This offering of Discrete Mathematics is designed to be an
introduction to the mathematical techniques and reasonings that are
required of a good computer scientist. Upon successful completion of
this course, students should be comfortable with tackling the
mathematical issues confronted in an Algorithms and Data Structures course. More importantly, you will begin to learn how to think like a computer scientist and see how solving problems often confronted in computer science can be fun and challenging!
Students should be comfortable with Basic Algebra such as seen at the high school level. The topics we
will cover in this course will include logic, proof techniques,
induction, recursion, combinatorics, basic probability, algorithm
analysis and efficiency, and discrete structures (including elementary
graph theory). No prior programming experience is required, but students will be encouraged to tackle small programming tasks.
Updates!
Class Mailing List
All students are required to join the mailing list. We will use the
list for answering general homework questions, posting announcements, etc. You can join the list be going to the
following url and following the instructions.
http://www.cs.nyu.edu/mailman/listinfo/g22_2340_001_su08

Textbooks
There will be one basic textbook and several suggested textbooks, from
which sections for reading may be chosen or sample bonus problems. We
will attempt to assign challenge problems continuously (mainly for extra credit).
Required

The required textbook will remain the same as last year. The following text is more appropriate for a graduate level course but also provides a good level of background for students who feel they may need it.
Discrete Mathematics and Its Applications (Hardcover)
Kenneth H Rosen
McGrawHill Science/Engineering/Math
6th edition (2007)  Make sure to get the 6th only!
ISBN:
There is also a students solutions handbook for the above book, available from Amazon, Barnes and Noble, etc.

Suggested/Supplemental  These texts are by no means required, but we may discuss parts of them in class; they also provide extra background and motivation for material covered.

How to Solve It  A New Aspect of a Mathematical Method by G. Polya

Introductory Graph Theory by Gary Chartrand (ISBN: 0486247759)

The Puzzling Adventures of Doctor Ecco by Dennis Shasha (ISBN:
0486296156)
 Doctor Ecco's Cyberpuzzles by Dennis Shasha (ISBN: 039305120X)

Homework
The homework will be designed to supplement readings and
lectures. The
best way to become adequately mathematically literate in this
material is through continuous exercises, so homework will given semiregularly and will be due the week following when it is assigned. Students can work with
others, but they must indicate on their homework with whom they have
worked (working together in no way affects your grade). Additionally, homework will be posted online the day it is handed out and students can present their solutions via email in case they are unable to attend a lecture. Collaboration is encouraged but must be acknowledged on the top of your assignment. See the Academic Integrity Policy for more information: http://www.cs.nyu.edu/web/Academic/Graduate/academic_integrity.html.
 Homework assignment #1 (Due 6/10/2008): hw1.pdf
 Homework assignment #2 (Due 7/1/2008): hw2.pdf
 Homework assignment #3 (Due 7/15/2008): hw3.pdf
 Homework assignment #4 (Due 7/29/2008): assign4.html

Student Presentations
Here is a list of all of the student presentations as well as copies
of their final papers. I will be adding to these as I receive them
(listed in presentation order):

Exams
There will be a midterm and a final. Dates to be decided. However, as noted below in grading, homework will be weighed more heavily, and exams will be mainly used so that students can evaluate their own progress and understanding of the material. The midterm may also be takehome.

Attendance/Class Participation
Regular attendance is the best way to stay current on the material, especially since we will be reviewing homework assignments and general questions. Plus, new material will be introduced weekly. However, we understand that many students have fulltime jobs during the summer. If you are interested in the class and are unsure how often you will be able to attend, email the instructor. Office hours will also be able for students who need to review certain topics. (The goal of the course is to adequately prepare you for the rest of the graduate program, so we want to make sure students feel comfortable.)
Additionally,
students will be assigned
challenge problems for presenting and leading a discussion for
510 minutes
of a class. They will be problems from Dennis Shasha's books  these problems are often difficult, but the answers are provided; presenting and discussing these problems will give students an opportunity to better understand how to think like a computer scientist when solving complex problems and how to present an interesting problem and its solution.

Grading
Grade distribution has not fully been decided; however, I often feel that homework better reflects students' abilities since not everyone does well on exams, so homework will factor more heavily into the equation:
Class Participation/Attendance = 5%
Homework = 45%
Exam = 25%
Final Presentation = 25% (5% outline + 10% presentation + 10% paper)
Additionally, please note that since the emphasis will be on teaching you as much as possible for preparation for the rest of the graduate program, testing in this course will not be overly intense. Students who routinely strive to complete the homework and stay current with lectures and reading can expect to receive good final grades. Further, extra credit will be available for students who want to work on more interesting problems and supplement their grades.

Collaboration
Syllabus
Lecture

Date 
Lecture Topic 
Reading 
1 
May
20 
Class to be rescheduled 

2 
May
27 
Introduction and Logic of Compound
Statements 
Lecture Notes and
Chapter 1
Notes (by J.L. Gross, courtesy of Eitan
Grinspun) 
3 
June
3 
Continuation
of last week + Start Logic of
Quantified Statements and Intro to Proofs 
Lecture Notes 
4 
June
10 
Continuation of Slides (Proofs, Set Theory, etc.)

Notes worth reading:
Chapter 2
Notes and
Chapter 3
Notes(by J.L. Gross, courtesy of Eitan Grinspun) 
5 
June
17 
Continuation


6 
June
24 
Continuation


7 
June
24 
Review some Hwk Problems, Discuss Pigeonhole Principle, Work on Sequences and Induction,
and Maybe Begin Probability

Lecture Slides 
