# MATH-UA.120: Discrete Mathematics Fall 2011

This is a past class.

 Class Time/Location Tuesday, Thursday 11:00am-12:50pm, 7 East 12th Street, Room 123 Instructor Andreas Kloeckner Email Office Courant Institute, Warren Weaver Hall, Room 1105A Office Hours Monday, Wednesday 4pm-5pm Class Webpage Email Listserv

## 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 0-471-47602-1

The book has a rather helpful companion web site which we will be using on occasion.

## Assessment

Homework
will be assigned weekly (generally assigned and collected on Thursdays). 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 the computation of final grades. Please talk to the instructor in cases of emergency.
Quizzes
There will be three quizzes, as indicated on the calendar below. They are tentatively scheduled as indicated in the syllabus below. Quizzes will start at the beginning of class and run for about 15-20 minutes. We will also drop the lowest quiz.
Midterms
There will be two midterm examinations, as indicated on the calendar below.
Final
The time for the cumulative final examination will be announced as the end of the semester draws near. 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 I Midterm II Final 10% 10% 20% 25% 35%

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 non-existent. 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.

# Tentative Calendar

 Week Day Book Section Topic/Notes 1 9/6 1.1 First Examples 9/8 1.2 Number Puzzles and Sequences 2 9/13 1.3 Truth-tellers, Liars, and Propositional Logic 9/15 1.4 Predicates 3 9/20 1.5 Quiz; Implications 9/22 2.1 Mathematical Writing 4 9/27 2.2 Proofs about Numbers 9/29 2.3 Mathematical Induction 5 10/4 2.5 Contradiction and the Pigeonhole Principle (taught by Matthew Elsey) 10/6 3.1, 3.2 Set Definitions and Operations (taught by Matthew Elsey) 6 10/11 Fall Break (no class) 10/13 Review 7 10/18 Midterm 1 on 1.1-2.5 10/20 3.3 Proving Set Properties 8 10/25 3.4 Boolean Algebra 10/27 4.1 Definitions of Functions, Diagrams 9 11/1 4.2 Quiz; Relations, Inverses, Composition 11/3 4.2 Relations, Inverses, Composition cont'd 10 11/8 4.3 Properties of Functions and Set Cardinality 11/10 4.4, 4.5 Properties of Relations, Equivalence Relations 11 11/15 Review 11/17 Midterm 2 on 2-4.5 12 11/22 5.1, 5.2 Intro to Combinatorics, Basic Rules for Counting 11/24 Thanksgiving Break (no class) 13 11/29 5.3, 5.4 Cominatorics and the Binomial Theorem, Binary Sequences 12/1 5.5 Recursive Counting 14 12/6 6.1, 6.2 Intro to Probability, Sum and Product Rules 12/8 6.3 Quiz; Probability in Games of Chance 15 12/13 7.1, 7.2 Graph Theory, Proofs about Graphs and Trees 12/15 Review 16 12/20 Final Exam 10am-11:50am