MATH 440 REAL ANALYSIS I

Course Syllabus

1. The Real Number System

a. Sets and Functions

b. The Real Numbers as an Ordered Field

c. The Axiom of Completeness

2. Sequences of Real Numbers

a. Convergence

b. Subsequences

c. The Bolzano-Weierstrass Theorem

3. The Topology of the Real Numbers

a. Open and Closed Sets

b. Compactness and the Heine-Borel Theorem

c. Connectedness

4. Series of Real Numbers

a. Tests for Convergence

b. Operations Involving Series

5. Continuous Functions

a. Limits and Continuity

b. Monotone and Inverse Functions

Prerequisites: MATH 220 and MATH 240 or permission of instructor

Click Here to return to courses offered.