Math 3371: Real Analysis

Fall 2020

General Information

Class meetings TF 2-2:50, W 3-3:50

Instructor: Chris Staecker (Personal Homepage)

Email: cstaecker@fairfield.edu

Textbook: Understanding Analysis by Abbott, second edition

Office Hours: TF 10-11, 1:30-2, W 10-11, 12-1, 2-3. All office hours by Zoom! Zoom link: https://fairfield.zoom.us/j/5514910533

Final Exam: Tuesday Dec 15, 3PM

Links

• Syllabus (PDF)

Class videos

Here is a YouTube playlist

• 9/1: Intro
• 9/2: Bounds, sup, and inf
• 9/4: The Axiom of Completeness
• 9/9: The Archimedean property
• 9/11: Cardinality
• 9/15: Countable vs uncountable
• 9/16: Convergent sequences
• 9/18: More convergence
• 9/22: Limit rules
• 9/23: More limit rules
• 9/25: Monotone convergence theorem
• 9/29: Subsequences and Bolzano Weierstrauss Theorem
• 9/30: Open sets
• 10/2: Closed sets
• 10/6: Closure
• 10/13: The Cantor set
• 10/14: Compact sets
• 10/16: Open covers & finite subcovers
• 10/20: The Heine-Borel Theorem
• 10/21: Connected sets
• 10/23: Thomae's function and epsilon-delta
• 10/27: More epsilon-delta
• 10/28: Sequential criterion for limits
• 10/30: Continuity
• 11/3: More continuity
• 11/4: Extreme value theorem
• 11/5: Uniform continuity
• 11/10: Intermediate Value Theorem
• 11/17: The derivative
• 11/18: The chain rule
• 12/1: Sequences of functions
• 12/2: Uniform convergence of sequences of functions
• 12/4: Series
• 12/8: More serieses
• 12/9: Rearranging series

Assignments

9/9: Homework #1

Section 1.2 #3ab, 10 (for the true ones, you don't need a real proof, just some words to explain)
Section 1.3 #1a, 1b (state it, don't prove it), 2, 7, 8
Professor's answers

9/16: Homework #2

Section 1.4 #3 (you should use the Archimedean property), 4, 8bc
Professor's answers

9/23: Homework #3

Section 1.5 #2, 5, 6a
Section 2.2 #2a, 4
Section 2.3 #1a
Professor's answers

9/30: Homework #4

Section 2.2 #2bc
Section 2.3 #3, 4ab, 7
Section 2.4 2 ,4b
Professor's answers

10/7: Homework #5

Section 2.5 1abc, 2ad
Section 3.2 2abc (read the definition of "isolated"), 3abc, 6ac
Professor's answers

10/21: Homework #6

Section 3.2 2d, 8abc (explain why)
Section 3.3 2abce, 4, 5cd
Professor's answers

10/28: Homework #7

Section 3.3 11 (forget about d)
Section 3.4 5, 7 (for these, look up the definition of "separated") (for 5, first show that U∩V is empty)
Sorry this assignment is so short! I didn't like the book's questions
Professor's answers

11/4: Homework #8

Section 4.2 5, 8abc, 9ab
Section 4.3 1
Professor's answers

11/11: Homework #9

Section 4.3 6abc, 7a, 8b
Section 4.4 1, 3, 8abc (for your "examples", you can just draw a graph if you want)
Professor's answers

11/11

Review sheet for Exam 2

12/2: Homework #10

Section 4.5 1, 2abcd, 6a, 7
Section 5.2 2, 3, 5
Section 5.3 3, 7
Professor's answers

12/9: Homework #11

Section 6.2 1, 2ab, 6abc, in #6 prove b is true for uniform convergence
Section 6.3 1

12/15: Homework #12 due, final project (optional) due

Homework #12: Do the "Series" problems on the final review sheet

Other stuff

Final review sheet
First (old) review sheet
Second (old) review sheet
Final project assignment

Class evaluation survey!

https://fairfield.campuslabs.com/eval-home/cei/math/3371/337101