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Exploratory Examples for Real Analysis (Classroom Resource Materials)

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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 ĺ 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.