Katz V. A History of Mathematics: An Introduction

2nd edition. — Addison-Wesley, 1998. — 856 p. — ISBN: 0321016181.One of the leading historians in the mathematics field, Victor Katz provides a world view of mathematics, balancing ancient, early modern, and modern history.In A Call For Change: Recommendations for the Mathematical Preparation of Teachers of Mathematics, the Mathematical Association of America's (MAA) Committee on the Mathematical Education of Teachers recommends that all prospective teachers of mathematics in schools develop an appreciation of the contributions made by various cultures to the growth and development of mathematical ideas; investigate the contributions made by individuals, both female and male, and from a variety of cultures, in the development of ancient, modern, and current mathematical topics; and gain an understanding of the historical development of major school mathematics concepts.
According to the MAA, knowledge of the history of mathematics shows students that mathematics is an important human endeavor. Mathematics was not discovered in the polished form of our textbooks, but often developed in intuitive and experimental fashion out of a need to solve problems. The actual development of mathematical ideas can be effectively used in exciting and motivating students today.
This new textbook in the history of mathematics grew out of the conviction that not only prospective school teachers of mathematics but also prospective college teachers of mathematics need a background in history to teach the subject more effectively to their students. It is therefore designed for junior or senior mathematics majors who intend to teach in college or high school and thus concentrates on the history of those topics typically covered in an undergraduate curriculum or in elementary or high school. Because the history of any given mathematical topic often provides excellent ideas for teaching the topic, there is sufficient detail in each explanation of a new concept for the future (or present) teacher of mathematics to develop a classroom lesson or series of lessons based on history. In fact, many of the problems ask the reader to develop a particular lesson. My hope is that the student and prospective teacher will gain from this book a knowledge of how we got here from there, a knowledge that will provide a deeper understanding of many of the important concepts of mathematics.