Differential and integral (single variable) calculus.
A little bit of linear algebra may be helpful, but is not required.
|Instructor:||Victor Reiner (You can call me "Vic").|
|Office: Vincent Hall 256
Telephone (with voice mail): 625-6682
|Classes:||Mondays and Wednesdays 3:35-5:00 PM in Vincent Hall 311|
|Office hours:||MWF 10:10-11AM, and also by appointment.|
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. There will also be some emphasis on different methods
of proof, including finding bijections between sets when possible.
(Note that Math 4707 is class which covers some of this material at a slightly lower-level, along with some of the graph theory covered in Math 5707).
|Required text:|| Applied combinatorics, 4th edition by Alan Tucker
John Wiley and Sons, 2002.
We intend to cover at least Chapters 5-9 of this book, along with other material.
|Level||Title||Author(s), Publ. info||Location|
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|
|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|
|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 Jan. 30. 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 given out on dates
to be determined later, each worth 15% of the course grade.
There will be one take-home final exam given out either
during the last week of class or final exam week,
worth 25% of the course grade. The remaining 30% 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 material 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.|
5.1 # 2,4,6,13,22,23,35,41
(section 5.2 moved to next homework)
5.2 # 3,4,10,19,27,38,44,53,59,68
5.3 # 2,3,6,10,20,29,30
5.4 # 9,10,23,44
5.5 # 2,11,14bcef,15,20,22
6.1 # 7,13,25,27
6.3 # 12,15,17
6.2 # 2,3,18,31
6.3 # 2,8,16
7.1 # 9,38
7.3 # 2
7.4 # 9
7.5 # 3
6.4 # 3, 12, 16, 19
8.1 # 6,14,16,18,25,28
8.2 # 2,8,11,25,36ab
8.3 # 1, 2cd, 10, 13, 14
|6|| Wed 5/1
(note: only 1 week!)
9.1 # 3,24
9.2 # 3,7,11
9.3 # 5(b)
9.4 # 3,16,19
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