MAT3333

From Department of Mathematics at UTSA
Revision as of 13:34, 25 March 2023 by Eduardo.duenez (talk | contribs) (Rewriting first couple weeks.)
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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:


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.