Discrete Mathematics G22.2340-001
Tuesdays 6:00-8:20 Room 101 or 102 WWH
|harper AT cs DOT nyu DOT edu|
|719 Broadway, Room 1212|| |
|(212) 998 3342|
|Office Hours: Mondays 5-7 and by appt.|
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.
5/16/06 - Course e-mail list subscription information has been posted below. Please subscribe yourself! Also, Lecture Notes for Chapter 1 and the lecture have been posted for the first class.
5/17/06 - I am required to remind everyone of the department's Academic Integrity Policy at http://www.cs.nyu.edu/web/Academic/Graduate/academic_integrity.html.
5/18/06 - Homework #1 has been posted at assign1.html, and is due on 5/23/06.
5/22/06 - Lecture Notes for the second lecture have been posted below. Also, in light of our discussion about flawed arguments from last week, take a look at the following blog: http://goodmath.blogspot.com/ called "Good Math Bad Math". I also may discuss Godel's Incompleteness Theorem a little this week, and for those interested, take a look at the articles from a recent Notices of the AMS (April 2006) devoted to his work.
5/25/06 - Homework #2 has been posted at assign2.html, and is due on 5/30/06.
5/31/06 - Homework #3 has been posted at assign3.html, and is due on 6/06/06.
06/06/06 - Lecture 4 Notes have been posted as well as notes for Chapters 2, 3 and 4
06/07/06 - Homework #4 has been posted at assign4.html, and is due on 6/13/06.
06/13/06 - Homework #5 has been posted at assign5.html, and is due on 6/13/06.
06/22/06 - Homework #6 has been posted at assign6.html, and is due on 6/2706.
7/11/06 - Solutions for assignment 6 have been posted below.
7/12/06 - Homework #8 has been posted. The additional homework problems are in the handout at Ch14HwkProbs.pdf. Also, make sure to read the Siegel/Cole Notes for understanding how to rank the functions. Try to read all of this material if possible.
7/19/06 - Homework #9 has been posted: Homework #9If you are curious about the class and would like to know more (or meet with me beforehand to talk about your background), e-mail me!
Class Mailing List
|Please sign up for the class mailing list ASAP. We will use this to send out announcements, etc., and students can use it to ask each other for homework help, discuss challenging problems, etc. Go to http://www.cs.nyu.edu/mailman/listinfo/g22_2340_001_su06 and put in the e-mail address you plan to use for the class (You can subscribe with multiple e-mail addresses) and a password, and you will receive a confirmation e-mail. If you want to send a message to the class, e-mail firstname.lastname@example.org|
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).
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.|
The homework will be designed to supplement readings and
best way to become adequately mathematically literate in this
material is through continuous exercises, so homework will given semi-regularly 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 on-line the day it is handed out and students can present their solutions via e-mail 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.
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 take-home.
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 full-time jobs during the summer. If you are interested in the class and are unsure how often you will be able to attend, e-mail 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.)
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:
encouraged to collaborate but are expected to indicate as such on any
homework turned in. Exams will be in class, so no collaboration will be allowed. See the Academic Integrity Policy for more information: http://www.cs.nyu.edu/web/Academic/Graduate/academic_integrity.html.
There will be a class mailing list, which will be posted here. All students will be required to join.
Still being decided, but the basic structure will follow previous years: (This is last year's syllabus posted here)
|1||May 16||Introduction and Logic of Compound Statements||Lecture Notes and
Chapter 1 Notes (by J.L. Gross, courtesy of Eitan Grinspun)
|2||May 23||Logic of Quantified Statements and Intro to Proofs||Lecture Notes|
|3||May 30||Elementary Number Theory, Set Theory and Methods of Proof||Continuation of Lecture 2 Notes|
|4||June 6||Pigeonhole Principle, Algorithms, Sequences and Mathematical Induction||Lecture 4 Notes and
Chapter 2 Notes, Chapter 3 Notes and Chapter 4 Notes(by J.L. Gross, courtesy of Eitan Grinspun)
|5||June 13||Counting||Chapter 5 Notes|
|6||June 20||Combinations, Permutations and Probability||Chapter 5 Notes|
|7||June 27||Probability and Asymptotics||Chapter 6 Notes|
|8||July 11||Recurrences and Sorting||Lecture 8 Notes|
|9||July 18||More recurrences and solving||Lecture 9 Notes|
|10||July 25||Graphs and Trees||Graphs and Trees Notes|
|11||August 1||Final Presentations|