Date |
Topic |
Reading Assignments |
Homework Assignments |
* |
| Monday, January 18 |
Note: Class meets 9:50-10:30 due to MLK day of dialogue.
Course Procedures and Policies
Thought Experiment |
Note to the Student
Chapter 0 |
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| Wednesday, January 20 |
Statements, Predicates and Quantifiers |
Sections 1.2-1.5 |
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| Friday, January 22 |
Compound Statements and Tautology
Learning from Truth Tables handout |
Sections 1.6-1.8 and 1.13 |
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| Monday, January 25 |
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. |
| Wednesday, January 27 |
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 from Learning from Truth Tables handout.
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| Friday, January 29 |
Sets and Set Notation
Subsets |
Sections 2.1-2.2 |
2.2.2, 2.2.4 and
Problem 1.
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| Monday, February 1 |
Set Operations |
Section 2.3 |
Turn in write-up of Problem 10 on the Practicing Proofs worksheet.
(Exercises, of course) and problems 2,3. Think hard about indexing sets. |
| Wednesday, February 3 |
The Algebra of Sets |
Section 2.4 to bottom of pg. 49. |
(Exercises, ALWAYS) and 2.4.8. |
| Friday, February 5 |
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)) |
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| Monday, February 8 |
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, February 10 |
Introduction to LaTeX |
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| Friday, February 12 |
In-Class Midterm #1 |
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| Monday, February 15 |
Introducing Power Sets |
Section 2.5 (again!) |
Write-ups due for 2.4.5(2) and 2.4.9(2)
2.5.4
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| Wednesday, February 17 |
Power Sets, cont.
Introduction to Mathematical Induction |
Section 3.1 |
2.5.5, Problem 8ab (Part c will be written up to turn in.) |
| Friday, February 19 |
Using Mathematical Induction |
Section 3.2 |
3.2.2, 3.2.5, 3.2.6
(To write up: 3.2.3, 3.2.4.)
Write-up of problem 8(c) (Chapter 2) and LaTeX assignment due |
| * |
| Monday, February 22 |
Introduction to Complete Induction |
Section 3.3 |
3.3.4
Write-ups of problem 3.2.3 and 3.2.4 due.
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| Wednesday, February 24 |
Finish Complete induction
Getting serious about using induction.
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3.3.3
(To write up: 3.3.2 and handout problems.)
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| Friday, February 26 |
Mathematical Induction---a work day. |
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| Monday, February 29 |
Relations |
Section 4.1 |
Problem 4.1.10, and problems 2 and 3 at the end of the chapter. |
| Wednesday, March 2 |
Introduction to Orderings---class work day. |
Section 4.2 through 4.2.18 |
Concentrate on definitions and examples
Induction Worksheet due. |
| Friday, March 4 |
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. |
Spring Break
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| Monday, March 21 |
Least upper bounds and the Least Upper Bound Property |
Rest of Section 4.2 |
4.2.22.
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| Wednesday, March 23 |
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, March 25 |
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, March 28 |
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, March 29.) |
| Wednesday, March 30 |
Equivalence classes and equivalence relations; 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, April 1 |
Functions---the basic ideas |
Section 5.1 |
Write-ups due for 4.2.25, 4.2.26. |
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| Monday, April 14 |
Functions---continued |
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5.1.13 & Problems 1acde, 2a, and 4.
(To write up: problems 1b, 2d, 3, and 5ab.) |
| Wednesday, April 6 |
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, April 8 |
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, April 11 |
Finish one-to-one and onto.
Composition of functions.
Inverse functions.
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Section 5.3 |
Write-ups due of Chapter 5 problems 1b, 2d, 3, and 5ab. |
| Wednesday, April 13 |
Inverse image of a set under a function.
Considering language for problem 5c (and various other friends.) |
Read relevant parts of section 5.2, again.
Section 5.3
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Group problems: 5.3.6.
((Theorem 5.2.9 and Problems 5c, 6, 9 and 15 will be written up)
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| Friday, April 15 |
Image of a set under a function. |
Section 5.3, again! |
Everyone: Extra exercise (handout)
Everyone: 5.3.12(1)
Group problems: 5.2.10, #7, 5.3.11, 5.3.12(2)
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| Monday, April 18 |
In-Class Midterm #2 |
| Wednesday, April 20 |
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, April 22 |
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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| Monday, April 25 |
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, April 27 |
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, April 29 |
Presentations on countability |
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Problems assigned to specific groups. |
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| Monday, May 2 |
Uncountable sets---discussion of
Cantor's diagonalization argument. |
Section 7.4 |
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| Wednesday, May 4 |
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, May 6 |
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.) Your take-home exam will ask you for some specific reading reflections and questions. We will use these to spark the discussion. |
Theorem 7.4.8 |
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Final Examination
Tuesday, May 10, 2016 from 10:30-11:30
Roundtable discussion
Comparing Cardinalities and the Continuum Hypothesis
This will constitute 10% of the grade on the Final Exam.
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