Date |
Topic |
Reading Assignment |
Homework Problems |
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| Friday, August 26 |
Course Procedures and Policies
Thought Experiment |
Note to the Student
Chapter 0 |
** |
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Monday, August 29 |
Mathematical Statements |
Sections 1.2-1.6 |
Discussion Problems 1, 5, 6.
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Wednesday, August 31 |
Tautology & Mathematical Arguments
Negation
Rules of Inference |
Sections 1.7-1.9 |
Turn-in Problems---Chapter 1: 7, 9abe, 11adf
Discussion Problems--- Chapter 1: 2, 8, 10, 13, 14 |
| Friday, Sept. 2 |
Reasoning and Proof |
Sections 2.1-2.4 |
Discussion Problems---All exercises and propositions in these sections. |
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Monday, Sept. 5 |
Reasoning and Proof---cont |
Sections 2.5-2.7 |
Discussion Problems---All exercises and propositions in these sections. |
Wednesday, Sept. 7 |
Reasoning and Proof---cont. |
Re-read parts of Chapter 2 with great care. Pay attention to details! |
Finish proofs and exercises from Chapter 2. |
Friday, Sept. 9 |
Sets, Subsets and Set Operations. |
Sections 3.1-3.2 and Section 3.3 through the middle of page. 61. |
Turn-in Probs---Chapter 2; 1, 3, 6.
Discussion Probs---Theorem 3.2.3, Proposition 3.2.5, Problems 1-6 in Chapter 3. |
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Monday, Sept. 12 |
Set Algebra |
Rest of Section 3.3 and 3.4 |
Theorems 3.3.10 and 3.3.13. Problems 11 and 12. |
| Wednesday, Sept. 14 |
Introduction to LaTeX |
| Friday, Sept. 16 |
Set Algebra, cont. |
Read Section 3.4 again! |
Theorems 3.4.6(1,2) and 3.4.7 (Parts 2 of each will be written up to turn in.) |
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Monday, Sept. 19 |
Finish Set Algebra
Power Sets |
Section 3.5 |
Theorems 3.5.4 and 3.5.5 and Problem 22. For practice with the definitions, also work on Problems 16, 17, 18. (Part c of 22 will be written up to turn in.) |
| Wednesday, Sept. 21 |
Finish Power Sets. |
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Friday, Sept. 23 |
Introduction to Mathematical Induction |
Sections 4.1 and 4.2 |
Parts 2 of Theorems 3.4.6 and 3.4.7 are due. (LaTeX'd) |
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Monday, Sept. 26 |
Using Mathematical Induction and Complete Induction |
Section 4.3 |
Presentation: Problems 1, 5 (and exercises!)
Write-up to turn in: Problem 2 (due today!)
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Wednesday, Sept. 28 |
Induction continued |
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Parts c of problem 22 (Chapter 3) due. (LaTeX'd)
Keep working on presentation problems! |
Friday, Sept. 30 |
Mathematical Induction----a work day. |
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Write-up to turn in: Problem 11. (Due today!)
Problems 3, 4, 6, 9, 10, and either (choose) 7 or 8 will be written up to turn in. |
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Relations |
Section 5.1-5.2 |
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Wednesday, October 5 |
Introduction to Orderings---class work day. |
Section 5.3 through theorem 5.3.20 |
Induction Problems due---at least three must be LaTeX'd. |
Friday, October 7 |
No Class---October Reading Days
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Monday, October 10 |
Orderings, cont.
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Re-read Section 5.3 through theorem 5.3.20. |
Theorems 5.3.15, 5.3.16 and 5.3.20; Problems 10 and 11. |
Wednesday, October 12 |
Finish Orderings
Introduction to Least Upper Bounds. |
Rest of Section 5.3 |
Problem 12. |
Friday, October 14 |
Least Upper Bounds and the Least Upper Bound Property. |
Re-read rest of Section 5.3 |
Theorem 5.3.24
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Monday, October 17 |
From relations to sets and back---work day! |
Section 5.4 through Corollary 5.4.17 |
Theorem 5.4.8 (Lemma 5.3.27 and Theorem 5.3.28 will be written up to turn in. You should do some serious preliminary thinking about these before the midterm.) |
Wednesday, October 19 |
Equivalence relations
Takehome Midterm Distributed! |
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Theorems 5.4.15, 5.4.16 and Corollary 5.4.17. |
Friday, October 21 |
In-Class Midterm |
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Monday, October 24 |
Equivalence relations, a work day. Takehome Midterm Due Tuesday October 25th at 5 p.m! |
Rest of Section 5.4 |
Lemma 5.4.20 and Theorem 5.4.21 will be written up to turn in. (We will work on these in class.) |
Wednesday, October 26 |
Introduction to Functions |
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Friday, October 28 |
Functions |
Section 6.1-6.2 through pg. 119 |
Exercises and ideas in class. |
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Monday, October 31 |
Class workday on functions---group assignments. |
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Lemma 5.3.27, Theorem 5.3.28, Lemma 5.4.20 and Theorem 5.4.21 are due. ( At least two of these must be LaTeX'd) |
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Composition and Inverses---composition and one-to-one/onto functions |
Section 6.2 |
ALL: 6.1.13, 1 bd
GPs: 6.2.3, 6.2.4
Write-up: 2d, 3 (due later, but start now!)
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Friday, November 4 |
Composition and one-to-one/onto functions |
Section 6.2 (again!) |
ALL: 4
GPs: 6.2.3(2), 6.2.4
Write-up: 5, 6 (due later, but start now!) |
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Monday, November 7 |
Finish Composition and one-to-one/onto functions
Inverses of functions
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GPs: 6.2.7
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Wednesday, November 9 |
Finish Inverses
Images, Inverse Images and Set Theory. |
Section 6.3 |
GPs: 6.3.6, 6.3.11
Problems 2d, 3, 5, 6 due! (LaTeX two of them.) |
Friday, November 11 |
Finish Images and Inverse Images |
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ALL: 9ab
GPs: , 6.3.12(1)
Write-up: 6.3.12(2)(due later, but start now!) |
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Monday, November 14 |
Finish Group Presentations
Galileo's Paradox and infinity
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ALL: 15.
Write-up: Problems 9cd and 16 (due later, but start now!) |
Wednesday, November 16 |
Introduction to Cardinality |
Section 8.1 |
Theorems 8.1.3 and 8.1.6 (and all exercises) |
Friday, November 18 |
What is an infinite set? |
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6.3.12(2), Problems 9cd, 15, and 16 due! (LaTeX at least one.) |
Thanksgiving Break |
Monday, Nov. 28 |
Presentations Section 8.2
Work day on Countable Sets |
Section 8.2 and Section 8.3---as you read think about the theorems in 8.3---what do they say? What do they tell us about countable sets? |
Corollaries 8.2.6 and 8.2.7;
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Wednesday, Nov. 30 |
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Monday, December 5 |
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Wednesday, December 7 |
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Friday, December 9 |
Takehome Final Distributed! |
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Final Examination
Takehome exam due at the time of the Inclass exam which is on
Tuesday, December 13, 2011 from 8:30 to 11:30 a.m
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