| 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 (he/him/his; Call me "Vic"). |
| ( Office: Vincent Hall 256, but I won't be there this semester! ) E-mail: reiner@math.umn.edu |
|
| Classes: | Mon-Wed 2:30-4:25pm via this
Zoom ID. Lectures are synchronous at the above class time, recorded, and posted to YouTube. Please attend the synchronous Zoom lectures, with cameras on, whenever possible. |
| Office hours: |
Tues-Thur 9:05-9:55am at the same Zoom ID. plus the last 25 minuutes of each lecture (Mon-Wed 4:00-4:25). To facilitate interactions, we are experimenting with a gather.town meeting room, password given in lecture. and Megan Smet set up a Discord server for us. |
| Required text: |
Discrete Mathematics: elementary and beyond, by Lovasz, Pelikan, and Vesztergombi
(2003, Springer-Verlag). One can download a free PostScript version of the book here, but it is not quite the final version of the book that we are using. |
| 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, 14, 15. We will also supplement the text with some outside material. |
| Group work: |
Occasionally some course material will be taught by having the students work together in small groups cooperatively, and students will be asked to explain their group's answer. Here are some relevant handouts for these exercises:
|
| Title | Author(s), Publ. info | Access |
|---|---|---|
| Applied Combinatorics | Keller and Trotter | free download |
| Generatingfunctionology | H. Wilf, AK Peters 2006 | free download |
| Foundations of Combinatorics with Applications | Bender and Williamson, Dover 2006 | free download |
| Graph theory with applications | Bondy and Murty | free download (out of print) |
| Invitation to Discrete Mathematics | Matousek and Nesetril, Oxford 1998 | (not free; booksellers) |
| Applied combinatorics | A. Tucker, Wiley & Sons 2004 | (not free; booksellers) |
| Introduction to graph theory | D. West, Prentice Hall 1996 | (not free; booksellers) |
| Supplementary materials: |
|
| Homework, exams, grading: |
There will be 5 homework assignments due usually every other week, submitted and returned through the course Canvas page, however
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. 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. |
| Grading scheme : |
|
| Assignment or Exam | Due date | Problems from Lovasz-Pelikan-Vesztergombi text, unless otherwise specified |
Lecture notes | Lecture videos |
|---|---|---|---|---|
| Homework 1 | Wed Sept 30 |
1.8 # 10,12,14,17,13,21,24,26,27 2.5 # 1,3,4(a),5,7,8 3.8 # 4,9 Out of 40 points, median was 36, mean 32.5, std deviation 9.8 |
Notes Batch 1 Notes Batch 2 Notes Batch 3 |
Sept. 9 Part1,
Part2 Sept. 14 Part1, Part2 Sept. 16 Part1 (no Part 2 that day; group work on Poker hand probabilities) Sept. 21 Part1, Part2 Sept. 23 (asynchronous) Part1, Part2 Sept. 28 Part1, Part2 Sept. 30 Part1, Part2 |
| Homework 2 | Wed Oct 14 |
1.8 # 33 3.8 # 8,11,12 4.3 # 5,8,9(a,b),11,12 Out of 40 points, median was 37.5, mean 33.2, std deviation 10.6 |
Notes Batch 4 Notes Batch 5 |
Oct. 5 Part1,
Part2 Oct. 7 Part1, Part2 (Oct. 12 had no video-- group work with handout on Stirling numbers of the 2nd kind) Oct. 14 Part1, Part2 Oct. 19 Part1, Part2 Oct. 21 Part1, Part2 |
| Exam 1 | Wed Oct 21 |
Here is Midterm 1 to be handed in at the course Canvas site. Out of 100 points, median was 98, mean 93, std deviation 8 |
||
| Homework 3 | Wed Nov 4 |
7.3# 4,5,9,10,13 8.5# 2,3,4,5,7,9,11 In this homework, assume graphs are simple, that is, with no parallel/multiple edges nor self-loops. In problem 7.3.4, only draw one example of each such graph, up to isomorphism. Out of 40 points, median was 37, mean 36, std deviation 3.5 |
Notes Batch 6 Notes Batch 7 |
Oct. 26 Part1, Part2 Oct. 28 Part1, Part2 Nov. 2 Part1, Part2 Nov. 4 Part1, Part2 Nov. 9 Part1, Part2 Nov. 11 Part1, Part2 |
| Homework 4 | Wed Nov 18 |
9.2# 3, 7 10.4# 5,6,11,13(a,b),15 In 10.4.11, the graph should have 2^3=8 vertices, and assume they mean a pair of subsets forms an edge exactly when one is a subset of the other, and their cardinality differs by one, e.g. {a} and {a,c}. Out of 40 points, median was 37, mean 35, std deviation 8 |
Notes Batch 8 |
Nov. 16 Part1, Part2 Nov. 18 Part1, Part2 |
| Exam 2 | Wed Nov 25 |
Here is Midterm 2 to be handed in at the course Canvas site. Out of 100 points, median was 85, mean 81, std deviation 14 |
||
| Homework 5 | Wed Dec 9 |
10.4 # 7 12.3 # 1, 2, 5, 6 13.4 # 1, 2, 7, 8, 9(a) 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. Out of 40 points, median was 35, mean 33, std deviation 8.5 |
Notes Batch 9 Notes Batch 10 Notes Batch 11 Notes Batch 12 |
Nov. 23 Part1,
Part2 Nov. 25 Part1, Part2 Nov. 30 Part1, Part2 Dec. 2 Part1, Part2 Dec. 7 Part1, Part2 Dec. 9 Part1, Part2 Dec. 14 Part1, Part2 Dec. 16 Part1, Part2 |
| Final Exam | Wed Dec 16 |
Here is the final exam to be handed in at the course Canvas site. Out of 100 points, median was 91, mean 89.5, std deviation 9.3 |