Calculus for Cranks

Nets Hawk Katz

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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.

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

“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
 

Calculus for Cranks stands out as an original and thoughtful tool guiding the student in developing their own intuition for mathematics. Nets Katz has succeeded in producing a really great addition to the pedagogical literature.”—David Fisher, Ruth N. Halls Professor of Mathematics at Indiana University

“As a mathematician and mathematics teacher, I find this approach to real numbers interesting, novel, and engaging. Nets Katz effectively introduces students to the rigorous nature of mathematics while staying relevant to biology, economics, and other disciplines.”—John Ross, Assistant Professor of Mathematics at Southwestern University
 
ISBN: 9780300242799
Publication Date: January 26, 2021
264 pages, 6 1/8 x 9 1/4