# MHF 3202: Sets and Logic University of Florida, Fall 2011

#### Instructor information:

Vince Vatter
Office: 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.

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 homework and quizzes will collectively count for 20% of your grade. The midterms will count for 50% of your grade. The final exam will count for 30%. No scores will be dropped.

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:

LectureDateTopicsSection(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:
• Tuesday, 12/13, 7:30–9:30am. Ugh.