In this book, the authors propose to develop a portion of mathematics from the beginning. They show that the theorems of abstract mathematics are true entirely by virtue of the meanings of the words and symbols involved.

Gleason\, Andrew

This classic is an ideal introduction for students into the methodology and thinking of higher mathematics. It covers material not usually taught in the more technically-oriented introductory classes and will give students a well-rounded foundation for future studies.

1. Sets 2. Logic 3. The Set-Theoretic Machinery 4. Mathematical Configurations 5. Equivalence 6. Order 7. Mathematical Induction 8. Fields 9. The Construction of the Real Numbers 10. Complex Numbers 11. Counting and the Size of Sets 12. Limits 13. Sums and Products 14. The Topology of Metric Spaces 15. Introduction to Analytic Functions