Mathematics for the liberal arts (2013)

PREFACE

This book is an introduction to mathematics history and mathematical concepts for liberal arts students. Students majoring in all fields can understand and appreciate mathematics, and exposure to mathematics can enhance and invigorate students’ thinking.

The book can be used as the basis for introductory courses on mathematical thinking. These courses may have titles such as “Introduction to Mathematical Thinking.” We describe the history of mathematical discoveries in the context of the unfolding story of human thought. We explain why mathematical principles are true and how the mathematics works. The emphasis is on learning about mathematical ideas and applying mathematics to real-world settings. Summaries of historical background and mini-biographies of mathematicians are interspersed throughout the mathematical discussions.

What mathematical knowledge should students have to read this book? An understanding of basic arithmetic, algebra, and geometry is necessary. This material is often taught in high school or beginning college-level courses. Beyond this background, the book is self-contained. Students should be willing to read the text and work through the examples and exercises. In mathematics, the best way (perhaps the only way) to learn is by doing.

Part I, comprising the first three chapters, gives an overview of the history of mathematics. We start with mathematics of the ancient world, move on to the Middle Ages, and then discuss the Renaissance and some of the developments of modem mathematics. Part II gives detailed coverage of two major areas of mathematics: calculus and number theory. These areas loom large in the world of mathematics, and they have many applications. The text is rounded out by appendices giving solutions to selected exercises and recommendations for further reading.

A variety of courses can be constructed from the text, depending on the aims of the instructor and the needs of the students. A one-semester course would likely focus on selected chapters, while a two-semester course sequence could cover all five chapters.

We hope that by working through the book, readers will attain a deeper appreciation of mathematics and a greater facility for using mathematics.

Thanks to the people who gave us valuable feedback about our writing: Linda Bindner, Robert Dobrow, Suren Fernando, David Garth, Amy Hemmeter, Mary Hemmeter, Daniel Jordan, Kenneth Price, Phil Ryan, Frank Sottile, Anthony Vazzana, and Dana Vazzana.

Thanks also to the Wiley staff for their assistance in publishing our book: Liz Belmont, Sari Friedman, Danielle LaCourciere, Jacqueline Palmieri, Susanne Steitz-Filler, and Stephen Quigley.