MAT4273

The textbook(s) for this course is [1] Undergraduate Topology, by R. H. Kasriel; topics from [2] Introduction to Analysis by W. R. Wade (Stone-Weierstrass Theorem).

A comprehensive list of all undergraduate math courses at UTSA can be found here.

The Wikipedia summary of topology and its history.

Topics List

Date	Sections	Topics	Prerequisite Skills	Student Learning Outcomes
Week 1	30-31	Algebraic Structure of the Real Numbers	Order of Operations	Review of algebraic properties of the Real Numbers
Week 1	30-31	Distance Between Two Points in the Real Numbers	Absolute Value Algebraic Structure of the Real Numbers	The distance between two point on the real line
Week 1	30-31	Limit of a sequence in the Real Numbers	Distance Between Two Points in the Real Numbers Suprema, Infima, and the Completeness Property	The definition of a limit of a sequence
Week 1	30-31	The Nested Interval Theorem for the Real Numbers	Limit of a sequence in the Real Numbers Intervals Suprema, Infima, and the Completeness Property Mathematical Induction	The nested intervals property in the real numbers
Week 2	34-38	Cauchy-Schwarz Formula	Absolute Value Inequalities	The Cauchy-Schwarz Formula
Week 2	34-38	Distance Between Two Points in Higher Dimensions	Distance Between Two Points in the Real Numbers	Distance formula for higher dimensions
Week 2	34-38	Open Subsets in Higher Dimensions	Open Intervals Suprema, Infima, and the Completeness Property	Definition of an open set Definition of an interior point
Week 2	34-38	Limit Points (or Cluster Points) in Higher Dimensions	Open Subsets in Higher Dimensions Limit of a sequence in the Real Numbers Mathematical Induction	Definition of a limit point (or cluster point) The limit point as the limit of a sequence
Week 3	39-40	Closed Subsets in Higher Dimensions	Limit Points (or Cluster Points) in Higher Dimensions Open Subsets in Higher Dimensions	Definition of a closed set Properties of a closed set
Week 3	39-40	Bounded sets in Higher Dimensions	Closed Subsets in Higher Dimensions Limit Points (or Cluster Points) in Higher Dimensions Open Subsets in Higher Dimensions	Definition of a bounded set Properties of a bounded set
Week 3	39-40	The Nested Interval Theorem in Higher Dimensions	The Nested Interval Theorem for the Real Numbers Bounded sets in Higher Dimensions	The nested intervals theorem in higher dimensions
Week 3	39-40	The Bolzano-Weierstrass Theorem in Higher Dimensions	The Bolzano Weierstrass Theorem Bounded sets in Higher Dimensions	The Bolzano Weierstrass Theorem in higher dimensions
Week 4	41-43	Convergent Sequences and the Cauchy Criterion in Higher Dimension	Open Subsets in Higher Dimensions Limit of a sequence in the Real Numbers The Cauchy Criterion for Convergence	Definition of a convergent sequence in higher dimensions The Cauchy criterion for convergence of sequences in higher dimensions
Week 4	41-43	Heine-Borel Theorem	Open Subsets in Higher Dimensions Closed and Bounded sets	Definition of an open cover for a set Definition of compactness The Heine-Borel Theorem
Week 4	41-43	Lindeloff Theorem	Heine-Borel Theorem Intervals Unions and Intersections of Sets	The Lindeloff Theorem
Week 4	41-43	[[]]
Week 4	41-43	[[]]
Week 4	41-43	[[]]
Week 4	41-43	[[]]
Week 4	41-43	[[]]