The Calculus Gallery
Quick Informations
Where to buy it: Princeton University Press
Author: William Dunham
Release date: July 21, 2008
Language: English
Personal Progress: Read completely
Review
Description
This book explores the story behind each breakthrough in Calculus and the life of the mathematician who originated it. For me, this book was the first to go deeply into the history and the context behind some of the most well-known results in Calculus. I find it very pleasant to see the early stages of Calculus and how it (very) slowly converges to the Calculus we know today. From the point of view of a student, it is also pleasant to see some of the greatest mathematicians making mistakes or even simply being wrong.
Prerequisites
To fully enjoy and understand this book, it would be better to know the basics of Real Analysis. The book Understanding Analysis is perfect to acquire this background in Analysis. However, this book can still be easily read and enjoyed with a simple background in Calculus.
Content
This book is divided into three parts, each part focuses on a century and presents four mathematicians of that period. The first part presents Newton, Leibniz, the Bernoullis and Euler, the second part presents Cauchy, Riemann, Liouville and Weierstrass, and the third part presents Cantor, Volterra, Baire and Lebesgue. This way of structuring the book really highlights how the philosophy of Calculus changed through the centuries.
Further Readings
The book From the Calculus to Set Theory 1630 - 1910 goes over the whole story of Calculus without focusing specifically on particular mathematicians or results. It goes more deeply into the life of the involved mathematicians and into the presented mathematics. I would say that reading the book From the Calculus to Set Theory would be a good way of completing the knowledge acquired from the Calculus Gallery.