Math 5705: Enumerative combinatorics

Spring 2005

Prerequisites: Differential and integral (single variable) calculus.
A bit of linear algebra may be helpful, but is not absolutely required.  
Instructor: Victor Reiner (You can call me "Vic"). 
Office: Vincent Hall 256
Telephone (with voice mail): 625-6682
Classes: Monday-Wednesday 3:35-5:00 PM in Amundsen Hall 116  
Office hours: Mon 2:30pm, Tues 4:40pm, and by appointment.  
Course content: This is a junior-senior level undergrad course on enumeration, that is, counting things.
Topics include elementary counting techniques, including the principle of inclusion-exclusion,
along with with more sophisticated techniques, such as generating functions and Polya theory.
Note that Math 4707 is class which covers some of this material at a somewhat lower-level, along with some of the graph theory covered in Math 5707.
WARNING: This class will use almost entirely the method of active learning in small groups.
Our text will be a sequence of problems to be solved, intended to guide the
student through most of the material that is often covered in this class
via more traditional lecture methods.
Required text: Combinatorics through guided discovery by Kenneth P. Bogart.
This is available in PDF here,
and copies are available for something like $10 or less
at Alpha Print in Dinkytown (1407 4th St SE, (612) 379-8535); ask for Bin 12.
Other useful texts
Level Title Author(s), Publ. info Location
Lower Applied combinatorics
with problem solving
Jackson and Thoro, Addison-Wesley 1990 On reserve in math library (for 4707)
Same Introductory combinatorics Bogart, Harcourt/Acad. Press 2000 On reserve in math library
Applied combinatorics Tucker, Wiley & Sons 2001 On reserve in math library
Introductory combinatorics Brualdi, Prentice Hall 1999 On reserve in math library
Higher Enumerative combinatorics,
Vols I, II
Stanley, Cambridge Univ. Press In math library, Call no. QA164.8 .S73 1997
Defy labels Generatingfunctionology Wilf, Academic Press 1994 In math library, Call no. QA353 .G44 W55 1994,
or download it for free.
Constructive combinatorics Stanton and White, 1986 In math library, Call no. QA164 .S79 1986
Homework: There will be homework assignments due every other week (except weeks with exams) at the beginning of the Wednesday class, starting with Wednesday February 2. The assignments will be mostly problems from the book, and I will try to hand out brief solutions or solution outlines. Late homework will not be accepted. I encourage collaboration on the homework, as long as each person understands the solutions, writes them up in their own words, and indicates on the homework page with whom they have collaborated.  
Exams and grading:  There will be three take-home midterm exams, each worth 10% of the grade, and one take-home final exam worth 20%. I will make a rough evaluation of your in-class group work participation and preparation, worth 5% of the grade. The remaining 45% of the course grade will be based on the quality and quantity of homework turned in.

Both the take-home midterm and final exams are to be open-book, open-notes, but there is to be no collaboration; the only human source you will be allowed to consult is the instructor.  
Policy on incompletes:  Incompletes will be given only in exceptional circumstances, where the student has completed almost the entire course with a passing grade, but something unexpected happens to prevent completion of the course. Incompletes will never be made up by taking the course again later. You must talk to me before the final exam if you think an incomplete may be warranted.  
Other expectations  This is a 4-credit course, so I would guess that the average student should spend about 8 hours per week outside of class to get a decent grade. Part of this time each week would be well-spent making a first pass through the next few problems in the book that we anticipate to cover in class that week, so that you can bring your questions/confusions to class and ask about them.
Class problems from Bogart's
Combinatorics through guided discovery
Chapter 1 #2,3,4,6,7,8,
Chapter 2 #81,
Chapter 3 #122,124,125,126,128,129,
Chapter 4 #178,179,181,183,185,187,189,190,192,194,195,197,
Chapter 5 #225,227,228,229,
Appendix C #373,376,377,378,380,
Chapter 6 248,249,254,256,257,258,259,274,288,291,293,294,295,
(didn't get to #310,314,322)
Homework assignments
Assignment or Exam Due date Problems
HW 1 Wed Feb. 2 Chapter 1, #17,19,26,27,32(c),37, 45
Chapter 1 Supp. Probs. #1,2,7
Midterm 1 Wed Feb. 9 Midterm 1 in PostScript, PDF
HW 2 Wed Feb. 23 Chapter 1, #50, 55, 56, 63
Chapter 1 Supp. Probs. #3,4,5,10
Chapter 2, # 72, 74
Midterm 2 Wed Mar. 2 Midterm 2 in PostScript, PDF
HW 3 Wed Mar. 23 Chapter 2 Supp. Prob. #3
Chapter 3 # 127, 137, 146, 147, 165, 170, 172
Chapter 3 Supp. Probs. #1,5,11
HW 4 Wed Apr. 6 Chapter 3 Supp. Prob. #2, 3, 7, 8, 12
Chapter 4 #184, 198, 210(a-g)
Midterm 3 Wed Apr. 13 Midterm 3 in PostScript, PDF
HW 5 Wed Apr. 27 Chapter 5 #236
Chapter 5 Supp. Probs. #1,2,5
Appendix C #372,374,375,379
Final exam Wed May 4 Final exam in PostScript, PDF

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