A Readable Introduction to Real Mathematics

• Main Authors: Rosenthal, Daniel (Author, http://id.loc.gov/vocabulary/relators/aut), Rosenthal, David (http://id.loc.gov/vocabulary/relators/aut), Rosenthal, Peter (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 2nd ed. 2018.
• Series: Undergraduate Texts in Mathematics,
• Subjects: Mathematics.; Number theory.; Geometry.; 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 teach mathematical thinking while conveying the beauty and elegance of mathematics. The book contains a...

Table of Contents:

• Preface to the Second Edition
• Preface for Readers
• Preface for Instructors
• 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
• 13. An Introduction to Infinite Series
• 14. Some Higher Dimensional Spaces
• Index.