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Counterexamples in Calculus

Sergiy Klymchuk


Winner Choice Outstanding Academic Title!

As a robust repertoire of examples is essential for students to learn the practice of mathematics, so a mental library of counterexamples is critical for students to grasp the logic of mathematics. Counterexamples are tools that reveal incorrect beliefs. Without such tools, learners' natural misconceptions gradually harden into convictions that seriously impede further learning. This slim volume brings the power of counterexamples to bear on one of the largest and most important courses in the mathematics curriculum. — Professor Lynn Arthur Steen, St. Olaf College, Co-author of Counterexamples in Topology

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.

Counterexamples 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; high school and college students as a learning resource;and as a professional development resource for calculus instructors.

In the electronic version page numbers that link to the suggested solutions can be found at the end of each problem statement.

Electronic ISBN:  9781614441090

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