A Readable Introduction to Real Mathematics

• Main Authors: Rosenthal, Daniel (Author), Rosenthal, David (Author), Rosenthal, Peter (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Series: Undergraduate Texts in Mathematics,
• Subjects: Mathematics.; Geometry.; Number theory.; Mathematics, general.; Number Theory.

Designed for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to engage the reader and to teach a real understanding of mathematical thinking while conveying the beauty...

Table of Contents:

• 1. Introduction to the Natural Numbers
• 2. Mathematical Induction
• 3. Modular Arithmetic
• 4. The Fundamental Theorem of Arithmetic
• 5. Fermat's Theorem and Wilson's Theorem
• 6. Sending and Receiving Coded Messages
• 7. The Euclidean Algorithm and Applications
• 8. Rational Numbers and Irrational Numbers
• 9. The Complex Numbers
• 10. Sizes of Infinite Sets
• 11. Fundamentals of Euclidean Plane Geometry
• 12. Constructability.