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Unformatted text preview: Discrete Mathematical Modeling Math 381 Course Notes University of Washington Prof. Sara Billey Winter Quarter, 2009 c circlecopyrt R. J. LeVeque 2 Acknowledgments : These notes are based on many quarters of Math 381 at the University of Washington. They have developed in a wiki fashion. The original notes were compiled by Randy LeVeque in Applied Math at UW. Tim Chartier and Anne Greenbaum contributed significantly to the current version in 20012002. Jim Burke contributed a portion of the chapter on linear programming. Sara Billey contributed a portion of the chapter on Stochastic Processes. We thank them for their efforts. Since this document is still evolving, we appreciate the input of our readers in improving the text and its content. Sara Billey adds: I have gotten a lot of inspiration for this course from the following sources: Operations Research by Wayne Winston. Mathematics in Service to the Community: Concepts and Models for Servicelearning in the Mathematical Sciences (Maa Notes #66) edited by Charles R. Hadlock. Discrete Mathematical Models: With Applications to Social, Biological, and Environmental Problems by Fred Roberts. Freakonomics by Steven Levitt and Stephen Dubner Three Cups of Tea: One Mans Mission to Promote Peace . . . One School at a Time by Greg Mortenson and David Oliver Relin Mountains beyond mountains by Tracy Kidder My friend Amy Smith: inventor of lowtech devices for use in developing countries. See http://en.wikipedia.org/wiki/Amy_Smith http://www.ted.com/index.php/talks/amy_smith_shares_simple_lifesaving_design.html The following information is the bibtex citation for these notes if you want to cite them as a reference: @Book{381notes, author = {Sara Billey, James Burke,Tim Chartier, Anne Greenbaum and Randy LeVeque}, title = {Discrete Mathematical Modeling: Math 381 Course Notes}, year = {2010}, publisher = {University of Washington}, } Math 381 Notes University of Washington Winter 2009 Contents 1 Introduction to Modeling 1 1.1 Lifeboats and life vests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The modeling process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 The goals of 381 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Graph Theory and Network Flows 9 2.1 Graphs and networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 The traveling salesman problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.1 Brute force search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.2 Counting the possibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.3 Enumerating all possibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Enumerating all possibilities ....
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This note was uploaded on 07/22/2010 for the course MATH 11853 taught by Professor Aravkin,aleksandry during the Summer '10 term at University of Washington.
 Summer '10
 Aravkin,AleksandrY
 Math, Three Cups of Tea

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