Date |
Topic |
Reading Assignments |
Homework Assignments |
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| Monday, January 18 |
Note: Class meets 10:40-11:20 due to MLK day of dialogue.
Course Procedures and online information.
Introduction to the Real Number system---The Field Axioms |
Sections 1.1 & 1.2 |
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| Wednesday, January 20 |
Field Axioms, cont. |
Excursion A |
Class: Problems 3 & 5 in section 1.2--- assigned in groups. |
| Friday, January 22 |
The Order Axioms |
Section 1.3 |
Class: Finish problems we were working on in class. Think about hard about Exercise 1.3.1.
Notebooks: Problems 4, 5, 8, & 9(cde) in section 1.3. (Note: you cannot use Thm. 1.3.6. on problems 4 and 5. Prove from the definitions.) |
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| Monday, January 25 |
The Order Axioms (cont.) |
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Class: Problem 10 in section 1.3
Parts 1,6, 8: Everyone. Parts 2, 3, 4, 5, 7: assigned in groups.
Notebooks: Problems 11 and 12 in section 1.3 |
| Wednesday, January 27 |
Absolute values and order, continued |
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| Friday, January 29 |
The Least Upper Bound Property |
Section 1.4 through theorem 1.4.7. |
Class: Problems 1 and 2 in section 1.4.
Notebook problems collected (through 1.3) |
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| Monday, February 1 |
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. Use the handout as a guide to thinking about this problem. Prove what you can.
Notebooks: Problems 3 and 6 in section 1.4
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| Wednesday, February 3 |
Measuring Distances |
Read Section 2.1 |
Class: Problems 1, 2, & 3 in Chapter 2.
Notebook Problems: 4 & 5 in Chapter 2. |
| Friday, February 5 |
Intro to Image Processing--a class laboratory. |
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Take online survey (see link in email)
Work through handout on image processing. |
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| Monday, February 8 |
Distances (cont.) |
Section 2.2 |
Notebook problems 3 & 6 from Section 1.4 due.
Notebooks: Problems 4 and 5 in Chapter 2. |
| Wednesday, February 10 |
Open Sets |
Section 3.1 through page 74. Pay careful attention to Theorem 3.1.7: Understand what it says; draw pictures that show the relationships. |
Notebook problems 4 & 5 in Chpt 2 due.
Class: Problems 3, and 4 in Section 3.1. |
| Friday, February 12 |
InClass Midterm # 1
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| Monday, February 15 |
Open Sets (cont) |
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Class: Problems 1 and 7(abc) in Section 3.1. |
| Wednesday, February 17 |
Open Sets and boundedness |
* |
Class: Problems 10 and 11 in Section 3.1.
Notebooks: Theorem 3.1.7 (3 implies 1) and Problems 2, 6, 7(d), and 8, 12(abcde) in Section 3.1.
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| Friday, February 19 |
Introducing sequences |
Section 0.4 through Exercise 0.4.12 |
Class: Problem 1 in 0.4
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| * |
| Monday, February 22 |
Introducing Convergence of Sequences |
Sections 3.2 and 3.3 |
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| Wednesday, February 24 |
Work day on convergence of sequences |
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Notebooks problems on Sections 3.1 due |
| Friday, February 26 |
Convergence of Sequences---Class presentations |
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Class: Problem 1, 2, 3, 4 and 7 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 5, 6, and 8 in Section 3.3.
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| Monday, February 29 |
Convergence of Sequences---Finish Class presentations from 3.3 |
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You should be working on the notebook problems for 3.3. so you can ask questions before break. |
| Wednesday, March 2 |
Sequences in R---a work day. (Problems 4 and 7 in Section 3.4 worked on in class.) |
Section 3.4 |
Be sure you are working on the Notebook problems from Section 3.3! |
| Friday, March 4 |
Finish sequences in R
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Section 3.4, again! Pay special attention to the proof of Theorem 3.4.11 (3) |
Notebooks: Problems 5 & 9 (cases 4 and 5, only) in Section 3.4 |
Spring Break
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| Monday, March 21 |
Sequential Limits in R and R^n---a work day. (Work on problems 1, 2(b), & 3 in Excursion D.) |
Excursion D |
Notebooks problems on Section 3.3 and 3.4 due by 5 p.m. on Tuesday, March 22. |
| Wednesday, March 23 |
Finish --- Sequential Limits in R and R^n |
Excursion D... again! |
Notebooks: Problems 2(ac) & 4 in Excursion D. |
| Friday, March 25 |
Limit Points and Closed Sets
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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
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| Monday, March 28 |
Finish Limit Points and Closed Sets.
Introducing Open sets, Closed sets, and the Closure of a set.
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Sections 3.5 and 3.6
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Notebooks: Problems 1(ab) and 4a in Section 3.5. And Problems 4 and 8 in Section 3.6
Notebook problems collected from Excursion D. |
| Wednesday, March 30 |
Open sets, closed set, and the closure of a set
Takehome Midterm
distributed |
Section 3.7 |
Class: Problems 4 & 5ab in Section 3.7.
Notebooks: Section 3.7:.Problems 1, 5c, and 6. |
| Friday, April 1 |
Image processing and Cauchy sequences--an in-class laboratory experience. |
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Takehome Midterm Due before 5 p.m. on Sunday, April 3. |
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| Monday, April 4 |
Finish open sets, closed set, and the closure of a set---class presentations
Cauchy Sequences and completeness, just a taste.
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| Wednesday, April 6 |
Limit of a function at a point |
Sections 4.1 and 4.2, Excursion E |
Class: 4th Property of Cauchy sequences (handout).
And problem 1 in Section 4.2.
Notebooks: Problems 1 and 2 in Section 6.2. Problem 2 in section 4.2.
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| Friday, April 8 |
Limits of real valued functions on R. |
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Notebooks problems collected from Sections 3.5, 3.6 and 3.7. |
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| Monday, April 11 |
Continuity |
Sections 4.3 |
Class: Problems 1, 2, and 4 in Section 4.3.
Notebooks: Problems 6a & 9 in Section 4.3.
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| Wednesday, April 13 |
Uniform Continuity |
Section 4.4 |
Class: Problems 1 and 2 in Section 4.4
Notebooks: Problems 3 and 4 in Section 4.4. |
| Friday, April 15 |
Uniform continuity, cont. |
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Class: Problem 3 in Section 6.1.
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| Monday, April 18 |
Work Day on real-valued functions |
Sections 5.1 & 5.3 |
Notebooks: Problem 6 in Section 5.1. Problems 1, 2, and 3 in Section 5.3. |
| Wednesday, April 20 |
More work on real-valued functions.
Introducing Compactness. |
Section 7.1 |
Notebook problems collected on Sections 6.2, 4.2, 4.3, and 4.4. |
| Friday, April 22 |
Compactness, continued. |
Section 7.1, again! |
Class: Problems 1, 2, 4 and 5 in Section 7.1. |
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| Monday, April 25 |
In-Class Midterm #2 |
| Wednesday, April 27 |
Compactness, continued.
Continuity and compactness |
Section 7.2 |
Class Problems: 11 in Section 7.1 and Problems 2 and 3 and in Section 7.2.
Notebooks: Problems 6 &14 in Section 7.1. Problems 4 & 5 in Section 7.2. |
| Friday, April 29 |
The Heine Borel Theorem. |
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Notebook problems collected on Sections 5.1 and 5.3.
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| Monday, May 2 |
Sequences of Functions |
Sections 12.1 and 12.2. |
Make sure to work on the notebook problems!
Class: Problems 2, 3, 4, 5 in Section 12.2 |
| Wednesday, May 4 |
Sequences of Functions---cont. |
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Class: Problems 6, 10(ab) and 11(bc) in Section 12.2
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| Friday, May 6 |
Exchanging the order of limiting processes..
Takehome Final Distributed. |
In preparation read, for big picture, Section 12.4. |
To turn in: Reading response on Section 12.4.---Will be used as the basis for roundtable discussion at the final.
Notebook problems on Sections 7.1 and 7.2. due.
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Takehome Final Exam due at 10:30 a.m. on Thursday, May 12.
Roundtable discussion
Switching the order of two limiting processes
This will constitute 10% of the grade on the Final Exam.
Thursday, May 12, 2016 from 10:30-11:30
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