Class Lectures: Tue, Fri 2:10 PM - 3:25 PM, HW 207 Professor Saad Mneimneh, HN 1090F Office hours: by appointment

Textbook Discrete Mathematics Elementary and Beyond Publisher: Springer Series: Undergraduate Texts in Mathematics Lovász, L., Pelikán, J., Vesztergombi, K. Edition 1, 2003 A preliminary version is online as lecture notes postscript pdf

Syllabus
Mostly the table of contents of the textbook, here.

Lectures
Lecture 1 - Correct and false proofs of Pythagoras theorem, proof by example (not a proof), proof by exhaustion (not always possible), Pythagorean triples
Lecture 2 - Logic of implication, what a proof really is, direct proof, contrapositive, proof by contradiction
Lecture 3 - Counting/overcounting, equalities with combinatorial arguments, pp. 1-4, 15-17
Lecture 4 - Sets, proof by picture (sometimes valid, try to avoid), subsets, pp. 4-13
Lecture 5 & 6- Counting ordered and non-ordered sets of certain size, pp. 19-21
Lecture 7 - Pascal triangle, Binomial theorem, pp. 43-44, 49-52
Lecture 8 - Selection with repetition, pp. 45-48, Inclusion-Exclusion principle, pp. 32-34
Lecture 9 - More on inclusion-exclusion, permuting hats, pigeon-hole principle pp. 34-36
Lecture 10 - Birthday paradox pp. 37-40, proof by induction, pp. 25-29
Lecture 11 - More examples of proof by induction
Lecture 12 - Fibonacci sequence, pp. 65-74
Lecture 13 - More on Fibonacci and solving recurrences
Lecture 14 - Traveling in Manhattan, Catalan numbers
Lecture 15 - Closed form of Catalan numbers
Lecture 16 - Indution, recurrences, and recursive algorithms, tower of hanoi
Lecture 17 - Tower of Hanoi, recursion, graphs, and more

Homework
Homework 0 Due 09/04/09 Solution grading sheet
Homework 1 Due 09/11/09 Solution grading sheet
Homework 2 Due 10/02/09 Solution grading sheet
Homework 3 Due 10/09/09 Solution grading sheet
Homework 4 Due 10/27/09 Solution

Grading policy

- There will be weekly homework.

- The solution of the homework will be posted the following week.

- The homework will not be collected, instead each student is required to 
  grade his/her homework.

- The grading will be done using two identical copies of a grading sheet that 
  will be provided, and one of them collected by the end of the two following 
  lectures.

- Each student will give a general grade for the entire homework on a scale
  of 1 to 5 (5 being the best). In addition, there will be specific 
  questions about the level of understanding for certain concepts explored in 
  the homework. The level of understanding can be:    
    1: non existent
    2: poor
    3: shallow
    4: appropriate
    5: deep

- This grading strategy will not affect the final grade. It's purpose is
  to make the student aware of his/her status.

- Each student is required to pick a lecture and scribe it. The choice will 
  be made before the lecture begins, mainly by volunteering. The student must
  submit this within two weeks.

- There will be a midterm test.

- There will be a final test.

- Each student is required to meet with the professor for 15 min during the
  last two weeks of the semester. The scheduling of this meeting is the 
  responsibility of the student. During this meeting, the student must bring
  all homework, be able to show how seriously he/she worked on each one and 
  explain some of the grades, and must be prepared to answer questions. 

- The final grade is based on:
    1: ability of the student to show sincere work on homework 5%
    2: discussion that took place during the meeting 10%
    3: midterm 20%
    4: final 30%
    5: project 20%
    6: attendance 5%
    7: scribing 5%
    8: grading sheets 5%

- project: to pick a topic among the ones explored in class and discuss some 
  applications of it in the field of computer science. The student should
  have an appropriate level of understanding for this topic in order to 
  discuss its applications.