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- Send me email (click here and delete "QQQ")
- Homepage: http://www.math.uconn.edu/~troby
- Math Dept. Office: MBS M404, phone: 860-486-8385

- Q Center Office: CUE 123, phone: 860-486-4433

- Office hours: Tuesday 2-3 in CUE 123 and by appointment. I'm happy to answer questions or schedule appointments anytime by email, which I check frequently.

* 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:

- constructing and carefully writing up rigorous proofs
- solving problems for which templates are not given
- presenting mathematics to others

* 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.

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.

MATH 297 LECTURE AND ASSIGNMENT SCHEDULE | |||
---|---|---|---|

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! | |

6-10 MARCH 2006 SPRING BREAK | |||

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) |

THURSDAY 30 MARCH 2006 MIDTERM EXAM | |||

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 |

- The fine Electronic Journal of Combinatorics also has has a directory of webpages of combinatorialists, survey articles, and more.
- A similar effort which includes the journal Annals of Combinatorics is run out of Nakai University by Bill Chen.
- Here is a powerpoint presentation put together by Liz Ginno of Cal State East Bay on how to use MathSciNet. The main site specfic difference is that to use MathSciNet from off-campus at UConn, you need to login to the Virtual Private Network site using your NetID.
- Here is a Handout on library resources also put together by Liz Ginno
- Here is the Practice Midterm
- Here is the Midterm
- Here are my Policies on rewrites.

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