The Text
From the Preface
Elementary calculus students develop intuitive concepts of limits,
derivatives, and integrals. While adequate for most, those who teach calculus
need a much deeper understanding. The purpose of this book is to present an
introductory course in analysis, rebuilding intuitive understandings with more
rigorous foundations, with emphases chosen for the practicing secondary teacher.
The text is based on a one semester, four credit hour, graduate course in our
Masters in Mathematics with a concentration in Secondary Education program.
Since we wish to cover a significant amount of material in one semester, some
topics will necessarily be given short attention and others are not covered.
This reduction allows us to introduce Lebesgue measure and integration. The last
chapter presents a set of special topics with ties to elementary calculus that
can be used as student projects. These topics can be studied in more depth if
time permits.
Abbreviated Table of Contents
- Chapter 1. Elementary Calculus
- Chapter 2. Introduction to Real Analysis
- Chapter 3. A Brief Introduction to Lebesgue Theory
- Chapter 4. Special Topics
- Appendices. Definitions and Theorems of Elementary Real Analysis, A Very Brief Calculus Chronology, Projects in Real Analysis
- Bibliography
- Index
Presentations
- ICTCM 20: “Using Maple in Advanced Calculus and Modern Algebra” — WmCB
Abstract: We present a discussion and demonstration of enhancing upper-level courses such as Modern Algebra and Advanced Calculus with Maple. Worksheets with embedded components that allow students to focus on concepts, rather than syntax, are highlighted.
| pdf (pdf) | Maple Demo (Maple 12 file) | Class material archives |
- ICTCM 19: “Using Maple in an Analysis for Teachers Graduate Course” — WmCB
Abstract: We will discuss how Maple can be used to enhance a masters level Analysis for Teachers course. Both aspects will be considered: Maple for the student’s use and Maple for the student’s student use.
| Slides (pdf) | Class notes (pdf) | Limits (Maple file) | Class material archives |
Files & Data
- Library of Congress Catalog Record
- An Example Concept Map of the Derivative
- Data Files (right-click the link and choose "save as...")
- US Population, 1630 to 2008
- Mathematician's Birthday Calendar [.ics format]
- Mathematical Genealogy Maps (data via the AMS's “Mathematics Genealogy Project”)
- Errata
- Not yet...
Note: If you have trouble with any of the links or with downloading any of the material, please contact me — there's a link at the bottom…