Overview

A new approach to the foundations of single variable calculus, based on the introductory course taught at Caltech In mathematics, “cranks” are people who insist they understand something new about math even when the world tells them they are doing it wrong. This introduction to calculus is written with those cranks in mind, based on the foundational course that Nets Katz teaches at Caltech. It emphasizes the practical purposes of the foundations, such as tracking errors in calculations. In addition to covering the basics of single variable calculus, the book outlines the mathematical method—the ability to express oneself with absolute precision and then to use logical proofs to establish that certain statements are universally true. Katz emphasizes conceptual clarity, as well as testing hypotheses and writing complete proofs. The result is a rigorous calculus book of use not only to future mathematicians but also to scientists and engineers.

Full Product Details

9780300242799

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Reviews

"""The author’s stress on repeatable techniques . . . and the real numbers treated as infinite decimals results in a distinctive excursion through familiar territory.”—Nick Lord, The Mathematical Gazette ""A very useful and constructive way to teach the subject.""—Dominic Thorrington, IMA “Every science and engineering student takes calculus, but few learn the subject with depth and rigor. Calculus for Cranks addresses this gap head-on, introducing fundamental concepts in analysis that are valuable for all students – not just math majors.”—Carina Curto, Professor of Mathematics, Pennsylvania State University   “Nets Katz has written a calculus textbook for students who don’t like being lied to. It will be essential for those who are constantly harassing their teachers with questions beginning with ‘why’ and ‘how.’”—Deane Yang, Professor of Mathematics, New York University   “Calculus for Cranks unspools like a good novel! Katz deftly weaves abstraction and computation into a single narrative, with an entertaining set of exercises along the way.”—Amie Wilkinson, Professor of Mathematics, University of Chicago   “Blending formal and informal insights, Katz pulls back the curtain on calculus, revealing its foundations, especially for those who think they’ve seen it before.”—Francis Su, author of Mathematics for Human Flourishing   “Calculus for Cranks is a beautiful, rigorous, intuitive, introduction to real and complex analysis starting from logical reasoning and the number system. I recommend it highly for serious students.”—Wilhelm Schlag, Professor of Mathematics, Yale University  "

The author's stress on repeatable techniques . . . and the real numbers treated as infinite decimals results in a distinctive excursion through familiar territory. -Nick Lord, The Mathematical Gazette A very useful and constructive way to teach the subject. -Dominic Thorrington, IMA Every science and engineering student takes calculus, but few learn the subject with depth and rigor. Calculus for Cranks addresses this gap head-on, introducing fundamental concepts in analysis that are valuable for all students - not just math majors. -Carina Curto, Professor of Mathematics, Pennsylvania State University Nets Katz has written a calculus textbook for students who don't like being lied to. It will be essential for those who are constantly harassing their teachers with questions beginning with 'why' and 'how.' -Deane Yang, Professor of Mathematics, New York University Calculus for Cranks unspools like a good novel! Katz deftly weaves abstraction and computation into a single narrative, with an entertaining set of exercises along the way. -Amie Wilkinson, Professor of Mathematics, University of Chicago Blending formal and informal insights, Katz pulls back the curtain on calculus, revealing its foundations, especially for those who think they've seen it before. -Francis Su, author of Mathematics for Human Flourishing Calculus for Cranks is a beautiful, rigorous, intuitive, introduction to real and complex analysis starting from logical reasoning and the number system. I recommend it highly for serious students. -Wilhelm Schlag, Professor of Mathematics, Yale University

Author Information

Nets Hawk Katz is International Business Machines Professor of Mathematics at the California Institute of Technology. He was a Guggenheim fellow in 2012 and the winner of the Clay Research Award in 2016.

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