Date
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Topic |
Reading Assignment
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Problems |
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Course Procedures and Policies
Thought Experiment |
Note to the Student
Chapter 0 |
** |
Wednesday, January 20 |
Mathematical Statements |
Sections 1.2-1.5 |
Problems 1, 3. |
Friday, January 22 |
Compound Statements
Negation
True or False? |
Sections 1.6-1.8 |
Problem 6. |
* |
Monday, January 25 |
Methods of Proof |
Sections 1.9-1.15 |
Problems 7, 8, 9. |
Wednesday, January 27 |
Sets and Set Notation
Subsets |
Sections 2.1-2.2 |
2.2.2
Problem 1. |
Friday, January 29 |
Set Operations |
Section 2.3 |
Problems 2, 3. |
* |
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The Algebra of Sets |
Section 2.4 to bottom of pg. 48 |
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Wednesday, February 3 |
Introduction to LaTeX |
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Friday, February 5 |
The Algebra of Sets (cont.) |
Rest of Section 2.4 |
2.4.5, 2.4.8, 2.4.9
(To write up: 2.4.5(2) and 2.4.9(2)) |
* |
Monday, February 8 |
Finish The Algebra of Sets
The Power Set |
Section 2.5 |
2.5.4, 2.5.5 |
Wednesday, February 10 |
The Power Set (cont.) |
* |
Problem 8 (part (c) will be written up.)
Write-ups due for 2.4.5(2) and 2.4.9(2) |
Friday, February 12 |
Introduction to Mathematical Induction |
Section 3.1 |
* |
* |
Monday, February 15 |
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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Wednesday, February 17 |
Introduction to Complete Induction |
Section 3.3 |
Write-ups of problem 8(c), Chapter 2 and 3.2.3 and 3.2.4 due. |
Friday, February 19 |
Complete Induction |
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3.3.3.
(To write up: 3.3.2 and handout problems.) |
* |
Monday, February 22 |
Mathematical Induction---a work day. |
* |
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Wednesday, February 24 |
Relations |
Section 4.1 |
Problem 4.1.10, and problems 2, 3, and 4 at the end of the chapter. |
Friday, February 26 |
Introduction to Orderings---class work day. |
Section 4.2 (through top of pg. 75.) |
Write-ups of induction problems due. |
* |
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Orderings---maximal/minimal elements, etc.
Introduction to the Least Upper Bound |
Rest of section 4.2 |
4.2.14, 4.2.15, 4.2.18. |
Wednesday, March 3 |
The Least Upper Bound Property |
* |
4.2.22.
(To be written up: 4.2.25 and 4.2.26) |
Friday, March 5 |
From relations to sets and back---work day! |
Section 4.3 (through pg. 81) . |
4.3.8 and problems on pgs 80-81. |
Spring Break |
Monday, March 22 |
Equivalence relations |
Rest of section 4.3 |
4.3.15, 4.3.16, 4.3.17
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Wednesday, March 24 |
Work on 4.3.20 and 4.3.21
Equivalence Classes
Takehome Midterm Distributed! |
* |
4.3.23
(To be written up: 4.3.20 and 4.3.21) Write-ups due for 4.2.25, 4.2.26. |
Friday, March 26 |
In-Class Midterm |
* |
Monday, March 29 |
Takehome Midterm Due Tuesday March 30th at 5 p.m!
Defining functions |
* |
* |
Wednesday, March 31 |
Functions---the basic ideas |
Section 5.1 |
Write-ups due of 4.3.20 and 4.3.21 |
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Functions---continued |
* |
5.1.13 & Problems 1, 2a, and 4.
(To write up: problems 2bd, 3, and 5.) |
* |
Monday, April 5 |
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.
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Wednesday, April 7 |
Composition and Inverses
Introducing images and inverse images |
Rest of section 5.2 |
Group Problems: 5.2.7 and 5.2.10.
(Theorem 5.2.9 will be written up.)
Write-ups due of problems 2bd, 3, and 5; Chapter 5. |
Friday, April 9 |
Inverse image of a set under a function. |
Section 5.3 |
Group problems: 5.3.6.* |
* |
Monday, April 12 |
Image of a set under a function. |
More on Section 5.3 |
Group problems: 5.3.11, 5.3.12 and Problem #6ab.
(Problems 6c, 9 and 15 will be written up) |
Wednesday, April 14 |
Finish Section 5.3
Introduction to Cardinality and infinite sets:
Galileo's paradox. |
Section 7.1 |
Write-up due of theorem 5.2.9. |
Friday, April 16 |
Cardinality and infinite sets |
Section 7.1 (again!) |
7.1.3, 7.1.5. |
* |
Monday, April 19 |
Cardinality and infinite sets---a discussion. |
Section 7.2
Read carefully for intuition. |
7.2.6, and 7.2.7--may assume result of 7.2.5 |
Wednesday, April 21 |
Infinite sets
Countable sets---general discussion |
Section 7.3 |
Problems from 7.3 assigned in groups |
Friday, April 23 |
Countable sets---work day |
Section 7.3---again! |
Write-ups due of problems 6c, 9 and 15 in chapter 5. |
* |
Monday, April 26 |
Uncountable sets---discussion of
Cantor's diagonalization argument. |
Section 7.4 |
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Wednesday, April 28 |
Uncountable sets---cont. |
Section 7.4---again! |
7.4.4, 7.4.5, 7.4.6, 7.4.7
Problems from 7.4 assigned in groups |
Friday, April 30 |
Countable and Uncountable sets---class presentations begin!!! |
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* |
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Countable and Uncountable sets---class presentations |
* |
* |
Wednesday, May 5 |
Countable and Uncountable sets---class presentations |
* |
* |
Friday, May 7 |
Comparing cardinalities: a discussion.
Course evaluations
Takehome Final Distributed! |
Section 7.5 |
* |
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Final Examination
Friday, May 14 at 1:30 p.m.
Takehome Final Due at the time of in-class exam.
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