Welcome to Tom Roby's Math 297 homepage! (Spring 2006)

(last updated: 2 March 2006)

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Class Information

COORDINATES: Lectures meet Tues/Thur. 12:30--1:45 in CUE 133. The registrar calls this Sec 002, #12292

PREREQUISITES: Consent of instructor. I hope most of you know some linear algebra (what's covered in 227 is plenty) and have had some experience doing proofs. If not, let me know so we can figure out additional resources that might help.

TEXT: Miklos Bona, Introduction to Enumerative Combinatorics, McGraw Hill, 2007[!]. ISBN-13: 978-0-07-312561-9, ISBN-10: 0-07-312561-X.

WEB RESOURCES: The homepage for this course is http://www.math.uconn.edu/~troby/Math297S06. It will include a copy of the syllabus and list of homework assignments. I will keep this updated throughout the semester.

This course has a WebCT VISTA homepage, with discussion forums that I strongly encourage you to use. Go to WebCT at http://webct.uconn.edu/. For help with WebCT go to http://irc.uconn.edu/Student_WebCT_HELP.htm .

LEARNING GOALS: Students will learn the basic techniques of enumerative combinatorics and how to apply these to a wide range of problems within discrete math. Specific content will include Chapters 1-3 of Bona, and a selection of topics from the rest of the book. (My favorites are chapters 4,5,8 and 9.)

More importantly, students will gain experience in skills of global importance within (and beyond) mathematics:

LEARNING: The only way to learn mathematics is by doing it! I expect everyone in this class to be actively engaged with material. Come to class prepared with questions. Don't hesitate to seek help from other students as well as me. Sometimes the point of view of someone who has just figured something out can be the most helpful.

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.

GRADING: Your grade will be based on a midterm exam, homework, and a project. The breakdown of points is:

Homework Midterm Project
30% 30% 40%

MIDTERM EXAM: Will cover all the material to that point in the term. It is scheduled for 23 March. No makeups can be given, so please mark your calendar now.

HOMEWORK: Homework will be assigned for each class, and should be attempted by the next class meeting. I will collect homework for each week on thursday of the following week. You can ask questions about the homework in one of the WebCT forums. Except for routine computations, you should always give reasons to support your work and explain your reasoning. I will collect homework and grade some (pseudo randomly selected) subset of the problems.

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 and using WebCT. It's OK to get significant help from any resource, but in the end, please write your own solution in your own words. Copying someone else's work without credit is plagiarism and will be dealt with according to university policy. It also is a poor learning strategy.

Bona has a section of "Exercises" for each chapter that come with complete solutions, as well as "Supplementary Exercises" without solutions. I recommend that you attempt most of the former, turning to the solutions as little as possible. Collected homework will generally be taken from the latter.

PROJECTS: are described in the link. Please select your research topics by 9 February. First drafts of papers are due 10 April. Presentations will start shortly thereafter.

Date Sections Topics Homework Problems
1/17 T S1.1-4 Basic Methods (Add, Sub, Mult., Div.) 1.10#1,3,5
1/19 R S1.4-1.5 Applications and Bijective Proofs 1.10#22,24,30
1/24 T S1.1-9 Applications & Bijective proofs 1.10#8,12,15,17,24,30,34
1/26 R S1.1-9 Applications and Pigeon Hole Principle 1.10#22,38,40
1/31 T S2.1-2 Compositions (weak and strict) 2.10#1,3,5,7,9,11
2/2 R S2.2 Stirling Numbers
2/7 T S2.2 Stirling & Bell Numbers 1.10#18,42; 2.10#14; Bin.Coef Boot Thm
2/9 R S2.3: Integer Partitions Select Research topics by today. 2.10#16-22
2/14 T S2.4 Inclusion-Exclusion Principle
2/16 R S2.5 The Twelvefold Way I Work on projects
2/21 T S2.5 The Twelvefold Way II
2/23 R S3.1-2 GeneratingFunctionology Homework #5
2/27 T S3.2 Solving recursions
3/2 R S.0.0 Snow Day--Class Cancelled!
3/14 T Old Homework Review HW#5 due
3/16 R S3.3 Products of Gen Fns 2.10#31,33,34,35,38,39 DUE
3/21 T
3/23 R Project Outlines AND HW rewrites due
3/28 T S1.1-3.3 Catchup & Review Day (Do Practice Midterm by today)
4/4 T S4.2.1 Stirling Numbers of the First Kind
4/6 R S4.2 More on Stirling Numbers HW7: Bona 3.10.#6-12,16,21
MONDAY 10 APRIL 2006, noon First Drafts DUE
4/11 T S4.3 Cycle Structure and Exp. Gen. Fns
4/13 R S4.4 Inversions Hand in HW7; HW8: TBA
4/18 T S5.1-2: Counting Graphs Diana & Marianne
4/20 R S5.3: Cayley's Thm Alon & Brianna Hand in Midterm Rewrites
4/25 T Dan, John, Kevin Hand in HW 8
4/27 R Isaac, Piku, Evals Hand in final versions of papers

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