Using Counter-Examples in Calculus

Using Counter-Examples in Calculus provides the serious (or, alternatively, mildly sadistic) mathematics lecturer with a cornucopia of counter-examples to falsify conjectures and expose sham statements in first-year undergraduate calculus.

The first chapter explains the use and importance of counter-examples; the second is a brief philosophical discussion on the relative merits of the use of pathological examples; the third chapter offers a list of almost 100 "false statements" spanning functions, continuity, differential and integral calculus. Chapter four forms the major part of the book providing detailed counter-examples to statements in chapter three, with open-ended questions for further exploration.

Who is it for? Lecturers of first-year calculus courses for mathematicians and keen undergraduates.

Presentation: The layout is systematic and clear. Each counter-example is illustrated with an explanatory graph.

Would you recommend it? An invaluable resource for lecturers committed to toughening up first-year problem sheets in mathematics calculus courses.