| 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 E-mail: reiner@math.umn.edu |
|
| 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. |
| 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 |
| Homework, exams, grading: |
There will be 5 homework assignments due usually every other week, but
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 : |
|
| 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. |