Elements of Modern Mathematics

An unusually thoughtful and well-constructed introduction to the serious study of mathematics, this book requires no background beyond high school courses in plane geometry and elementary algebra. From that starting point, it is designed to lead readers willing to work through its exercises and problems to the achievement of basic mathematical literacy. The text provides a fundamental orientation in modern mathematics, an essential vocabulary of mathematical terms, and some facility in the use of mathematical concepts and symbols. From there, readers will be equipped to move on to more serious work, and they'll be well on the way to having the tools essential for work in the physical sciences, engineering, and the biological and social sciences.
Starting with elementary treatments of algebra, logic, and set theory, the book advances to explorations of plane analytic geometry, relations and functions, numbers, and calculus. Subsequent chapters discuss probability, statistical inference, and abstract mathematical theories. Each section is enhanced with exercises in the text and problems at the end. Answers to the exercises and some of the problems are included at the end of each section.

Kenneth O. May (1915–77) was Chairman of the Department of Mathematics at Carleton College and the author of several other mathematical texts, including Elementary Analysis and Measure and the Integral. He was instrumental in the founding of the International Commission on the History of Mathematics and was the first editor of its journal, Historia Mathematica.

Table of Contents:
Preface
Note to the Student
Note to the Teacher
1. Elementary Algebra
2. Elementary Logic
3. Elementary Theory of Sets
4. Plane Analytic geometry
5. Relations and Functions
6. Numbers
7. Calculus
8. Probability
9. Statistical Inference
10. Abstract Mathematical Theories
Appendixes
Index