13/12/16 NYU Discrete Mathematics Home Page

cs.nyu.edu/courses/summer03/G22.2340-001/ 1/4

Discrete Mathematics

G22.2340-001Summer 2003

Tuesday 6:00-8:20pmRoom 102, Warren Weaver Hall

Instructor

David Tanzer tanzer@cs.nyu.edu Room 401, Warren Weaver Hall Office hours: Tuesday 8:20 to 9:30 pmPhone: (212) 998-3018

Teaching Assistant

Elif Tosuntosun@cs.nyu.edu Room 1210, 719 Broadway (at the 12th floor, dial 83339 to reach her) Office hours: Tuesday 5:00 - 6:00, Thursday 1:00 - 2:00 Phone: (212) 998-3339

Announcement

Midterm is Tues. July 1, in class. Closed book.

Textbook

Discrete Mathematics with Applications, 2nd edition by Susanna S. Epp,Brooks/Cole Publishing Company, 1995

Tentative schedule

Lecture Date Lecture Topic Reading

1 May 20 Logic of Compound Statements Chapter 1

2 May 27 Logic of Quantified Statements Chapter 2

3 June 3Elementary Number Theory and Methods ofProof

Chapter 3

4June10

Sequences and Mathematical Induction Chapter 4

13/12/16 NYU Discrete Mathematics Home Page

cs.nyu.edu/courses/summer03/G22.2340-001/ 2/4

5June17

Set Theory Chapter 5

6June24

Counting Chapter 6

7 July 1 Functions Chapter 7

8 July 8 Recursion Chapter 8

9 July 15 O-notation and Efficiency of Algorithms Chapter 9

10 July 22 RelationsChapter10

11 July 29 Graphs and TreesChapter11

12 Aug 5 Final exam

Very Important: Because this course is preparation for Fundamental Algorithms,students who have taken Fundamental Algorithms and obtained a grade B or betterCANNOT be registered for the Discrete Mathematics class.

Class Notes

I will be using notes written by Professor Bukharovich. They are well-connected withthe textbook. I am presently making some small modifications and adaptations. I willnotify the class when the next batch is ready.

Lecture 1: Logic of Compound Statements Lecture 2: Logic of Quantified Statements Lecture 3: Elementary Number Theory Lecture 4: Sequences and Mathematical Induction Lecture 5: Set Theory Lecture 6: Counting and Probability Lecture 7: Functions Lecture 8: Recursion Lecture 9: Graphs and Trees

Course Responsibilities

There will be weekly homework assignments. The purpose of them is to get you tolive and breathe the mathematics that we will be covering. It will be most helpful toregard them as a fun challenge.

13/12/16 NYU Discrete Mathematics Home Page

cs.nyu.edu/courses/summer03/G22.2340-001/ 3/4

You may work with up to ONE partner, in which case you should hand in one copywith both of your names signed to it. Hidden collaborations will be regarded ascheating. We will be discussing the homework problems in class on the day thatthey are due. Therefore, you must hand them in either at the beginning of class, oremail them BEFORE class to the TA. In the absence of a documented medical orfamily emergency, late homeworks will not be accepted.

There will be one midterm and a final. No programming assignments will be given.Your lowest homework score will be dropped from the grade computation. Thecourse grade will be computed as follows: 30% homework, 25% midterm, 40% final,5% contribution to group discussions.

This last 5% will be based upon my assessment of the extent of your constructiveparticipation in group discussions, both in class and on the course mailing list. Thisis a judgement call that I alone will make; it is not a function of the number of bytesposted to the list, etc. The more that you can focus on the content of the class, themore you will get out of it and the better you will do. So, on to the numbers.

Course Mailing List

You must subscribe to the course mailing list, because this is how we will besending you timely adminstrative information about the course, and because I amhoping to foster group discussions of our math topics and problems. To subscribe,go to http://www.cs.nyu.edu/mailman/listinfo/g22_2340_001_su03. After you aresubscribed, to post to the list -- which is by all means encouraged -- send email toG22_2340_001_su03@cs.nyu.edu.

Here are the archives of all the postings to the class mailing list.

Any math-based discussion is pertinent to the list (with the one exception that youshould NOT use the list to discuss or solve current homework problems). Goodthings to post are questions about parts of the material that you are grappling with,e.g., about the meanings of the definitions, or about how the theorems are proven orused. I would especially like for us to put together a collection of problems along withdiscussions, approaches and solutions to them. Here are some sources ofproblems that are already at hand: the exercises in the lecture notes, and theexercises in the text (the ones which are not assigned for homework). Once aproblem has been "opened up," then let's try to solve it out loud. DO NOT WORRYABOUT SAYING WRONG THINGS about the problems we are considering. Errorsare stepping-stones along the path to the truth of the matter; a "half-baked", partialor mistaken solution contributed by A may well stimulate B to express a validsolution. Also, even if a problem has been solved one way, feel free to contributesolutions that take different approaches. I am hoping to extract highlights from thelist and post them to a "course book" section of the web page.

Group Discussion

Problems related to Chapters 1,2: problems_logic.txt

13/12/16 NYU Discrete Mathematics Home Page

cs.nyu.edu/courses/summer03/G22.2340-001/ 4/4

Here are the guidelines for the discussion. You are each assigned one of theproblems. Your only responsibility is to think about it, for up to a few days, and thento start the discussion thread which will hopefully lead to its solution. If you solve it, ofcourse, that's also good. If not, then indicate whatever any partial results you mayhave, approaches that you believe are worthwhile, difficulties that you encountered,etc. I will eventually assemble the solutions into a companion file to the problems file.

To start a thread for your problem, the subject of your email should just be "ProblemN". PLEASE do not start a thread for a problem that has been assigned tosomebody else. Once a thread has been started, then all are invited to participate.The subject line in this case should just be "Re: Problem N". Also, anyone feel freeto start a thread on any of the problems that are not assigned to individuals, or anyof the problems which were originally sent to the list, but which I didn't include in thefile.

Note: I left out many problems which were fine, in order to obtain a good balance oftypes of problems, so don't be concerned about whether your submission made itsway to the file.

Homework

Assignment Due Date Solution

1. Homework 1 Tue., May 27 Solution 1

1. Homework 2 Tue., June 3 Solution 2

1. Homework 3 Tue., June 17 Solution 3

1. Homework 4 Tue., June 24 Solution 4

1. Homework 5 Tue., July 15 Solution 5

1. Homework 6 Tue., July 22 Solution 6

1. Homework 7 Tue., July 29 Solution 7

Midterm solutions.

Thanks to Elif for the solutions.