Counterexamples in calculus - Sergiy Klymchuk

Counterexamples in Calculus serves as a supplementary resource to enhance the learning experience in single variable calculus courses. This book features carefully constructed incorrect mathematical statements that require students to create counterexamples to disprove them. Methods of producing these incorrect statements vary. At times the converse of a well-known theorem is presented. In other instances crucial conditions are omitted or altered or incorrect definitions are employed. Incorrect statements are grouped topically with sections devoted to: functions, limits, continuity, differential calculus and integral calculus. This book aims to fill a gap in the literature and provide a resource for using counterexamples as a pedagogical tool in the study of introductory calculus. In that light it may well be useful for high school teachers and university faculty as a teaching resource, for high school and college students as a learning resource, and as a professional development resource for calculus instructors.

Dr Sergiy Klymchuk is an Associate Professor of the School of Computing and Mathematical Sciences at the Auckland University of Technology, New Zealand. He has 29 years of experience teaching university mathematics in different countries. He was born in Ukraine in 1958. Since 1996 he has lived in New Zealand. His PhD (1988) from Odessa National University, Ukraine was in differential equations. At present his main research interests are in mathematics education. He is a member of the Royal Society of New Zealand. He is also a member of a number of international groups in mathematics education including International Group for the Psychology in Mathematics Education (PME) and International Community of Teachers of Mathematical Modelling and Applications (ICTMA). Apart from Counterexamples in Calculus he also has written Paradoxes and Sophisms in Calculus as a supplementary resource to enhance teaching and learning of introductory calculus. He has more than 140 publications including three books on popular mathematics and science that have been, or are being, published in 11 countries: Money Puzzles, Science Puzzles and Shape Puzzles.