The Elements of Advanced Mathematics, Fourth Edition is the latest edition of the author’s bestselling series of texts. Expanding on previous editions, the new Edition continues to provide students with a better understanding of proofs, a core concept for higher level mathematics. To meet the needs of instructors, the text is aligned directly with course requirements.

The author connects computationally and theoretically based mathematics, helping students develop a foundation for higher level mathematics. To make the book more pertinent, the author removed obscure topics and included a chapter on elementary number theory. Students gain the momentum to further explore mathematics in the real world through an introduction to cryptography. These additions, along with new exercises and proof techniques, will provide readers with a strong and relevant command of mathematics.

  • Presents a concise presentation of the material
  • Covers logic, sets and moves to more advanced topics including topology
  • Provides greater coverage of number theory and cryptography
  • Streamlined to focus on the core of this course


chapter 1|33 pages

Basic Logic

chapter 2|31 pages

Methods of Proof

chapter 3|17 pages

Set Theory

chapter 4|43 pages

Relations and Functions

chapter 5|21 pages

Axioms, Paradoxes, and Rigor

chapter 6|57 pages

Number Systems

chapter 7|15 pages

More on the Real Number System

chapter 8|29 pages

A Glimpse of Topology

chapter 9|18 pages

Elementary Number Theory

chapter 10|18 pages

Zero-Knowledge Proofs and Cryptography

chapter 11|33 pages

Examples of Axiomatic Theories