Paradoxes and Sophisms in Calculus
Mathematical Association of America (Verlag)
978-0-88385-781-6 (ISBN)
In the study of mathematics, surprising and counterintuitive examples can offer a fascinating insight into the development of the subject, and inspire a learner's passion for discovery. With a carefully chosen selection of so-called paradoxes and sophisms, this book offers a delightful supplementary resource to enhance the study of single variable calculus. By paradox, the authors mean an unexpected statement that looks invalid, but is in fact true. The word sophism describes intentionally invalid reasoning that looks formally correct, but, in fact, contains a subtle mistake or flaw. This collection of over fifty paradoxes and sophisms showcases the subtleties of calculus and leads students to contemplate the underlying concepts. Sophisms and paradoxes from the areas of functions, limits, derivatives, integrals, sequences and series are explored, with full explanations provided for each example. The book is an ideal resource for those studying or teaching calculus at high school and university level.
Sergiy Klymchuk is an Associate Professor of the School of Computing and Mathematical Sciences at Auckland University of Technology, New Zealand. He is a Fellow of the Institute of Mathematics and its Applications and a member of the Royal Society of New Zealand (RSNZ). He has more than 160 publications including three books on popular mathematics and science – Money Puzzles, Science Puzzles and Shape Puzzles, that have been, or are being, published in 11 countries. His book Counterexamples in Calculus received an Outstanding Academic Title award from Choice magazine of the American Library Association in 2010. Susan Staples is an Associate Professor of Mathematics at Texas Christian University. She served for ten years as graduate director of the TCU MAT program and continues to enjoy working with local teachers. She is the recipient of teaching awards from the University of Michigan, the University of Texas, and Texas Christian University. Her professional memberships include the MAA, AMS, AWM, NCTM and AAUW. Her graduate work was supported by an AAUW Fellowship. Currently she holds positions on two editorial boards for the MAA – The American Mathematical Monthly and the Classroom Resources Material book series.
Introduction; Part I. Paradoxes: 1. Functions and limits; 2. Derivatives and integrals; Part II. Sophisms: 3. Functions and limits; 4. Derivatives and integrals; Part III. Solutions to Paradoxes: 5. Functions and limits; 6. Derivatives and integrals; Part IV. Solutions to Sophisms: 7. Functions and limits; 8. Derivatives and integrals; References.
| Reihe/Serie | Classroom Resource Materials |
|---|---|
| Zusatzinfo | 3 Halftones, black and white; 40 Line drawings, black and white |
| Verlagsort | Washington |
| Sprache | englisch |
| Maße | 153 x 228 mm |
| Gewicht | 170 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 0-88385-781-2 / 0883857812 |
| ISBN-13 | 978-0-88385-781-6 / 9780883857816 |
| Zustand | Neuware |
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