Introduction to Advanced Mathematics, 2/e (IE-Paperback)

Description:

For a one-quarter/semester, sophomore-level transitional (“bridge”) course that supplies background for students going from calculus to the more abstract, upper-division mathematics courses. Also appropriate as a supplement for junior-level courses such as abstract algebra or real analysis.

Focused on “What Every Mathematician Needs to Know,” this text provides material necessary for students to succeed in upper-division mathematics courses, and more importantly, the analytical tools necessary for thinking like a mathematician. It begins with a natural progression from elementary logic, methods of proof, and set theory, to relations and functions; then provides application examples, theorems, and student projects.

Table of Contents:

1. Introduction to Logic.

2. Methods of Proof.

3. Set Theory.

4. Cartesian Products and Functions.

5. Relations.

6. Cardinality.

7. Number Theory.

8. Rings and Integral Domains.

9. Limits and the Real Numbers.