Date |
Topic |
Reading Assignment |
Homework Problems |
| |
| Monday, January 16 |
Course Procedures and Policies
Introducing Real Analysis
|
A Note to the Student (xxi)
What is Analysis? and
The Role of Abstraction
pgs. 3-6 |
** |
| Wednesday, January 18 |
The Field Axioms |
Sections 1.1 & 1.2 |
Class: Exercises and Problems 3 & 5 in section 1.2---assigned in groups.
|
| Friday, January 20 |
The Order Axioms |
Section 1.3 |
Class: Exercise 1.3.1.
Notebooks: Problems 4, 5 8, & 9(bf) in section 1.3. (Note: you cannot use Thm. 1.3.6. on problems 4 and 5. Prove from the definitions.) |
| * |
| Monday, January 23 |
The Order Axioms (cont.) |
Excursion A |
Class: Problem 10 in section 1.3
(Parts assigned individually to students)
Notebooks: Problems 11 and 12 in section 1.3 |
| Wednesday, January 25 |
The Least Upper Bound Property |
Section 1.4 through theorem 1.4.7. |
Class: Problems 1 and 2 in section 1.4. |
| Friday, January 27 |
The Least Upper Bound Property |
Rest of Section 1.4 (proof of Theorem 1.4.8 is optional) |
Class: Problem 8 in section 1.4.
Notebook problems collected (through 1.3) |
| * |
| Monday, January 30 |
The Least Upper Bound Property
|
* |
Notebooks: Problems 4 & 6 in section 1.4 |
| Wednesday, February 1 |
QUIZ #1---Thm. 1.4.4
Distances |
Section 2.1 |
Class: Problems 1, 2, & 3 in Chapter 2. |
| Friday, February 3 |
Distances (cont.) |
Section 2.2 |
Notebooks: Problems 4 and 5 in Chapter 2. |
| * |
| Monday, February 6 |
Open Sets |
Section 3.1 |
Class: Problems 1, 3, and 4 in Section 3.1. |
| Wednesday, February 8 |
Open Sets |
|
Class: Problems 7(abc), 10, 11 in Section 3.1. |
| Friday, February 9 |
Open Sets (cont.) |
* |
Notebooks: Problems 2, 6, 7(d), and 8, 12(abcde) in Section 3.1.
Notebooks problems collected (Section 1.4 and Chpt 2) |
| * |
| Monday, February 13 |
Finish with Open Sets
Introducing Sequences |
Section 0.4 through Exercise 0.4.12 |
|
| Wednesday, February 15 |
Finish Sequences
Introducing Convergence of Sequences.
|
Sections 3.2 and 3.3 |
Class: Problem 1 in 0.4
|
| Friday, February 17 |
Convergence of Sequences |
|
Notebooks problems collected on Sections 3.1 |
| * |
| Monday, February 20 |
Convergence of Sequences---Class presentations |
|
Class: Problem 1, 2, 3 in Section 3.3 and Problem 2 in Section 3.4. (Note, you do not need to read Section 3.4 to do problem 2! It's just a good convergent sequence problem.) |
| Wednesday, February 22 |
Convergence of Sequences---Continue Class presentations |
|
Class: Problems 4 and 7 in Section 3.3.
Notebooks: Problems 5, 6, and 8 in Section 3.3. |
| Friday, February 24 |
Convergence of Sequences---Finish Class presentations
|
* |
|
| * |
| Monday, February 27 |
QUIZ #2---Thm. 3.3.7
Sequences in R |
Section 3.4 |
Notebooks problems collected on Section 3.3. |
| Wednesday, February 29 |
Sequences in R
|
Excursion D |
Class: Problems 4, 7 in Section 3.4.
Notebooks: Problems 5 & 9 (cases 4 and 5, only) in Section 3.4. |
| Friday, March 2 |
Sequential Limits in R and Rn |
Excursion D --- again! |
Class: Problems 1, 2(b), & 3 in Excursion D.
Notebooks: Problem 4 in Excursion D. |
Spring Break
|
| Monday, March 19 |
Limit Points and Closed Sets |
Sections 3.5 and 3.6 |
Class: Problem 3 in Section 3.5, and Problems 2, 3, and 5 in Section 3.6 |
| Wednesday, March 21 |
Limit Points and Closed Sets---cont. |
|
Notebooks: Problems 1(ab) and 4a in Section 3.5. And Problems 4 and 8 in Section 3.6 |
| Friday, March 23 |
Open sets, closed set, and the closure of a set--- an introduction and work day |
Section 3.7 |
Notebooks problems collected from Sections 3.4 and Excursion D. |
| * |
| Monday, March 26 |
Open sets, closed set, and the closure of a set---class presentations |
|
Class: Problems 4 & 5ab in Section 3.7.
Notebooks: Section 3.7:.Problems 1, 5c, and 6. |
| Wednesday, March 28 |
Limit of a function at a point---a work day. |
Sections 4.1 and 4.2 |
Class: Problem 1 in Section 4.2.
Notebooks: Problem 2 in section 4.2.
Notebooks problems collected from Sections 3.5, 3.6 and 3.7. |
| Friday, March 30 |
Continuity
Takehome Midterm Distributed
Midterms will cover material through section 3.7. |
Section 4.3 |
Class: Problems 1, 2, and 4 in Section 4.3. |
| * |
| Monday, April 2 |
In-Class Midterm
Will include a request to prove theorem 3.5.1---this will count as Quiz #3.
|
| Wednesday, April 4 |
Carol out of town---class will not meet. |
| Friday, April 6 |
Finish Continuity and introduce Uniform Continuity |
Section 4.4 |
Notebooks: Problems 6 & 9a in Section 4.3.
Takehome Midterm Due |
| * |
| Monday, April 9 |
Finish Uniform Continuity |
|
Class: Problems 1 and 2 in Section 4.4
Notebooks: Problems 3 and 4 in Section 4.4. |
| Wednesday, April 11 |
Work Day on real-valued functions |
Sections 5.1 & 5.3
Excursion E |
|
| Friday, April 13 |
QUIZ #4---Thm. 4.3.5
Discussion: some interesting questions. |
|
Notebooks: Problem 6 in Section 5.1. Problems 1, 2, and 3 in Section 5.3.
Problems 1(a,c,e) in Excursion E.2
Notebook problems collected on Sections 4.2, 4.3, and 4.4. |
| * |
| Monday, April 16 |
Introducing Compactness |
Section 7.1 |
Class: Carefully think through Example 7.1.2. Work throught Exercise 7.1.5 and Problem 5 in Section 7.1. |
| Wednesday, April 18 |
Continuity and compactness |
Section 7.2 |
Class: Problem 3 in Section 7.1. Problems 3 and 5 in Section 7.2.
Notebooks: Problems 6, 14, & 15 in Section 7.1. Problems 2 & 4 in Section 7.2. |
| Friday, April 20 |
Finish continuity and compactness
|
|
Notebook problems collected on Sections 5.1, 5.3 and Exc E.2. |
| * |
| Monday, April 23 |
Completeness---just a taste
|
Sections 6.1 and 6.2. |
Notebooks: Problem 3 in Section 6.1. |
| Wednesday, April 25 |
The Heine Borel Theorem---(lecture) |
|
|
| Friday, April 27 |
Sequences of Functions |
Sections 12.1 and 12.2. |
Class: Problems 2, 3, 4, 5 in Section 12.2 (assigned to pairs)
Notebook problems collected on Sections 7.1, 7.2 and 6.1 . |
| * |
| Monday, April 30 |
Sequences of Functions---cont. |
* |
Class: Problems 6, 10(ab) and 11(bc) in Section 12.2
Notebooks: Problems 7, 9, 10(cd), and 11(de) in Section 12.2. |
| Wednesday, April 2 |
Interchange of Limit Operations |
Section 12.4 through the bottom of page 251. |
Class: Problems 2 & 4(a) in Section 12.4. |
| Friday, May 4 |
Term-by-term differentiation of sequences of Functions.
Takehome Final Exam Distributed! |
Section 12.4; proof of Theorem 12.4.4. |
Notebooks problem collected on section 12.2.
|
| |
Final Examination
Takehome exam due at beginning of in-class exam
1:30 p.m. on Tuesday, May 8
In-class will include Quiz #5 on 7.1.6 and 7.1.8
|