Calculus Deconstructed: A Second Course in First-Year Calculus (Mathematical Association of America Textbooks)

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9780883857564: Calculus Deconstructed: A Second Course in First-Year Calculus (Mathematical Association of America Textbooks)

Calculus Deconstructed is a thorough and mathematically rigorous exposition of single-variable calculus for readers with some previous exposure to calculus techniques but not to methods of proof. This book is appropriate for a beginning Honors Calculus course assuming high school calculus or a "bridge course" using basica analysis to motivate and illustrate mathematical rigor. It can serve as a combination textbook and reference book for individual self-study. Standard topics and techniques in single-variable calculus are presented in context of a coherent logical structure, building on familiar properties of real numbers and teaching methods of proof by example along the way. Numerous examples reinforce both practical and theoretical understanding, and extensive historical notes explore the arguments of the originators of the subject.

No previous experience with mathematical proof is assumed: rhetorical strategies and techniques of proof (reductio ad absurdum, induction, contrapositives, etc.) are introduced by example along the way. Between the text and exercises, proofs are available for all the basic results of calculus for functions of one real variable.

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Book Description:

A thorough and mathematically rigorous exposition of single-variable calculus for readers with some previous experience of calculus techniques. This book can be used as a textbook for an undergraduate course on calculus or as a reference for self-study.

About the Author:

Zbigniew H. Nitecki received his SB from the University of Chicago in 1965, his MA (1967) and Ph.D. (1969) from the University of California, Berkley. He is currently a professor of mathematics at Tufts University, where has been since 1972.

Mr. Nitecki has previously held positions as a Gibbs Instructor at Yale, an assistant professor at CCNY, and has held numerous short term positions at Brown, Northwestern, and George-August Universität, Göttingen, Germany. He has also held various visiting research positions at the Institut des Hautes Etudes Scientifiques (Paris), the Institut Non-Linéaire (Nice) and the University of Warwick (Coventry). He has served as the first program director for the Geometric Analysis Program at the National Science Foundation and is a contributing editor for Real Analysis Exchange and an associate editor for Qualitative Theory of Dynamical Systems.

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