Date |
Topic |
Reading |
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| Friday, August 29 |
Introduction to the Real Number system---The Field Axioms |
Sections 1.1 & 1.2 |
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Monday, Sept. 1 |
Field Axioms, cont. |
Sections 1.1 & 1.2 (again); be sure to work on the exercises as you work through the section!
Excursion A---first pass |
Class: Problems 3 & 5 in section 1.2 |
Wednesday, Sept. 3 |
The Order Axioms |
Section 1.3 |
Class: Exercises
1.3.1. (assigned in groups)
Notebooks: Problems 4, 5, 8, & 9(cde) in section 1.3. (Note: you may not use Thm. 1.3.6. on problems 4 and 5. Prove from the definitions.) |
Friday, Sept. 5 |
The Order Axioms (cont.) |
Excursion A---second pass. |
Class: Problem 10 in section 1.3 (assigned in groups)
Notebooks: Problems 11 and 12 in section 1.3 |
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Monday, Sept. 8 |
Absolute values and order, continued |
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Wednesday, Sept. 10 |
The Least Upper Bound Property |
Section 1.4 through Theorem 1.4.7. |
Class: Problems 1 and 2 in section 1.4.
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Friday, Sept. 12 |
The Least Upper Bound Property |
Rest of Section 1.4 (proof of Theorem 1.4.8 is optional) |
Notebook problems collected (through 1.3)
Class: Problem 8 in section 1.4. Use the handout as a guide to thinking about this problem. Prove what you can.
Notebooks: Problems 3, 6 and 8cde in section 1.4 |
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Monday, Sept. 15 |
Measuring Distances |
Read Section 2.1 |
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| Wednesday, Sept. 17 |
Intro to Image Processing--a class laboratory. |
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Work through Maple lab on gradients and handout on signal noise. |
| Friday, Sept. 19 |
Distances (cont.) |
Section 2.2 |
Class: Graph metric problem from Handout.
Problem 2 in Chapter 2.
Notebooks: Problems 4, 5, and 6 in Chapter 2. |
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Monday, Sept. 22 |
Open Sets |
Section 3.1 |
Class: Problems 1 (1 implies 2 and 2 implies 3, only), 3, and 4 in Section 3.1. |
Wednesday, Sept. 24 |
Open Sets |
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Class: Problems 7(abc), 10, 11 in Section 3.1. |
Friday, Sept. 26 |
Open Sets (cont.) |
* |
Notebooks: Problems 1 (3 implies 1) 2, 6, 7(d), and 8, 12(abcde) in Section 3.1.
Notebooks problems Chpt 2 due. |
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Monday, Sept. 29 |
Finish with Open Sets
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Introducing sequences
. |
Section 0.4 through Exercise 0.4.12 |
Class: Problem 1 in 0.4
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Friday, October 3 |
Finish sequences
Introducing Convergence of Sequences |
Sections 3.2 and 3.3 |
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Monday, October 6 |
Convergence of Sequences |
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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.) Notebooks problems on Sections 3.1 due |
Wednesday, October 8 |
No class. Prof. Schumacher out of town. |
Friday, October 10 |
No class---October Break!
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Monday, October 13 |
Convergence of Sequences---Continue Class presentations |
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Class: Problems 4 and 7 in Section 3.3.
Notebooks: Problems 5, 6, and 8 in Section 3.3. |
Wednesday, October 15 |
Sequences in R |
Section 3.4 |
Class: Problems 4, 7 in Section 3.4.
Notebooks: Problems 5 & 9 (cases 4 and 5, only) in Section 3.4 |
Friday, October 17 |
Sequences in R, cont.
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Notebooks problems collected on Section 3.3. |
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Monday, October 20 |
Sequential Limits in R and R^n |
Excursion D |
Work on Class Problems: 1, 2(b), & 3 in Excursion D. |
Wednesday, October 22 |
Finish --- Sequential Limits in R and R^n
Limit Points and Closed Sets |
Sections 3.5 and 3.6
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Class: Problem 3 in Section 3.5, and Problems 2, 3, and 5 in Section 3.6
Notebooks: Problem 4 in Excursion D. |
Friday, October 24 |
In class midterm
Takehome Midterm
distributed |
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Monday, October 27 |
Image processing and Cauchy sequences--an in-class laboratory experience. |
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Takehome Midterm Due before 5 p.m. on Tuesday, October 28. |
Wednesday, October 29 |
Limit Points and Closed Sets, cont. |
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Notebooks: Problems 1(ab) and 4a in Section 3.5. And Problems 4 and 8 in Section 3.6 |
Friday, October 31 |
Open sets, closed set, and the closure of a set--- an introduction and work day |
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Notebooks problems collected from Sections 3.4 and Excursion D. |
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Open sets, closed set, and the closure of a set---class presentations |
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Class: Problems 4 & 5ab in Section 3.7.
Notebooks: Section 3.7:.Problems 1, 5c, and 6. |
Wednesday, November 5 |
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.
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Friday, November 7 |
Continuity |
Section 4.3 |
Class: Problems 1, 2, and 4 in Section 4.3.
Notebooks problems collected from Sections 3.5, 3.6 and 3.7. |
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Monday, November 10 |
Finish Continuity |
Section 4.4 |
Notebooks: Problems 6a & 9 in Section 4.3.
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Wednesday, November 12 |
Uniform Continuity |
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Class: Problems 1 and 2 in Section 4.4
Notebooks: Problems 3 and 4 in Section 4.4. |
Friday, November 14 |
Uniform continuity, cont. |
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Monday, November 17 |
Work Day on real-valued functions |
Sections 5.1 & 5.3
Excursion E |
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 |
Wednesday, November 19 |
More work on real-valued functions. |
Read sections 5.1 and 5.3 and Excursion E again! |
Notebook problems collected on Sections 4.2, 4.3, and 4.4. |
Friday, November 21 |
Completeness---just a taste
|
Sections 6.1 and 6.2. |
Class: Problem 1 in Section 6.1
Notebooks: Problem 3 in Section 6.1 and Problem 1 in Section 6.2 |
Thanksgiving Break |
Monday, December 1 |
Introducing Compactness |
Section 7.1 |
Class: Carefully think through Example 7.1.2. Work throught Exercise 7.1.5 |
Wednesday, December 3 |
Compactness, continued.
Continuity and compactness |
Section 7.2 |
Notebook problems collected on Sections 5.1, 5.3, Excursion E, Chapter 6.
Class: Problems 3 and 5 in Section 7.1. Problem 3 in Section 7.2.
Notebooks: Problems 6 &14 in Section 7.1. Problems 2 & 5 in Section 7.2. Without proving problem 4, comment on the result. What does it tell you? Why is this significant? |
Friday, December 5 |
Finish with Continuity and compactness |
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Class problems assigned to groups. |
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The Heine Borel Theorem. |
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Work on notebook problems! |
Wednesday, December 10 |
Sequences of Functions |
Sections 12.1 and 12.2. |
Notebook problems on Sections 7.1 and 7.2. due by 5 pm.
Class: Problems 2, 3, 4, 5 in Section 12.2 (assigned in groups for presentation on this day.)
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Friday, December 12 |
Sequences of Functions---cont. |
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Class: Problems 6, 10(ab) and 11(bc) in Section 12.2
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Final Examination
In-Class Exam: Thursday, December 18, 2014 from 1:30-4:30
Takehome exam: Distributed the last day of class and Due at the time of the In-class exam. |