MAT3213

From Department of Mathematics at UTSA
Revision as of 12:06, 14 August 2020 by Eduardo.duenez (talk | contribs) (Topic list Weeks 1&2.)
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The textbook for this course is Introduction to Real Analysis by Bartle and Sherbert

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

The Wikipedia summary of Real Analysis.

Topics List

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1

1.1

Sets:Definitions Sets:Operations Functions:Definition Functions:Domain Functions:Range Functions:Injective Functions:Bijective Functions:Composition Functions:Inverse Functions:ForwardImage Functions:InverseImage Functions:Restriction


Week 2

1.2

NaturalNumbers:Well-Ordering Proofs:Induction Induction:Variants


Week 3

1.3


Finite and Infinite Sets Countable Sets


Week 3

2.1

Algebraic Properties of the Real Numbers


Week 3

2.1

Rational and Irrational Numbers


Week 2

2.1

The Ordering Properties of the Real Numbers


Week 2

2.1

Inequalities


Week 2/3

2.2

Absolute Value and the Real Line


Week 3

2.3

Suprema, Infima, and the Completeness Property


Week 3

2.4

Applications of the Supremum Property


Week 3/4

2.5

Intervals


Week 4

3.1

Sequences and Their Limits


Week 4

3.2

The Limit Laws for Sequences


Week 4/5

3.3

Monotone Sequences


Week 5

3.4

Subsequences


Week 5

3.4

The Bolzano Weierstrass Theorem


Week 5/6

3.4

The Limit Superior and Limit Inferior


Week 6

3.5

The Cauchy Criterion for Convergence


Week 6

3.6

Properly Divergent Sequences


Week 6/7

3.7

Introduction to Infinite Series


Week 12

4.1

Cluster Points


Week 12

4.1

The Definition of the Limit of a Function


Week 12/13

4.1

The Sequential Criterion and Divergence Criteria


Week 13

4.2

The Limit Theorems for Functions


Week 14

4.3

One Sided Limits


Week 14/15

4.3

Infinite Limits and Limits at Infinity