Instructor: Anar Akhmedov
Lectures: MW 2.30p - 4.25p in Vincent Hall 113.
E-mail: akhmedov@math.umn.edu
Office Hours: Monday and Wednesday 4.35pm - 5.35pm. If you have questions, I encourage you to come to my office hours. This would be the best time to talk to me and address questions you have about the course material, homework assignments, grading, exams, etc. My office is in room 355 of the Vincent Hall.
Prerequisites: Math 2243 and Math 2283 or Math 3283.
Textbook:
Discrete Mathematics, Elementary and Beyond, by Lovasz, Pelikan, and Vesztergombi, Springer. The textbook is available at the University bookstore, and also on reserve in the Mathematics Library.
| Title | Author(s), Publ. info | Location |
|---|---|---|
| Combinatorics and Graph Theory | J. Harris, J. Hirst, and M. Mossinghoff, Springer 2008 | On reserve in math library |
| Introduction to Graph Theory | D. West, Prentice Hall 1996 | On reserve in math library |
Course Outline: In this course we will learn basics of enumerative combinatorics and graph theory. We plan to cover Chapters 1 - 8 and 10 - 13 of the textbook. The main topics are: sets and counting, the inclusion-exclusion principle and applications, the pigeonhole principle, permutation and combinations, the binomial coefficents and Pascal's triangle, Fibonacci and Lucas numbers, combinatorial probability, divisibility of integers, Fermat's little theorem, graphs and trees, planar graphs, Eulerian and Hamiltonian graphs, matching in graphs, coloring maps and graphs, Ramsey theory.
Course Syllabus: Click here to download course syllabus in PDF format.
Web page: http://www.math.umn.edu/~akhmedov/M4707.html.
Grading: The course grade will be based on five bi-weekly homework assignments, two in-class midterm examinations,
and a comprehensive take-home final, with the following weights:
Exams: There will be two in-class midterm examinations (Wednesday, March 3 and Wednesday, April 14) and a comprehensive take-home final examination (due Wednesday, May 5). Notes, books, or calculators will not be permitted for exams. You may bring a formula sheet: 8.5" x 11" written on one side, in your own handwriting. Each midterm exam will be 150 points (15% of the course grade), and the final exam will be 300 points (30% the course grade). NO MAKE UP EXAMS WILL BE GIVEN. Please bring your student ID to the exam. If you have any problem with the grading of your exam, you must bring it to my attention immediately (the same day the tests are returned)! Otherwise, I'll not be able to make any changes.
Homework: There will be 5 biweekly homeworks in this course, each worth 80 points. Homework will be a fundamental part of this course, and will be worth 400 points (40% of the course grade). NO LATE HOMEWORK WILL BE ACCEPTED. The first homework assignment will be due on February 10. You may collaborate on the homework problems, but you must write your own solutions. Please staple your homework before handing it in. If you have questions about the homework, it is best to ask during my office hours.
| Assignment | Problems from the Text |
|---|---|
| Homework 1 due Feb 10 | Chapter 1
Problems 1.8.10, 1.8.12, 1.8.14, 1.8.16, 1.8.21, 1.8.23, 1.8.27, 1.8.29, 1.8.33 Chapter 2
Chapter 3
|
| Homework 2 due Feb 24 | Chapter 4
Problems 4.3.5, 4.3.6, 4.3.8, 4.3.9, 4.3.11, 4.3.14 Chapter 5
|
| March 3 | MIDTERM I with Solutions
|
| Homework 3 due March 31 | Chapter 6
Problems 6.10.4, 6.10.5, 6.10.6, 6.10.7, 6.10.9, 6.10.12, 6.10.17, 6.10.19, 6.10.22. Chapter 7
|
| Homework 4 due Apr 12 |
Chapter 8
Problems 8.5.2, 8.5.3, 8.5.4, 8.5.6, 8.5.7, 8.5.8, 8.5.11 Chapter 10
|
| April 14 | MIDTERM II
|
| Homework 5 due May 3 | Chapter 11
Problems 11.3.2, 11.3.3, 11.3.4, 11.3.5, 11.3.6, 11.3.7 Chapter 12
Chapter 13
|
| DUE: Monday, May 10 (2.00pm - 5.00pm, Vincent Hall 355) | TAKE HOME FINAL with SOLUTIONS
|