Mathematics in 10 Lessons

Mathematicians know two things that others do not. They know first that all mathematics flows from a few fundamental principles. Second, they know that aesthetic considerations provide both the motivation for mathematics and the standards for evaluating mathematics research once it is done.

In an earlier book, The Art of Mathematics, I presented to an intended audience of humanists the notion of mathematics as art. There, I emphasized the importance that mathematicians place on aesthetics as they create and then evaluate mathematics. The Art of Mathematics is a book about mathematics rather than a book of mathematics. The present book is unapologetically a mathematics book. Mathematics in Ten Lessons: The Grand Tour contains real mathematics, presented from the point-of-view of fundamental principles.

The topics in Ten Lessons range from basic logic to calculus. The topics are given in ten chapters, with each chapter being essentially a separate lesson. The basic notion is that there exists a large number of educated, intelligent, non-technical people who, for one reason or another, would like to understand some non-trivial mathematics. Moreover they can obtain this understanding provided the mathematics is presented slowly and carefully through the emphasis on fundamental principles. Mathematics in Ten Lessons does exactly that. Each topic begins at the beginning. Almost no prior mathematical knowledge is assumed.