An Approach through Problems
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A conceptually clear induction to fundamental analysis theorems, a tutorial for creative approaches for solving problems, a collection of modern challenging problems, a pathway to undergraduate research—all these desires gave life to the pages here.
This book exposes students to stimulating and enlightening proofs and hard problems of classical analysis mainly published in The American Mathematical Monthly.
The author presents proofs as a form of exploration rather than just a manipulation of symbols. Drawing on the papers from the Mathematical Association of America's journals, numerous conceptually clear proofs are offered. Each proof provides either a novel presentation of a familiar theorem or a lively discussion of a single issue, sometimes with multiple derivations.
The book collects and presents problems to promote creative techniques for problem-solving and undergraduate research and offers instructors an opportunity to assign these problems as projects. This book provides a wealth of opportunities for these projects.
Each problem is selected for its natural charm—the connection with an authentic mathematical experience, its origination from the ingenious work of professionals, develops well-shaped results of broader interest.
Table of Contents
Chapter2: Infinite Numerical Series
Chapter 3: Continuity
Chapter 4: Differentiation
Chapter 5: Integration
Chapter 6: Sequences and Series of Functions
Chapter 7: Improper and Parametric Integration
Appendix A: A List of Problems from MAA
Hongwei Chen received his Ph.D. from North Carolina State University in 1991. He is currently a professor of mathematics at Christopher Newport University. He has published more than 60 research papers in analysis and partial differential equations. He also authored Monthly Problem Gems also published by CRC Press and Excursions in Classical Analysis published by the Mathematical Association of America.