### Course Syllabus - Fall 2010

From the College Catalog : Emphasis is on enumerative combinatorics. Topics include multinomial coefficients, generating functions, SDRs, Polya's enumeration theory, pigeon-hole principle, inclusion/exclusion and Moebius inversion of finite posets. Topics may also include introduction to designs and finite geometry.

Prerequisites: Undergraduate combinatorics/graph theory and undergraduate algebra courses would be useful, but are not required.

Text: Roberts & Tesman, Applied Combinatorics, 2nd Ed., CRC Press, 2009.

Exams: There will be two exams (midterm and final) - dates below - and it will be highly likely that at least one of them will be a take-home.

Homework: Homework will be assigned from the text and also on handout sheets. Specific assignments will be submitted for grading.

Students may be expected to put homework assignments on the board (details will be discussed in class).

Paper: A paper is required in this course. There will be a list of research articles from which you will select one to read and report on (no duplicates, first come first served).

Presentation: A 15-minute presentation to the class on the topic of your paper will be required at the end of the semester.

Homework and Exams (70%)
Depth paper in a subject covered in class (20%)
In class presentation of paper (10%)

There's no curving of exam grades : A(100-90) B(89-80) C(79-70) D(69-60) F( < 60). Plusses and minuses may be used in final grades at my discretion.

Syllabus:
DateChapterTopic and Sections
8/24 - 9/2Chap. 2 Counting (§ § 10,11,13,14,16,19)
9/7 - 9/14Chap. 5 Generating Functions (§ § 1-5)
9/16 - 9/23 Chap. 6 Recurrence Relations (§ § 1-4)
9/28 - 9/30Chap. 7 PIE (§ § 1-2)
10/5 - 10/14Chap 8 Polya Counting (§ § 1-6)
10/14Midterm Exam
10/19 - 10/28Chap 9 Design Theory (§ § 1-5)
11/2 - 11/11 Chap 10 Coding Theory (§ § 1-5)
11/16 - 11/18Chap 4 Relations, Dilworth's Theorem, Moebius Inversion (§ § 1-4)
11/22 - 11/28Fall Break (Thanksgiving)
11/30 - 12/2Chap 12 SDR's - Hall's Theorem (§ 2)
11/30Papers Due
12/7 - 12/9Student Presentations
12/14 Final Exam Due
Note: Any and all of the above is open to negotiation.

And here is the obligatory notice from CLAS