Daily Syllabus, Math 301 Real Analysis, Fall 2021
Be sure to check back, because this will be updated during the semester.
- All section numbers refer to Understanding Analysis, Second Edition by Abbott
- OFP refers to a pre-class onCourse forum posts
- PS refers to Problem Sets uploaded to onCourse
| Week | Major Topics | Tuesday 9:30 - 11:50 |
Thursday 9:30 - 11:50 |
||
|---|---|---|---|---|---|
| 1 | Welcome to Real Analysis! | 8/31 |
1.3 The Axiom of Completeness
OFP due Wed 9/1 @ midnight Bio Sheet due Wed 9/1 @ midnight |
9/2 | 1.4 Consequences of Completeness |
| 2 |
What distinguishes \( \mathbb{Q} \) and \( \mathbb{R} \)? How do you compare the size of infinite sets? OFP due Mon 9/6 @ midnight |
9/7 |
1.4 Consequences of Completeness
OFP response due Wed 9/8 @ midnight |
9/9 |
1.5 Cardinality
PS #1 due Thursday 9/9 @ midnight PS #1 peer eval due Friday 9/10 @ midnight |
| 3 |
\( \mathbb{R} \) and \( \mathbb{Q} \) have different cardinatlities
OFP due Mon 9/13 @ midnight |
9/14 |
1.5 Cardinality (continued)
OFP response due Wed 9/15 @ midnight |
9/16 |
1.5 Cardinality (continued)
PS #2 due Thursday 9/16 @ midnight PS #2 peer eval due Friday 9/17 @ midnight |
| 4 |
How many different infinities are there? \( P(\mathbb{N})\sim \mathbb{R} \) OFP due Mon 9/20 @ midnight |
9/21 |
1.6 Cantor's Theorem
OFP response due Wed 9/22 @ midnight |
9/23 |
1.6 Cantor's Theorem (continued)
PS #3 due Thursday 9/23 @ midnight PS #3 peer eval due Friday 9/24 @ midnight |
| 5 | Algebraic and topological definitions of convergence | 9/28 |
2.2 The Limit of a Sequence 2.3 The Algebraic and Order Limit Theorems Cheat Sheet for Exam 1 due @ 8:00 am Exam 1 covers thru 1.6 |
9/30 |
2.4 The Monotone Convergence Theorem
Exam 1 due @ midnight |
| 6 |
Every bounded sequence has a convergent subsequence An equivalent condition for convergence OFP due Mon 10/4 @ midnight Title for Book Review due Monday 10/4 @ midnight |
10/5 |
2.5 Subsequences and the Bolzano-Weierstrass Theorem
OFP response due Wed 10/6 @ midnight |
10/7 | 2.6 The Cauchy Criterion |
| 7 | No class meetings this week due to Fall Break and MAP Day | 10/12 | Fall Break | 10/14 | MAP Day |
| 8 |
Thow away the middle third Intro to the topology of \( \mathbb{R} \) OFP due Mon 10/18 @ midnight |
10/19 |
3.1 The Cantor Set
OFP response due Wed 10/20 @ midnight |
10/21 |
3.2 Open and Closed Sets
PS #4 due Thursday 10/21 @ midnight PS #4 peer eval due Friday 10/22 @ midnight |
| 9 |
Limit points on closed sets That's a continuous function? OFP due Mon 10/25 @ midnight |
10/26 |
3.3 Compact Sets
OFP response due Wed 10/27 @ midnight |
10/28 |
4.1 Examples of Dirichlet & Thomae 4.2 Functional Limits PS #5 due Friday 10/29 @ midnight PS #5 peer eval due Friday 10/29 @ midnight |
| 10 |
Consequences of continuity
OFP due Mon 11/1 @ midnight |
11/2 |
4.3 Continuous Functions
OFP response due Wed 11/3 @ midnight |
11/4 | 4.4 Continuous Functions on Compact Sets |
| 11 |
The IVT is "obvious" but slippery to prove
OFP due Mon 11/8 @ midnight Progress Report on Book Review due Monday 11/8 @ midnight |
11/9 |
4.5 The Intermediate Value Theorem
OFP response due Wed 11/10 @ midnight |
11/11 |
5.2 Derivatives and the Intermediate Value Property
PS #6 due Thursday 11/11 @ midnight PS #6 peer eval due Friday 11/12 @ midnight |
| 12 |
The MVT is "obvious" but slippery to prove A continuous function with "corners" everywhere |
11/16 |
5.3 The Mean Value Theorem
Cheat Sheet for Exam 2 due @ 8:00 am Exam 2 covers thru 4.5 |
11/18 |
5.4 A Continuous Nowhere-Differentiable Function
Exam 2 due Friday 11/19 @ midnight |
| 13 |
Uniform convergence is your friend
OFP due Mon 11/22 @ midnight |
11/23 | 6.2 Uniform Convergence of a Sequence of Functions | 11/25 | Thanksgiving Break |
| 14 |
Uniform convergence is really your friend
OFP due Mon 11/29 @ midnight |
11/30 |
6.3 Uniform Convergence and Differentiation
OFP response due Wed 12/1 @ midnight |
12/2 |
6.4 Series of Functions 6.5 Power Series |
| 15 |
Polynomials are a universal gadget for continuous functions
OFP due Mon 12/6 @ midnight Book Review due Monday 12/6 @ midnight |
12/7 |
6.7 The Weierstrass Approximation Theorem
PS #7 (not collected) |
12/9 |
6.7 The Weierstrass Approximation Theorem (continued)
Cheat Sheet for Exam 3 due @ 8:00 am |
| Finals Period | 12/14 | 12/16 | Exam 3 due Thursday 12/16 @ midnight |