MHF 3202: Sets and Logic
University of Florida, Fall 2011
Instructor information:
Vince VatterOffice: Little Hall 412
Office hours: Mondays 3:00–3:55, Wednesdays 1:55–2:45, and by appointment
Office phone: (352) 392-0281 extension 245
Email: vatter at ufl dot edu
Text:
How to prove it: a structured approach, 2nd edition, by Velleman.Course Objectives:
Examples of sets, operations on sets, set algebra, Venn diagrams, truth tables, tautologies, applications to mathematical arguments and mathematical induction.Grading:
We will have (roughly) weekly homework and quizzes, three in-class midterm exans and a comprehensive final exam. The dates of the in-class midterm exams are:
- Friday, September 16,
- Friday, October 14, and
- Friday, November 18.
The final grades will be curved, but will be no tougher than the 10-point scale: 90%–100% will be some form of A, 80–90% will be at least some form of B, etc. After each midterm, you will receive a projected grade.
If you have a disagreement with the grading of one of your solutions, I ask that you submit a written request for reconsideration within one month.
Tentative Schedule:
| Lecture | Date | Topics | Section(s) |
|---|---|---|---|
| 1 | M 8/22 |
Introduction Supplemental reading: Tim Gowers, Welcome to the Cambridge Mathematical Tripos |
Introduction |
| 2 | W 8/24 |
Deductive reasoning and logical connectives Suggested exercises: 1, 3, 5 Supplemental reading: Tim Gowers, Basic logic — AND and OR and Basic logic — NOT |
1.1 |
| 3 | F 8/26 | Truth tables Suggested exercises: 1, 9, 11, 16, 18 |
1.2 |
| 4 | M 8/29 | Variables and sets Suggested exercises: 5, 6, 8 |
1.3 |
| 5 | W 8/31 | Operations on sets Suggested exercises: 1, 3, 4, 8, 10, 12 |
1.4 |
| 6 | F 9/2 | Implication Suggested exercises: 1, 4, 6, 8 Quiz #1: pdf or tex |
1.5 |
| M 9/5 | Class canceled for Labor Day | ||
| 7 | W 9/7 | Quantifiers Suggested exercises: 1, 4, 7 |
2.1 |
| 8 | F 9/9 |
More quantifiers Suggested exercises: 1, 4, 6, 8, 11 Homework #1 assigned: pdf or tex |
2.2 |
| 9 | M 9/12 |
More sets Suggested Exercises: 1, 2, 3, 11, 13, 15 |
2.3 |
| W 9/14 |
Group review for Midterm #1: pdf or tex Homework #1 due |
||
| F 9/16 | Midterm #1: pdf or tex (covers Chapters 1&2) | ||
| M 9/18 |
Discussion of Midterm #1 Evaluations collected: pdf or tex Homework #2 assigned: pdf or tex |
||
| W 9/20 | Review for Midterm #1 Redux | ||
| F 9/22 |
Midterm #1 Redux: pdf or tex (covers Chapters 1&2) Bonus comic |
||
| 10 | M 9/26 |
Proof strategies Suggested exercises: 1, 2, 3, 4, 9, 15 |
3.1 |
| 11 | W 9/28 |
Proofs involving negations and conditionals Suggested exercises: 1, 8, 11 |
3.2 |
| 12 | F 9/30 |
Proofs involving quantifiers Suggested exercises: 2, 7, 9, 14, 20, 23 |
3.3 |
| 13 | M 10/3 |
Proofs involving "and"s and "iff"s Suggested exercises: the ones with stars |
3.4 |
| 14 | W 10/5 |
Proofs involving "or"s Suggested exercises: the ones with stars |
3.5 |
| F 10/7 |
Review (problems from the book as requested) Quiz #2: pdf or tex Homework #3 assigned: pdf or tex |
||
| M 10/10 | Group review for Midterm #2 | ||
| W 10/12 |
Review for Midterm #2 Homework #3 due |
||
| F 10/14 | Midterm #2 pdf or tex (covers Sections 3.1–3.5) | ||
| 15 | M 10/17 |
Existence and Uniqueness proofs Suggested exercises: the ones with stars |
3.6 |
| 14 | W 10/19 |
More proofs! Suggested exercises: 1 and 4 |
3.7 |
| 15 | F 10/21 |
Ordered pairs and Cartesian products Suggested exercises: 1, 2, 6, 8 |
4.1 |
| 16 | M 10/24 |
Relations Suggested exercises: 1, 4, 7, 10 |
4.2 |
| 17 | W 10/26 |
More relations! Suggested exercises: 1, 3, 10, 17, 20 Homework #4 assigned: pdf or tex |
4.3 |
| F 10/28 |
Brief time for questions, by request (special guest lecturer!) Quiz #3 (covering suggested exercises from 4.1, 4.2, and 4.3) |
||
| 18 | M 10/31 |
Ordering relations Suggested exercises: stared problems |
4.4 |
| 19 | W 11/2 |
Closures Suggested exercises: stared problems Homework #4 due |
4.5 |
| F 11/4 | Class canceled for Homecoming | ||
| 20 | M 11/7 |
Equivalence relations Suggested exercises: stared problems Homework #5 assigned: pdf or tex |
4.6 |
| 21 | W 11/9 |
Equivalence relations, again |
4.6 |
| F 11/11 | Class canceled for Veterans Day | ||
| 22 | M 11/14 |
A brief discussion of functions Homework #5 due |
5.1–5.3 |
| W 11/16 | Review for Midterm #3 | ||
| F 11/18 | Midterm #3 pdf or tex (covers only Chapter 4) | ||
| M 11/21 | Discussion of Midterm #3 | ||
| 23 | W 11/23 | Optional review | |
| F 11/25 | Class canceled for Thanksgiving | ||
| 24 | M 11/28 |
Mathematical induction! Suggested exercises: 1, 2, 5, 8, 10, 14, 19 |
6.1 |
| 25 | W 11/30 |
More induction! Suggested exercises: 2, 4, 5, 6, 8, 12 (Mini) Homework #6 assigned: pdf or tex |
6.2 |
| 26 | F 12/2 |
Even more induction! (Mini) Homework #6 due (Mini) Homework #7 assigned: pdf or tex |
6.2 |
| M 12/5 |
Review for final exam I (Mini) Homework #7 due |
||
| W 12/7 | Review for final exam II | ||
Final exam:
|