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Revision as of 11:43, 20 February 2025
MATH 4317 covers elementary real analysis, up to but not including differentiation. Specific topics include real numbers, topology of Euclidean spaces, Cauchy sequences, completeness, continuity and compactness, uniform continuity, series of functions, Fourier series.
It is a 3 credit-hour course, required for the mathematics major. It consists almost entirely of proofs.
Topic List
The topics can vary widely from one professor to another.
Professor McCuan teaches a version of the class which heavily emphasizes constructions, leading up to the construction of the real numbers. This takes up more than half of the semester.
Other professors discuss constructions summarily, for only a few weeks, before moving on to other topics.
Class Structure
For some professors, lecture, homework, exam.
For others, giving class presentations of proofs is an important component.
Prerequisite Knowledge
MATH 2106 (Foundations of Mathematical Proof)
Equivalent Courses
None
Resources
Authors of some textbooks used in previous semesters include Gunn, Bartle, and Tao.
A Course in Real Analysis with lecture and solved exercises.
