Some previous exposure to graph theory may be helpful, but is definitely not necessary.
|Instructor:||Victor Reiner (You can call me "Vic").|
|Office: Vincent Hall 256
Telephone (with voice mail): 625-6682
Monday, Wednesday, Friday 12:20-1:10 PM
in Vincent Hall 207
|Office hours:||Mondays 1:25, Wednesdays 11:15, and also by appointment.|
This is a junior-senior level undergrad course on various methods
used in combinatorial optimization. Topics we hope to discuss include:
|Texts:|| Linear programming, by Vasek Chvatal, W.H. Freeman and Co., 1983.|
This should be available at the bookstore.
A course in combinatorial optimization , lecture notes by Alexander Schrijver.
Hopefully most of you can print it from here in PostScript or PDF, or maybe we'll get some copies reproduced.
Here is a handout (PostScript, PDF) on the built-in linear programming commands
in Maple, Mathematica, and MATLAB.
|Level||Title||Author(s), Publ. info||Location|
|Same or lower||Linear programming and its applications||J. K. Strayer, Springer-Verlag 1989||On reserve in math library|
|Introduction to linear optimization||D. Bertsimas and J.N. Tsitsiklis, Athena Scientific, 1997.||In Walter library, call no. T57.74 .B465|
|Introduction to operations reserach||F. Hillier and G. Lieberman, Holden-Day 1986||On reserve in math library|
|Linear programming: methods and applications||S. Gass, McGraw-Hill 1985||On reserve in math library|
|Higher||Theory of linear and integer programming||A. Schrijver, Wiley and Sons 1998||On reserve in math library|
|Combinatorial optimization: algorithms and complexity||C. Papadimitriou and K. Steiglitz, Dover reprints||In Walter library, call no. QA402.5 .P37|
I also found the following on-line list of linear programming books (by B. Engel at Purdue) to be useful.
|Topic||Title||Author(s), Publ. info||Location|
|Graph algorithms/theorems||Intro. to Graph theory, 2nd edition||D. West, Prentice Hall 2001||On reserve in math library|
|Stable matching|| Stable marriage and its relation
to other combinatorial problems
|D.E. Knuth, Amer. Math. Society 1997||In math library, call no. QA164 .K5913 1997|
|Assignment or Exam||Due date||Problems|
|Homework 1||Wed Feb. 4||
1.1, 1.2(i), 1.4, 1.6, 1.7, 1.10
|Homework 2||Wed Feb. 18||
1.1, 1.2, 1.3, 1.4, 1.6,
2.1(a) (via dictionaries; show each dictionary and pivot step),
2.1(b) (via tableaux; show each tableau and pivot step),
2.2, 3.1, 3.9(a,b)
|Midterm exam I||Wed Feb. 25||Exam I in PostScript, PDF|
|Homework 3||Wed 3/10||
5.1, 5.4, 7.1 (do 2.1(a,c) only), 9.1, 9.2, 11.1
|Homework 4||Wed 3/31||
Chvatal's Exercises 15.1, 15.5, 15.12
Schrijver's Exercises 2.24, 3.2, 3.3, 3.4, 3.5
|Midterm exam II||Wed Apr. 7||Exam II in PostScript, PDF|
|Homework 5||Wed 4/21||
Schrijver's Exercises 3.20, 3.23(i), 5.7(i)
plus these non-Schrijver problems in PostScript, PDF
(and for a bonus challenge, try Schrijver's Exercise 3.11).
|Homework 6||Fri 4/30||Schrijver's Exercises 5.8(i), 5.9, 5.11, 5.13, 5.14, 5.17|
|Final exam||Fri 5/7||Exam I in PostScript, PDF|
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