Combinatorics -- Fall 2003
Meeting Time/Place: Tues/Fri 9:50-11:10 in Hill 525.
Course Text: Extremal Combinatorics by Stasys Jukna

Instructor: Professor Michael Saks
Office: Hill 430 (Busch campus)
e-mail:saks@math.rutgers.edu

Basic Course Information

This course is the first part of a two semester advanced introduction to combinatorial theory, with an emphasis on extremal combinatorics. We will work from the textbook about 2/3 of the time. The text will be supplemented by readings that are on reserve in the library, and by the class lectures, which will often depart from the text.

The grade in the course is based on problem sets. There will approximately 6 problem sets, which will normally be assigned every other week. There are no exams.

Prerequisites: For Mathematics Ph.D. students: no formal prerequisites. For graduate students from other departments and undergraduates: permission of instructor. At various points in the course, we will need a variety of standard undergraduate material: linear algebra (350), advanced calculus (411), complex analysis (403) and elementary probability theory (477).

Written Assignments

Assignments will be posted at least two weeks before the due date. (Note: Problem numbers on assignments correspond to Jukna's book)
Assignment 1 (Due Friday September 19) pdf
Assignment 2 (Due Friday October 3) pdf
Assignment 3 (Due Friday October 17) pdf October 12 version
Assignment 4 (Due Tuesday November 4) pdf November 2 version
Assignment 5 (Due Tuesday November 25) pdf November 18 version
Assignment 6 (OPTIONAL -- Due Friday, December 12) pdf December 5 version

Homework Format
To make it easier for me to grade, please follow these guidelines on your written work:
  • Use standard 8 by 11 sheets of paper with no ragged edges.
  • Your name should appear at the top of each page. Pages should be numbered and stapled together.
  • You should have a cover page that gives your name and a table with three columns. The first column lists each of the assigned problems in the order that they appear on the assignment (whether you did them all or not). The second column contains the number of the page of your work where the solution to the problem appears (or the words ``Not done'' if you did not do it.) The third column is left blank for me to record the score.

    Collaboration on homework
    You will get the most benefit from the problem assignments if you do most of the work on your own. However, there is also a benefit to be gained by discussing problems with other students or with me, particularly if you are stuck on a problem. Here is my policy on outside help:
  • No written work pertaining to an assignment is to be given to or obtained from others.
  • You may discuss problems with others, but the final write-up of your solutions should be done independently. This means that you should not be sitting with other students when you write up your solutions.
  • I am fairly generous about giving hints and partial solutions to homework in my office hours. However, my policy is that you can't take notes on my hints, you must understand them sufficiently to be able to reconstruct them yourself later.
  • The solutions to a number of the problems in this course can be found in some of the books on reserve or in other literature. The problems are intended for you to do, not to look up. If you do read about a problem elsewhere, then you should (a) do your write-up of the problem ``closed book'' and (b) properly acknowledge your use of the book (see below).
  • Discussions about a problem, hints received, etc. (including office hour hints), reference to books other than the course text, must be acknowledged in your homework. This means that immediately following your written solution, you should write something like ``Acknowledgement: John Smith gave me a hint on this problem'', ``Acknowledgement: I worked with Jane Jones on this problem'', or whatever is appropriate.