saintmarys.edu/-jsnow.

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

Sommaire

Boundedness of Sets
Introducing the "Epsilon Definition" of Least Upper Bound
Introduction to the Formal Definition of Convergence
Experience with the Definition of the Limit of a Sequence
Experience with the Negation of the Definition of Convergence
Algebraic Combinations of Sequences
Conditions Related to Convergence
Understanding the Limit Superior and the Limit Inferior
Continuity and Sequences
Another Definition of Continuity
Experience with the Ε - δ Definitions of Continuity and Limit
Uniform Convergence of a Sequence of Functions
Appendix : Visual Guides

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Caractéristiques techniques

	PAPIER
Éditeur(s)	The Mathematical Association of America (MAA)
Auteur(s)	Joanne E. Snow, Kirk E. Weller
Collection	Classroom Resource Materials
Parution	01/10/2004
Nb. de pages	139
Format	19 x 26,5
Couverture	Broché
Poids	331g
Intérieur	Noir et Blanc
EAN13	9780883857342
ISBN13	978-0-88385-734-2