This book is designed for a wide variety of college and university students, including those who have never had a course in high school mathematics. It is written in the hope that these students and others will want to become involved in mathematics so that they can learn to appreciate, understand, use, and enjoy it. A major objective is to present an interesting approach to mathematics that does not involve complicated algebraic manipulations. The topics were chosen on the basis of affirmative answers to each of the following questions: (1) Is it mathematically significant? (2) Is it easy to understand? (3) Is it interesting?
The chapter titles are as follows: (1) "Mathematical Recreations," (2) "What Is Mathematics?" (3) "Logic," (4) "Sets and Paradoxes," (5) "Geometry," (6) "Counting and Probability," (7) "Statistics," (8) "Linear Algebra," (9) "Game Theory," (10) "Calculus," (11) "Computers," and there is an appendix on the real number system. The first four chapters do not require any algebra; Chapter 5 introduces some basic rules of algebra via geometry; and the appendix presents some basic properties of the real numbers in an intuitive way. There is no attempt to present a formal development of the real number system.
The book can be used a s text in a variety of ways. For example, Chapters 1 through 4 can be used for a one-quarter course; Chapters 1 through 6 can be used for a one-semester course. the instructor may also want to have students present reports on the lives of mathematicians or on mathematical topics related to the course. The Suggestions for Further reading may help students select topics of real interest.
Students in the social, natural, and mathematical sciences may find some of the chapters to be of special interest. In particular, Chapters 6, 7, 8, 9, and 11 may be of special interest to those in the social sciences; Chapters 6, 7,8, 10, and 11 may be of special interest to those in the natural sciences; and Chapters 2, 3, 4, 10, and 11 may be of special interest to those in the mathematical sciences.
Although the book has been written for the novice, some of the problems may challenge students with a good background in high school mathematics. Those problems that have been rated "more challenging" or "optional" are preceded by the symbol *.Contents