Math 4707: Introduction to combinatorics and graph theory

Spring 2008

Prerequisites: Math 2243 and either Math 2283 or 3283 (or their equivalent).
Students will be expected to know some calculus and linear algebra,
as well as having some familiarity with proof techniques, such as mathematical induction.  
Instructor: Victor Reiner (You can call me "Vic"). 
Office: Vincent Hall 256
Telephone (with voice mail): 625-6682
Classes: Mon-Wed 3:35-5:00pm, Vincent Hall 206. 
Office hours: Monday 12:20pm, Tuesday 3:35pm, Friday 11:15am; also by appointment. 
Required text: Discrete Mathematics: elementary and beyond, by Lovasz, Pelikan, and Vesztergombi (2003, Springer-Verlag).
Course content: This is a course in discrete mathematics, emphasizing both techniques of
enumeration (as in Math 5705) as well as graph theory and optimization (as in Math 5707),
but with somewhat less depth than in either of Math 5705 or 5707.
We plan to cover most of the above text, skipping Chapters 6 and 15, possibly also Chapter 14.
We will also likely supplement the text with some outside material.

Warning: Occasionally some course material will be taught by having the students
work together in small groups cooperatively. Students will also be asked to come to the board
to explain their group's answer.
Other useful texts
Title Author(s), Publ. info Location
Invitation to Discrete Mathematics Matousek and Nesetril, Oxford 1998 On reserve in math library
Applied combinatorics A. Tucker, Wiley & Sons 2004 On reserve in math library
Introduction to graph theory D. West, Prentice Hall 1996 On reserve in math library
There will be 5 homework assignments due usually every other week, but
  • 2 weeks where there will be a week-long take-home midterm exam,
  • a week at the end with a week-long take-home final exam.
Tentative dates for the assignments and exams are in the schedule below.

I encourage collaboration on the homework, as long as each person understands the solutions,
writes them up in their own words, and indicates on the homework page their collaborators.

The take-home midterms and final exam are open-book, open-library, open-web,
but in contrast to the homework on exams, no collaboration or consultation of human sources is allowed.

Late homework will not be accepted. Early homework is fine, and can be left in my mailbox
in the School of Math mailroom near Vincent Hall 105.

Homework solutions should be well-explained-- the grader is told not to give credit for an unsupported answer.
Complaints about the grading should be brought to me.

Final course grade basis :
  • Homework = 50% of grade
  • Each of 2 midterms = 15% of grade
  • Final exam = 20% of grade
Homework assignments
Assignment or Exam Due date Problems from Lovasz-Pelikan-Vesztergombi text,
unless otherwise specified
Homework 1 2/13 1.8 # 10,14,16,21,24,26,29,33
2.5 # 1,4(b),5,7,8
3.8 # 4,8,9,11,12
Homework 2 2/27 4.3 # 5,8,9(a,b),11,12 (6 was removed)
5.4 # 1,2,3,4
Exam 1 3/5 Midterm exam 1 in PostScript, PDF.
Homework 3 3/26 7.3# 4,5,9,10,13
8.5# 2,3,4,5,7,9,11
Homework 4 4/9 9.2# 3, 7
10.4# 5,6,7,11,13(a,b),15
Exam 2 4/16 Midterm exam 2 in PostScript, PDF.
Homework 5 4/30 12.3 # 1, 2, 5, 6
Correct the hypotheses of 12.3.6 by assuming also
that every vertex has degree 3. And here is a
hint for 12.3.5: first note that the Petersen graph
has no cycles shorter than 5-cycles.
13.4 # 1, 2, 7, 8, 9(a)
Final Exam 5/7 Final exam in PostScript, PDF.
Back to Reiner's Homepage.