V63.0120: Discrete Mathematics Spring 2011
This is a past class.
Class Time/Location 
Monday, Wednesday 3:30pm5:20pm Silver Center rm. 514 
Instructor 
Andreas Kloeckner 
Office 
Courant Institute, Warren Weaver Hall, Room 1311 
Office Hours 
Monday, Wednesday 2pm3pm 
Class Webpage 

Email Listserv 
http://lists.tiker.net/listinfo/discrete11, discrete11@tiker.net, archive 
Contents
Topics and goals
Our major goal will be to familiarize ourselves with some of the important tools of discrete mathematics.
 Mathematical language, logic, writing, and proof
 Set theory
 Functions and Relations
 Combinatorics and discrete probability
 Graph theory and trees
Text
Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns, and Games, by Douglas E. Ensley and J. Winston Crawley. Wiley, ISBN 0471476021
The book has a rather helpful companion web site which we will be using on occasion.
Summary of Chapters 4 through 7 by Ashish Myles
Assessment
 Homework
 will be assigned weekly (generally assigned and collected on Mondays). In fairness to the other students in the course, late homework will generally not be accepted. We will, however, drop the lowest homework score in computation of final grades. Please talk to the instructor in cases of emergency.
 Quizzes
 There will be five quizzes, generally on Wednesdays. They are tentatively scheduled as indicated in the syllabus below. Quizzes will start at the beginning of class and run for about 1520 minutes. We will also drop the lowest quiz.
 Midterm
 There will one midterm examination, on March 9 in class.
 Final
 The cumulative final examination for this course is scheduled as indicated on the calendar below. We will not be able to accommodate early finals for nonacademic, nonemergency reasons. Please plan your travel schedule accordingly.
Grades will be computed by a weighted average:
Homework 
Quizzes 
Midterm 
Final 
10% 
20% 
30% 
40% 
Final scores will be converted to letter grades beginning with the following scale:
93 
90 
87 
83 
80 
75 
65 
50 
A 
A 
B+ 
B 
B 
C+ 
C 
D 
As for a curve, these cutoffs might be adjusted, but only in the downward direction (to make letter grades higher).
On the homework, each problem will be worth three points, assigned as follows:
Points 
Description of Work 
3 
Work is completely accurate and essentially perfect. Work is thoroughly developed, neat, and easy to read. Complete sentences are used. 
2 
Work is good, but incompletely developed, hard to read, unexplained, or jumbled. Answers which are not explained, even if correct, will generally receive 2 points. Work contains the 'right idea' but is flawed. 
1 
Work is sketchy. There is some correct work, but most of the work is incorrect. 
0 
Work minimal or nonexistent. Solution is completely incorrect. 
For the purposes of assembling the final grade, the grade on each homework set is converted to a percentage of all achievable points, on a scale from 0 to 100.
Material about Tests
Homework
 Teaching/DiscreteMathSpring2011/HomeworkSet01
 Teaching/DiscreteMathSpring2011/HomeworkSet02
 Teaching/DiscreteMathSpring2011/HomeworkSet02/CommonMistakes
 Teaching/DiscreteMathSpring2011/HomeworkSet03
 Teaching/DiscreteMathSpring2011/HomeworkSet03/9c
 Teaching/DiscreteMathSpring2011/HomeworkSet03/CommonMistakes
 Teaching/DiscreteMathSpring2011/HomeworkSet04
 Teaching/DiscreteMathSpring2011/HomeworkSet05
 Teaching/DiscreteMathSpring2011/HomeworkSet05/CommonMistakes
 Teaching/DiscreteMathSpring2011/HomeworkSet06
 Teaching/DiscreteMathSpring2011/HomeworkSet06/CommonMistakes
 Teaching/DiscreteMathSpring2011/HomeworkSet07
 Teaching/DiscreteMathSpring2011/HomeworkSet07/CommonMistakes
 Teaching/DiscreteMathSpring2011/HomeworkSet08
 Teaching/DiscreteMathSpring2011/HomeworkSet08/CommonMistakes
 Teaching/DiscreteMathSpring2011/HomeworkSet09
 Teaching/DiscreteMathSpring2011/HomeworkSet09/CommonMistakes
 Teaching/DiscreteMathSpring2011/HomeworkSet10
 Teaching/DiscreteMathSpring2011/HomeworkSet10/CommonMistakes
 Teaching/DiscreteMathSpring2011/HomeworkSet11
 Teaching/DiscreteMathSpring2011/HomeworkSet11/CommonMistakes
 Teaching/DiscreteMathSpring2011/HomeworkSet11/Section5.3Problem36
 Teaching/DiscreteMathSpring2011/HomeworkSet12
Tentative Calendar
Week 
Day 
Book Section 
Topic/Notes 
1 
1/24 
1.1 
First Examples 
1/26 
1.2 
Number Puzzles and Sequences 

2 
1/31 
1.3 
Truthtellers, Liars, and Propositional Logic 
2/2 
1.4 
Predicates 

3 
2/7 
1.5 
Quiz; Implications 
2/9 
2.1 
Mathematical Writing 

4 
2/14 
2.2 
Proofs about Numbers 
2/16 
2.3 
Mathematical Induction 

5 
2/21 
President's day (no class) 

2/23 
2.5 
Quiz; Contradiction and the Pigeonhole Principle 

6 
2/28 
3.1, 3.2 
Set Definitions and Operations (taught by Dr. Wesley Pegden) 
3/2 
3.3 
Proving Set Properties (taught by Dr. Wesley Pegden) 

7 
3/7 
Review 

3/9 
Midterm on 1.13.3 

8 
3/14 
Spring Recess (no class) 

3/16 
Spring Recess (no class) 

9 
3/21 
3.4 
Boolean Algebra 
3/23 
4.1, 4.2 
Definitions of Functions, Diagrams, Relations, and Inverses, Composition 

10 
3/28 
4.3 
Properties of Functions and Set Cardinality (taught by Dr. Michael O'Neil) 
3/30 
4.4 
Properties of Relations 

11 
4/4 
4.5 
Quiz; Equivalence Relations 
4/6 
5.1, 5.2 
Intro to Combinatorics, Basic Rules for Counting 

12 
4/11 
5.3 
Cominatorics and the Binomial Theorem 
4/13 
5.4 
Binary Sequences 

13 
4/18 
5.5 
Quiz; Recursive Counting 
4/20 
6.1, 6.2 
Intro to Probability, Sum and Product Rules 

14 
4/25 
6.3 
Probability in Games of Chance 
4/27 
7.1, 7.2 
Graph Theory, Proofs about Graphs and Trees 

15 
5/2 
7.3 
Quiz; Isomorphism and Planarity 
5/4 
Review 

16 
5/9 
Review 

5/11 
Final Exam 4:00pm5:50pm 
(see also the academic calendar)