Analysis I

3 Credits · Level: Undergraduate

This is the first part of the two semester advanced calculus sequence ( MATH 3310 & MATH 4310 ) which provides a rigorous treatment of topics in calculus with the emphasis on proofs of major theorems. Topics include the basic properties of the real numbers and n-dimensional Euclidean space, the basic topology of metric spaces including compactness and connectedness, the theory of numerical sequences and series, and the properties of continuous functions, differentiable functions and integrable functions on the real line. This course is expected to result in an appreciation of some of the central theorems of analysis on the real line, such as the Mean Value Theorem, Inverse Function Theorem and Taylor’s formula.