Calculus Gems

George F. Simmons




Mathematical Association of America

A classic book is back in print! It can be used as a supplement in a Calculus course, or a History of Mathematics course. The first half of Calculus Gems entitles, Brief Lives is a biographical history of mathematics from the earliest times to the late nineteenth century. The author shows that Science and mathematics in particular is something that people do, and not merely a mass of observed data and abstract theory. He demonstrates the profound connections that join mathematics to the history of philosophy and also to the broader intellectual and social history of Western civilization. The second half of the book contains nuggets that Simmons has collected from number theory, geometry, science, etc., which he has used in his mathematics classes. G.H. Hardy once said, A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. This part of the book contains a wide variety of these patterns, arranged in an order roughly corresponding to the order of the ideas in most calculus courses. Some of the sections even have a few problems. Professor Simmons tells us in the Preface of Calculus Gems: I hold the naïve but logically impeccable view that there are only two kinds of students in our colleges and universities, those who are attracted to mathematics; and those who are not yet attracted, but might be. My intended audience embraces both types. The overall aim of the book is to answer the question, What is mathematics for? and with its inevitable answer, To delight the mind and help us understand the world.