Date |
Topic |
Reading Assignment |
Assigned Problems |
| |
Monday, January 13 |
Statements, Predicates and Quantifiers |
Sections 1.2-1.5 |
|
| Wednesday, January 15 |
Compound Statements and Tautology
Learning from Truth Tables handout |
Sections 1.6-1.8 and 1.13 |
|
| Friday, January 17 |
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. |
| * |
| Monday, January 20 |
Reasoning and Proof: Class presentations and discussion of Selected Proofs from the Practicing Proof Techniques handout. |
|
Hand in group write-ups of exercises 3 and 4 on Learning from Truth Tables handout. (See instructions after each exercise.)
Note: MLK day. Class meets from 12:20-1:00
|
| Wednesday, January 22 |
Reasoning and Proof, continued. |
Re-read Sections 1.9-1.15 |
|
| Friday, January 24 |
Sets and Set Notation
Subsets |
Sections 2.1-2.2 |
2.2.2, 2.2.4 and
Problem 1. |
| * |
| Monday, January 27 |
Set Operations |
Section 2.3 |
(Exercises, of course) and problems 2,3. Think hard about indexing sets.
Turn in write-up of Problem 10 on the Practicing Proofs worksheet. |
| Wednesday, January 29 |
The Algebra of Sets |
Section 2.4 to bottom of pg. 49. |
(Exercises, ALWAYS) and 2.4.8. |
| Friday, January 31 |
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)) |
| * |
| Monday, February 3 |
Introduction to LaTeX |
| Wednesday, February 5 |
Finish The Algebra of Sets
Introducing Power Sets |
Section 2.5 |
2.5.4, 2.5.5 |
| Friday, February 7 |
The Power Set, cont. |
Section 2.5 (again!) |
Problem 8ab (Part c will be written up to turn in.)
Write-ups due for 2.4.5(2) and 2.4.9(2) |
| * |
| Monday, February 10 |
Introduction to Mathematical Induction |
Section 3.1 |
|
| Wednesday, February 12 |
Using Mathematical Induction |
Section 3.2 |
3.2.2, 3.2.5, 3.2.6
(To write up: 3.2.3, 3.2.4.) |
| Friday, February 14 |
Introduction to Complete Induction |
Section 3.3 |
3.3.4
|
| * |
| Monday, February 17 |
Finish Complete induction
Getting serious about using induction.
|
|
3.3.3
(To write up: 3.3.2 and handout problems.)
Write-ups of problem 8(c), Chapter 2 and 3.2.3 and 3.2.4 due. |
| Wednesday, February 19 |
Mathematical Induction---a work day. |
|
|
| Friday, February 21 |
Relations |
Section 4.1 |
Problem 4.1.10, and problems 2 and 3 at the end of the chapter. |
| * |
| Monday, February 24 |
Introduction to Orderings---class work day. |
Section 4.2 through 4.2.18 |
Concentrate on definitions and examples |
| Wednesday, February 26 |
Orderings---maximal/minimal elts, etc.
|
Section 4.2 throught 4.2.18 (again!) |
4.2.14, 4.2.15, 4.2.18. |
| Friday, February 28 |
Least upper bounds and the Least Upper Bound Property |
Rest of Section 4.2 |
4.2.22.
Induction Worksheet due. |
Spring Break |
| Monday, March 17 |
Work day on problems 4.2.25 and 4.2.26
|
|
Be able to explain what 4.2.25 and 4.2.26 are saying. (To be written up.)
|
| Wednesday, March 19 |
From relations to sets and back
Takehome midterm distributed
|
Section 4.3 (through pg. 81) . |
4.3.8 and problems on pgs 80-81. |
| Friday, March 21 |
In-Class Midterm |
| * |
| Monday, March 24 |
Equivalence relations---a work day.
4.3.15, 4.3.16, and 4.3.17 |
|
(Takehome Midterm due before 5 pm on Tuesday, March 26.) |
| Wednesday, March 26 |
Equivalence classes and equivalence relations; Work on Work on 4.3.20 and 4.3.21
|
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!)
|
| Friday, March 28 |
Functions---the basic ideas |
Section 5.1 |
Write-ups due for 4.2.25, 4.2.26. |
| * |
| Monday, March 31 |
Functions---continued |
|
5.1.13 & Problems 1acde, 2a, and 4.
(To write up: problems 1b, 2d, 3, and 5.) |
| Wednesday, April 2 |
One-to-one and onto
Composition |
Section 5.2 through problem 5.2.6 |
Group Problems: 5.2.3, 5.2.4
Everyone: 5.2.5.
Write-ups due of 4.3.20 and 4.3.21 |
| Friday, April 4 |
Composition and Inverses
Introducing images and inverse images |
Rest of section 5.2 |
Class Problems (everyone): 7 and 5.2.10.
(Theorem 5.2.9 will be written up.) |
| * |
| Monday, April 7 |
Inverse image of a set under a function. |
Section 5.3 |
Group problems: 5.3.6
Write-ups due of Chapter 5 problems 1b, 2d, 3, and 5. |
| Wednesday, April 9 |
Image of a set under a function. |
More on Section 5.3 |
Group problems: 11a, 5.3.11, 5.3.12,
(Problems 6, 9 and 15 will be written up) |
| Friday, April 11 |
Continue Group Presentations |
|
|
| * |
| Monday, April 14 |
Are some infinities bigger than others? Galileo's Paradox and infinite sets. |
Section 7.1 |
Theorems 7.1.3 and 7.1.5 |
| Wednesday, April 16 |
Cardinality and infinite sets---a discussion. |
Section 7.2
Read carefully for intuition. |
7.2.6, and 7.2.7--may assume result in 7.2.3 and 7.2.5
|
| Friday, April 18 |
Infinite sets---more discussion. |
|
Write-ups due of Chapter 5 problems Thm. 5.2.9, 6, 9, 15 |
| * |
| Monday, April 21 |
Countable sets---general discussion |
Section 7.3 |
|
| Wednesday, April 23 |
Countable sets---work in groups. |
Section 7.3 |
Problems assigned to specific groups. |
| Friday, April 25 |
Presentations on countability |
|
|
| * |
| Monday, April 28 |
Uncountable sets---discussion of
Cantor's diagonalization argument. |
Section 7.4 |
|
| Wednesday, April 30 |
Continue discussion of uncountable sets.
|
Section 7.4 (again!) |
Corollaries 7.4.4, 7.4.5, 7.4.6, and Exercise 7.4.8 |
| Friday, May 2 |
Proof of generalized Cantor diagonalization Argument.
General discussion of comparing Cardinalities and the Continuum Hypothesis.
Takehome Final Distributed.
|
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.) |
Turn in reading responses for sections 7.5 and 7.6. |
| |
| |
Final Examination
1:30 p.m. on Friday, May 9, 2014 |