Elements of Advanced Mathematics

•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 10 is expanded.•The author introduces groups much earlier, as this is an incisive example of an axiomatic theory. Coverage of group theory, formerly in Chapter 11, has been moved up, this is an incisive example of an axiomatic theory.