Synopses & Reviews
This is a foundational course book for introductory honors calculus. In addition to exploring the practical purposes of the foundations of calculus, Katz emphasizes achieving conceptual clarity, testing and checking hypotheses, and writing complete proofs. This rigorous course book is intended both for future mathematicians and for those in broader STEM fields.
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.