The Elements of Advanced Mathematics: Edition 5

What sets the book apart is the excellent writing style, exposition, and unique and thorough sets of exercises. This edition offers a more instructive preface to assist instructors on developing the course they prefer. The prerequisites are more explicit and provide a roadmap for the course. Sample syllabi are included.

As would be expected in a fifth edition, the overall content and structure of the book are sound.

This new edition offers a more organized treatment of axiomatics. Throughout the book, there is a more careful and detailed treatment of the axioms of set theory. The rules of inference are more carefully elucidated.

Additional new features include:

• An emphasis on the art of proof.
• Enhanced number theory chapter presents some easily accessible but still-unsolved problems. These include the Goldbach conjecture, the twin prime conjecture, and so forth.
• The discussion of equivalence relations is revised to present reflexivity, symmetry, and transitivity before we define equivalence relations.
• The discussion of the RSA cryptosystem in Chapter 8 is expanded.
• The author introduces groups much earlier. Coverage of group theory, formerly in Chapter 11, has been moved up; this is an incisive example of an axiomatic theory.

Recognizing new ideas, the author has enhanced the overall presentation to create a fifth edition of this classic and widely-used textbook.