Title: Foundations of Analysis

Description: A careful study of the theory underlying topics in one-variable calculus, with an emphasis on those topics arising in high school calculus. The real number system. Limits of functions and sequences. Differentiations, integration, and the fundamental theorem. Infinite series.

Prerequisite: C or higher in MAT 200 or MAT 250 or permission of instructor; C or higher in one of the following: MAT 203, 205, 211, 307, AMS 261, or A- or higher in MAT 127, 132, 142, or AMS 161

Credits: 4

Textbook:

Introduction to Real Analysis (4th edition) by Bartle and Sherbert

Note: Subject to change - do not buy before confirming with the course instructor

Major Topics Covered:

Definition of Real Numbers

Completeness Axiom and Least Upper Bound

Bounded and Unbounded Sets

Limit of a Sequence

Cauchy Sequences

Subsequences

Bolzano-Weierstrass Theorem

Series

Convergence Tests

Continuous Functions

Intermediate Value Theorem

Derivatives, Mean Value Theorem

Riemann Integral and Fundamental Theorem of Calculus

Undergraduate Bulletin Course Information

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