Conquering Mathematics: From Arithmetic to Calculus

We have designed and written this book. not as a text nor for the professional mathematician. but for the general reader who is naturally attracted to mathematics as a great intellec tual challenge. and for the special reader whose work requires him to have a deeper understanding of mathematics than he acquired in school. Readers in the first group are drawn to mental recreational activities such as chess. bridge. and various types of puzzles. but they generally do not respond enthusiastically to mathematics because of their unhappy learning experiences with it during their school days. The readers in the secondgrouptum to mathematics as a necessity. but with painful resignation and considerable apprehension regarding their abilities to master the branch ofmathematics they need in their work. In either case. the fear of and revulsion to mathematics felt by these readers usually stem from their earlier frustrating encounters with it. vii viii PREFACE This book will show these readers that these fears, frustrations, and general antipathy are unwarranted, for, as stated, it is not a textbook full of long, boring proofs and hundreds of problems, rather it is an intellectual adventure, to be read with pleasure. It was written to be easily accessible and with concern for the mental tranquilityofthe reader who willexperience considerable fulfillment when he/she sees the simplicity of basic mathematics. The emphasis throughout this book is on the clear explanation of mathematical con cepts.