Date |
Topic |
Reading Assignment |
Homework |
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| Friday, August 30 |
Course Procedures and Policies
Thought Experiment |
Note to the Student
Chapter 0 |
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Monday, Sept. 2 |
Mathematical Statements |
Course Procedures (online)
Sections 1.2-1.5 |
Problems 1, 3. (And all Exercises---always part of the assignment!) |
Wednesday, Sept. 5 |
Compound Statements
Negation
True or False? |
Sections 1.6-1.8 |
Problem 6. |
Friday, Sept. 7 |
Reasoning and Proof |
Finish Chapter 1
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8 |
Monday, Sept. 9 |
Reasoning and Proof, cont. |
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Turn in Handout: Learning from Truth Tables.
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Wednesday, Sept. 11 |
Sets and Set Notation
Subsets |
Sections 2.1-2.2 |
2.2.2, 2.2.4 and
Problem 1. |
Friday, Sept. 13 |
Set Operations |
Section 2.3 |
Problems 2, 3. |
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Monday, Sept. 16 |
The Algebra of Sets |
Section 2.4 to bottom of pg. 49. |
(Exercises, of course) and 2.4.8. |
| Wednesday, Sept. 18 |
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. 20 |
Introduction to LaTeX |
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Monday, Sept. 23 |
Finish The Algebra of Sets
Introducing Power Sets |
Section 2.5 |
2.5.4, 2.5.5 |
Wednesday, Sept. 25 |
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) |
Friday, Sept. 27 |
Introduction to Mathematical Induction |
Section 3.1 |
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Monday, Sept. 30 |
No Class; Professor Schumacher out of Town |
Wednesday, October 2 |
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, October 4 |
Introduction to Complete Induction |
Section 3.3 |
3.3.4 |
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Monday, October 7 |
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 8(c), Chapter 2 and 3.2.3 and 3.2.4 due. |
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Mathematical Induction---a work day. |
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Friday, October 11 |
No class---October Reading Days! |
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Monday, October 14 |
Observation Systems---a work day |
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Wednesday, October 16 |
Observation Systems---class presentations |
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Write-ups of induction problems due Thursday, October 17 by 4 p.m. |
Friday, October 18 |
Relations |
Section 4.1 |
Problem 4.1.10, and problems 2 and 3 at the end of the chapter. |
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Monday, October 21 |
Introduction to Orderings---class work day. |
Section 4.2 through 4.2.18 |
Concentrate on definitions and examples |
Wednesday, October 23 |
Orderings---maximal/minimal elts, etc.
Takehome Midterm Distributed |
Section 4.2 throught 4.2.18 (again!) |
4.2.14, 4.2.15, 4.2.18. |
Friday, October 25 |
In-Class Midterm |
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Monday, October 28 |
Least upper boundss and the Least Upper Bound Property |
Rest of Section 4.2 |
4.2.22.
(Takehome Midterm due before 5 pm on Tuesday, October 29.) |
Wednesday, October 30 |
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.
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Friday, November 1 |
From relations to sets and back---work day! |
Section 4.3 (through pg. 81) . |
4.3.8 and problems on pgs 80-81. |
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Equivalence relations |
Rest of section 4.3 |
4.3.15, 4.3.16, 4.3.17
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Wednesday, November 6 |
Equivalence Classes
Work on 4.3.20 and 4.3.21
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4.3.23
(To be written up: 4.3.20 and 4.3.21) |
Friday, November 8 |
Functions---the basic ideas |
Section 5.1 |
Write-ups due for 4.2.25, 4.2.26. |
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Monday, November 11 |
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 13 |
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, November 15 |
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.) |
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Monday, November 18 |
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, November 20 |
Image of a set under a function. |
More on Section 5.3 |
Group problems: 5.3.11, 5.3.12, 11b.
(Problems 6, 9 and 15 will be written up) |
Friday, November 22 |
Continue Group Presentations |
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Thanksgiving Break |
Monday, December 2 |
Finish Chapter 5. |
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Wednesday, December 4 |
Introduction to Cardinality: Galileo's Paradox and Infinite Sets. |
Section 7.1 |
Theorems 7.1.3 and 7.1.5
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Friday, December 6 |
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
Write-ups due of Chapter 5 problems Thm. 5.2.9, 6, 9, 15 |
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Infinite sets
Countable sets---general discussion |
Section 7.3 |
Problems from 7.3 assigned in groups |
Wednesday, December 11 |
Uncountable sets---discussion of
Cantor's diagonalization argument. |
Section 7.4 |
Problems from 7.4 assigned in groups
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Friday, December 13 |
Cardinality---bringing it all together
Takehome Final Distributed |
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Final Examination
In-class Exam at 1:30 p.m on Friday, December 20th
Takehome Exam is distributed on the last day of class and is due at the beginning of the inclass exam. |