MAT3333

Course name

MAT 3333 Fundamentals of Analysis and Topology.

Catalog entry: MAT 333 Fundamentals of Analysis and Topology. Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor. Topology of the real line. Introduction to point-set topology.

Prerequisites: MAT 1224 and MAT 3003.

Sample textbooks:

• John M. Erdman, A Problems Based Course in Advanced Calculus. Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
• Jyh-Haur Teh, Advanced Calculus I. ISBN-13: 979-8704582137.

Topics List

(Section numbers refer to Erdman's book.)

1 1 2 3

Week	Sections	Topics	Student Learning Outcomes
Section 1.1. Appendices C, G & H.	Operations, order and intervals of the real line.	Arithmetic operations of ℝ. Field axioms. Order of ℝ. Intervals: open, closed, bounded and unbounded.
1.1-1.2	Basic topological notions in the real line.	Intervals of the real line. Distance. Neighborhoods and interior of a set.
2.1–2.2	Elementary topology of the real line.	Open subsets of ℝ. Closed subsets of ℝ.
3.1–3.3	Continuous functions on subsets of the real line.	Continuity at a point. Continuous functions on ℝ. Continuous functions on subsets of ℝ.