Date |
Topic
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Reading Assignment |
Homework |
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| Friday, August 28 |
Course Procedures and Policies
Thought Experiment |
Note to the Student
Chapter 0 |
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Monday, Aug. 31 |
Statements, Predicates and Quantifiers |
Sections 1.2-1.5 |
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Wednesday, Sept. 2 |
Compound Statements and Tautology
Learning from Truth Tables handout |
Sections 1.6-1.8 and 1.13 |
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Friday, Sept. 4 |
Practicing Proof Techniques handout |
Sections 1.9-1.12 and 1.14-1.15
Authority in Proof handout |
Do warm-up Exercises and Problems 6a and 7a on Practicing Proof Techniques Handout. |
8 |
Monday, Sept. 7 |
Reasoning and Proof: Class presentations and discussion of Selected Proofs from the Practicing Proof Techniques handout. |
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Hand in group write-ups of exercises 3 and 4 on Learning from Truth Tables handout.
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Wednesday, Sept. 9 |
Sets and Set Notation
Subsets |
Sections 2.1-2.2 |
2.2.2, 2.2.4 and
Problem 1.
Turn in write-up of Problem 10 on the Practicing Proofs worksheet. |
Friday, Sept. 11 |
Set Operations |
Section 2.3 |
(Exercises, of course) and problems 2,3. Think hard about indexing sets.
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Monday, Sept. 14 |
The Algebra of Sets |
Section 2.4 to bottom of pg. 49. |
(Exercises, ALWAYS) and 2.4.8. |
| Wednesday, Sept. 16 |
The Algebra of Sets (cont.) |
Rest of Section 2.4 |
2.4.5, 2.4.9
(To write up: 2.4.5(2) and 2.4.9(2)) |
| Friday, Sept. 18 |
Introduction to LaTeX |
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Monday, Sept. 21 |
Finish The Algebra of Sets
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Section 2.5 |
2.4.5(1), 2.4.9(1), 2.5.5 (2) |
Wednesday, Sept. 23 |
Introducing Power Sets |
Section 2.5 (again!) |
2.5.4, 2.5.5 (1), Problem 8ab (Part c will be written up to turn in.)
Write-ups due for 2.4.5(2) and 2.4.9(2) |
Friday, Sept. 25 |
In-Class Midterm #1 |
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Monday, Sept. 28 |
Power Sets, cont.
Introduction to Mathematical Induction |
Section 3.1 |
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Wednesday, Sept. 30 |
Using Mathematical Induction |
Section 3.2 |
3.2.2, 3.2.5, 3.2.6
(To write up: 3.2.3, 3.2.4.) |
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Introduction to Complete Induction |
Section 3.3 |
3.3.4
Write-up of problem 8(c) (Chapter 2) due
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Monday, October 5 |
Finish Complete induction
Getting serious about using induction.
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3.3.3
(To write up: 3.3.2 and handout problems.)
Write-ups of problem 3.2.3 and 3.2.4 due. |
Wednesday, October 7 |
Mathematical Induction---a work day. |
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Friday, October 9 |
No class---October Break |
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Monday, October 12 |
Relations |
Section 4.1 |
Problem 4.1.10, and problems 2 and 3 at the end of the chapter. |
Wednesday, October 14 |
Introduction to Orderings---class work day. |
Section 4.2 through 4.2.18 |
Concentrate on definitions and examples
Induction Worksheet due. |
Friday, October 16 |
Orderings---maximal/minimal elts, etc.
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Section 4.2 throught 4.2.18 (again!) |
4.2.14, 4.2.15, 4.2.18. |
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Monday, October 19 |
Least upper bounds and the Least Upper Bound Property |
Rest of Section 4.2 |
4.2.22.
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Wednesday, October 21 |
Work day on problems 4.2.25 and 4.2.26
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Be able to explain what 4.2.25 and 4.2.26 are saying. (To be written up.)
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Friday, October 23 |
From relations to sets and back
Takehome midterm distributed
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Section 4.3 (through pg. 81) . |
4.3.8 and problems on pgs 80-81. |
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Monday, October 26 |
Equivalence relations---a work day.
4.3.15, 4.3.16, and 4.3.17 |
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(Takehome Midterm due before 5 pm on Tuesday, October 27.) |
Wednesday, October 28 |
Equivalence classes and equivalence relations; Work on Work on 4.3.20 and 4.3.21
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Rest of section 4.3 |
4.3.23
Understand and be able to explain what 4.3.20 and 4.3.21 are saying. (To be written up!)
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Friday, October 30 |
Functions---the basic ideas |
Section 5.1 |
Write-ups due for 4.2.25, 4.2.26. |
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Functions---continued |
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5.1.13 & Problems 1acde, 2a, and 4.
(To write up: problems 1b, 2d, 3, and 5.) |
Wednesday, November 4 |
One-to-one and onto
Composition |
Section 5.2 through problem 5.2.6 |
Group Problems: 5.2.3,
Write-ups due of 4.3.20 and 4.3.21 |
Friday, November 6 |
Continue work on one-to-one and onto.
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Read through rest of section 5.2 |
Group Problems: 5.2.4
Everyone: 5.2.5. |
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Monday, November 9 |
Images and inverse images
Introducing
inverse functions
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Section 5.3 |
Group problems: 5.3.6
Write-ups due of Chapter 5 problems 1b, 2d, 3, and 5ab. |
Wednesday, November 11 |
Inverse functions, cont.
Considering language for problem 5c (and various other friends.) |
Read relevant parts of section 5.2, again. |
Class Problems (everyone): 7 and 5.2.10.
(Theorem 5.2.9 will be written up.) |
Friday, November 13 |
Image of a set under a function. |
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Group problems: 5.3.11, 5.3.12(2)
Everyone: 5.3.12(1)
(Problems 6, 9 and 15 will be written up) |
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Monday, November 16 |
In-Class Midterm #2 |
Wednesday, November 18 |
Are some infinities bigger than others? Galileo's Paradox and infinite sets. |
Section 7.1 |
Theorems 7.1.3 and 7.1.5
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Friday, November 20 |
Cardinality and infinite sets---a discussion. |
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Write-ups due of Chapter 5 problems Thm. 5.2.9, 5c, 6, 7, 9, 15
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Thanksgiving Break |
Monday, November 30 |
Infinite sets---a general discussion |
Read Section 7.2 carefully for intuition.
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7.2.6, and 7.2.7--may assume 7.2.3 and 7.2.5 |
Wednesday, December 2 |
Countable sets. |
Section 7.3 |
7.3.3---for presentation.
Read and think about Theorems 7.3.4, 7.3.5, and Exercise 7.3.9---what do they say? Intuitively, why do you think they are true? |
Friday, December 4 |
Presentations on countability |
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Problems assigned to specific groups. |
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Monday, December 7 |
Uncountable sets---discussion of
Cantor's diagonalization argument. |
Section 7.4 |
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Wednesday, December 9 |
Continue discussion of uncountable sets.
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Section 7.4 (again!) |
Corollaries 7.4.4, 7.4.5, 7.4.6, and Exercise 7.4.7 |
Friday, December 11 |
Proof of generalized Cantor diagonalization Argument.
Takehome Final Distributed.
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In preparation for the "Roundtable discussion" at the time of the final, read (for big picture) 7.5 and 7.6 (Skip the proof of the Schroeder Bernstein Theorem. But think about why the result is NOT obvious.) |
Theorem 7.4.8 |
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Final Examination
Monday, December 14 at 3:30-4:30 p.m.
Roundtable discussion
Comparing Cardinalities and the Continuum Hypothesis
This will constitute 10% of the grade on the Final Exam.
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