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Questions or Comments?
- Send me email (click here and delete "QQQ")
- Homepage: http://www.math.uconn.edu/~troby
- Offices: MBS M404 and CUE 123: phone: 860-486-8385
- Office hours: Tuesday 1:00-1:40, Thursday 10-10:50 in MSB 404 and by appointment. You can often find me in CUE 123 on MWF 9:30-11:30 (but safest to call first). I'm happy to answer questions or schedule appointments by email, which I check frequently.
Class Information
COORDINATES: Classes meet Tuesdays and Thursdays 11-12:15 in MSB 311. The registrar calls this Section 001, #9939.
PREREQUISITES: Math 2710 (old 213) or Math 2142 (old 244).
TEXT: Miklos Bona: A Walk through Combinatorics, 2nd Ed. Available in the bookstore. Let me know if you have any trouble getting it.
WEB RESOURCES: The homepage for this course is http://www.math.uconn.edu/~troby/Math3250F08/.
GRADING: Your grade will be based on a midterm exam, a final exam, homework, and quizzes.
The breakdown of points is:
| Midterm | Final | Homework | Quizzes
|
|---|---|---|---|
| 25% | 35% | 20% | 20% |
EXAMS: The exam dates are already scheduled, so please mark your calendars now (midterm on 14 October, final on 12 December). No makeups will be given; instead if you have an approved reason for missing an exam, the final will count for the appropriately higher percentage.
CONTENT: Combinatorics is related to the word "combinations", and much of the field deals with counting problems ("enumeration"). More broadly, combinatorics considers discrete structures, such as graphs, (as opposed to the continuous structures considers in calculus and analysis) and questions that go beyond simply counting the number of possibilities. With the advent of computers in the second half of the last century, such questions have become increasingly important in applications as well as more managable to solve. Specifically, we plan to go through the following topics from the text:
- Pigeon-Hole Principle;
- Permutations & Combinations;
- Binomial Theorem;
- Partitions:
- Sieve methods (Principle of Inclusion-Exclusion);
- Generating functions;
- Graph theory;
- Trees;
- Matchings;
- and Partially-ordered sets ("Posets").
DISABILITIES If you have a documented disability and wish to discuss academic accommodations, or if you would need assistance in the event of an emergency, please contact me as soon as possible.
LEARNING: The only way to learn mathematics is by doing it! Complete each assignment to the best of your ability, and get help when you are confused. Come to class prepared with questions. Don't hesitate to seek help from other students. Sometimes the point of view of someone who has just figured something out can be the most helpful.
We will often spend classtime doing things in groups, presenting mathematics to one another, or having interactive discussions. There will not be time for "cover" all material in a lecture format so you will need to read and learn some topics from the book.
QUIZZES & HOMEWORK Quizzes will be given on many Tuesdays based on the previous week's material. Homework will be assigned weekly. I will collect homework (usually on Thursdays) and grade a pseudorandom sample of it. Trying to do all the homework problems by Tuesday is a good way to study for the quiz.
You may find some homework problems to be challenging, leading you
to spend lots of time working on them and sometimes get frustrated.
This is natural. I encourage you to work with other people in person
or electronically. It's OK to get significant help from any
resource, but in the end, please write your own solution in your own
words.
| 3250 LECTURE AND ASSIGNMENT SCHEDULE | |||
|---|---|---|---|
| Date | |
|
|
| 8/26 T | Ch. 1 | Pigeon-Hole Principle | |
| 8/28 R | Ch. 3 | Permutations | HW1 (due 9/4): #15,16,17,20,21,22,25 |
| 9/2 T | Ch. 3 | Permutations & words | Quiz #1 (Ch. 1 #1,10,12) |
| 9/4 R | Ch. 4 | Combinations | HW2 (due 9/11): Ch. 3: #25-43odd |
| 9/9 T | Ch. 4 | Binomial Theorem & Pascal's Triangle | Quiz #2 (Ch. 3: #1-19odd) |
| 9/11 R | Ch. 4 | Identities using Binomial Thm and bijections | HW3 (due 9/18) Ch.4: #31,32,33,36,37,43,44,46 |
| 9/16 T | Ch. 4 | Going over HW | Quiz #3 (Ch.4: #3,4,8,9,11,14,16,17,25) |
| 9/18 R | Ch.4-5 | Multinomial Thm & Partitions | |
| 9/23 T | Ch. 5 | Stirling Numbers (2nd kind) | HW4 (due 10/2): Ch. 5: 16-30even |
| 9/25 R | Ch. 5 | Integer Partitions | Quiz #4 (Ch.5: #1-8) |
| 9/30 T | Ch. 5 | The Twelvefold Way | |
| 10/2 R | Ch. 8 | Generating Fns | HW5 (due 10/9): Ch. 8: #23,25,27,28,29 |
| 10/7 T | Ch. 8 | Products of OGF; OGF for partitions | Quiz #5 (Ch.8: #2,4,7-10) |
| 10/9 R | Ch. | Compositions of OGF; EGF? | |
| 10/14 T | Ch. | Review for Midterm | Do Practice Midterm by today |
| THURSDAY 16 OCTOBER: MIDTERM EXAM | |||
| 10/21 | Ch. 6 | Permutations & Cycles | |
| 10/23 | Ch. 6 | Stirling Numbers (first kind) | Class Feedback Due |
| 10/28 | Ch. 7 | Perms with restricted cycles | Quiz #6 (Ch. 6: #1-8,12,16) |
| 10/30 | Ch. 7 | Inclusion-Exclusion | HW 6: Ch. 6: #26-34 |
| 11/4 | OUT SICK | NO Quiz on ch.7 (Ch. 7: 1-4,6,10) | |
| 11/6 | Ch. 7, 9 | PIE; Graph Thy | HW7 (Due 11/13): Ch. 7: 15,16; Ch.9: 25,26,27,29,33,34,39 |
| 11/11 | Ch. 9 | Hamiltonian Cycles & Isomorphisms | Quiz #7 (Ch. 9: 1-11) |
| 11/13 | Ch. 10 | Trees & Cayley's Thm | HW8 (Due 11/20+): Ch. 10 #21,24,25,28,29,31,32) |
| 11/18 | Ch. 10 | Proof of Cayley's Thm. | |
| 11/20 | Ch. 10 | Algebraic Graph Thery | Quiz #8 (Ch. 10: 1-4, 9) |
| 23-29 NOVEMBER THANKSGIVING RECESS, NO CLASSES | |||
| 12/2 | Counting Walks in graphs | ||
| 12/4 R | Walks in the complete graph | ||
| FRIDAY 12 DECEMBER 15:30-17:30 FINAL EXAM IN MSB 219 (NOT OUR USUAL ROOM!) | |||
Interesting Links
- Maybe I'll add some later.
NEWS & NOTES
- Here are the solutions to the practice midterm.
- Here is the practice final.
- Here are (a little late) the solutions to the practice final.
- REVIEW SESSION: Wednesday 10 December 3:00-5:00, meet near MSB404 and we'll find a room (which will be posted on my office door).
Back to my home page.