Resources for Math 381

Books

• W. L. Winston, Operations Reseach: Applications and Algorithms, Thompson - Brooks/Cole, Belmont, CA, 2004 pdf.
• Applied Mathematical Programming by Bradley, Hax, and Magnanti (Addison-Wesley, 1977). pdf (20 meg)   pdf (chapter 9, Integer Programming, only)
• Basic Probability Theory, by Robert B. Ash. pdf chapters.

• F. S. Roberts, Applied Combinatorics, Prentice-Hall, Englewood Cliffs, N.J., 1984.
• F. S. Roberts, Discrete mathematical models, with applications to social, biological, and environmental problems, Prentice-Hall, Englewood Cliffs, N.J., 1976.
• D. P. Gaver and G. L. Thompson, Programming and probability models in operations research, Brooks/Cole Pub. Co., 1973.
• F. S. Hillier and G. J. Lieberman, Introduction to operations research, McGraw-Hill, New York, 1995.
• M. M. Meerschaert, Mathematical Modeling, Academic Press, San Diego, 1993.
• S. M. Ross, A Course in Simulation, Macmillan Publishing Company, New York, 1990.
• W. L. Winston, Operations Research; Applications and Algorithms, Brooks/Cole, 2004.

Blogs

• Punk Rock Operations Research

Software

• PARI/GP. Free, open source library and command-line front end computer algebra system. I use this all the time. Exact calculations are on of its strengths.
• Sage. Free, open source computer algebra system. Very powerful, can do anything Mathematica, Maple, Matlab, etc. can do, but it is free. Nice tools for studying graphs, good plotting tools, lots of great stuff.
• R. Free software environment for statistical computing and graphics. Can do LP, IP, MDS, and lots of other stuff.
• lpsolve. Free, open source LP solver. Easier to use for LPs than R.
• LaTeX. THE way to typeset mathematics and mathematical works. Totally free.

Examples and things to inspire project ideas

• Linear programming
• Gerald G. Brown and Robert F. Dell, Formulating Integer Linear Programs: A Rogues' Gallery. pdf.
• Software
• lpsolve - this is perhaps the best free LP solver; you can find a version that will run on most any machine
• Sourceforge page
• lp-format
• options when running lpsolve
• Diet problem
• "The Diet Problem", George B. Dantzig,Interfaces,Vol. 20, No. 4, The Practice of Mathematical Programming (Jul. - Aug., 1990), pp. 43-47
• Wikipedia page for Stigler_diet
• Transportation problem
• Shun-Chen Liu, "The Transportation Problem: LP Formulations"
• Knapsack problem
• Silvano Martello and Paolo Toth, Knapsack Problems. See Chapter 2, especially.
• Cellular automata
• Robert A. Bosch, Integer Programming and Conway's Game of Life, SIAM Review, 41(1), pp.594-604, pdf
• Chess-related
• L.R. Foulds and D.G. Johnston, An Application of Graph Theory and Integer Programming: Chessboard Non-attacking puzzles, Mathematics Magazine, Vol. 57, No. 2, (Mar. 1994), pp. 95-104. link.
• Martin J. Chlond, (2010) Puzzle-Knight Domination of 2-D Surfaces: A Spreadsheet Approach. INFORMS Transactions on Education 10(2):98-101.pdf
• Puzzles
• Fumika Kino and Yushi Uno, An Integer Programming Approach to Solving Tantrix on Fixed Boards, Algorithms, 2012, 5, 158-175.pdf.
• Andrew C. Bartlett et al, An Integer Programming Model for the Sudoku Problem. pdf.
• W. J. M. Meuffels and D. den Hertog, Solving the Battleship Puzzle as an Integer Programming Problem, Informs: Transactions on Education, Vol. 10, No. 3, May 2010, pp. 156-162. pdf.
• J. M. Wilson, Crossword Compilation Using Integer Programming, 1989. pdf.
• Scheduling
• Lorraine Trilling, Alain Guinet, Dominique Le Magny, Nurse scheduling using integer linear programming and constraint programming, 12th IFAC Symposium on Information Control Problems in Manufacturing INCOM 2006, Sep 2007, Saint-Etienne, France. Elsevier, 3, pp.651-656, 2006. link.
• Music
• Iannis Xenakis, Formalized Music: Thought and Mathematics in Computation, 1992, Pendragon Press [see chapter IV]. pdf
• Tsubasa Tanaka and Koichi Fujii, Describing Global Musical Structures by Integer Programming on Musical Patterns, in Mathematics and Computation in Music, Volume 9110, pp. 52-63. link
• Manufacturing
• Carina Pimentel et al, A Scheduling Model For A Knitting Planning Problem, Manufacturing Fundamentals: Necessity and Sufficiency, Chapter 16. pdf.
• Other
• Diane Perez, How Do Restaurants Use Linear Programming for Menu Planning? (This is not well written, but it might give you some ideas.)
• A blog post connecting linear programming and World of Warcraft. link.
• Paying off debt efficiently (StackExchange question). link.
• Dynamic linear programming
• C. D. Throsby, Some Notes On Dynamic Linear Programming, Review of Marketing and Agricultural Economics, 01/1962, 30(02)
• Graph theory
• Awesome wikipedia page of named graphs
• Big list of what Sage can do with graphs
• graph coloring
• Graph coloring at Wikipedia
• Mathematics of Sudoku
• traveling salesman problem (TSP)
• TSP at Wikipedia
• From Donald Davendra (Ed.), "Traveling Salesman Problem, Theory and Applications", Chapter 1: Rajesh Matai, Surya Prakash Singh and Murari Lal Mittal, Traveling Salesman Problem: An Overview of Applications, Formulations, and Solution Approaches.pdf.
• Approximating algorithms
• Birsen Irem Selamoglu and Abdellah Salhi, The Strip Algorithm Revisited, International Conference on Metaheuristics and Nature Inspired Computing (2014). pdf.
• Applications
• Welding
• Andras Kovacs, Task Sequencing for Remote Laser Welding in the Automotive Industry, Proceedings of the 23rd International Conference on Automated Planning and Scheduling, pp 457-461. pdf.
• Surgery
• JL Falcon, X Chen, GG, Hamad, The traveling salesman problem in surgery: economy of motion for the FLS Peg Transfer task, Surg Endosc 2013 May:27(5):1636-41. link.
• small-world networks
• Wikipedia links:
• small-world networks
• small-world experiment
• clustering coefficient
• average shortest path
• Watts-Strogatz model
• Jeffrey Travers and Stanley Milgram, An Experimental Study of the Small World Problem, Sociometry, Vol. 32, No. 4, (Dec. 1969), pp. 425-443. pdf.
• NY Times article about Facebook small world calculation. link.
• Information about the Erdos number graph. link.
• Collaboration in artistic performance
• Brian Uzzi and Jarrett Spiro, Collaboration and Creativity: The Small World Problem, American Journal of Sociology, 111(2) (September 2005): 447-504. pdf.
• Markov chains
• References
• Wai-Ki Ching and Michael K. Ng, Markov Chains: Models, Algorithms and Applications, Spring Science+Business Media, Inc., 2006. pdf.
• Applications
• General
• Philipp Von Hilgers and Amy N. Langville, The Five Greatest Applications of Markov Chains. pdf.
• Biology
• Elise F. Zipkin, Christopher S. Jennelle, and Evan G. Cooch, A primer on the application of Markov chains to the study of wildlife disease dynamics, Methods in Ecology & Evolution 2010,1, 192-198. pdf.
• Chemistry
• Sebastião J. Formosinho, A Markov Chain for Simulating the Time Evolution Drug in Pharmokinetics Systems, Revista Portuguesa de Química, 26, 14 (1984). pdf.
• Social mobility
• Valentino Dardanoni, Measuring Social Mobility, Journal of Economic Theory, 61, 372-394 (1993). pdf
• Games
• Jason A. Osborne, Markov Chains for the RISK Board Game Revisited, Mathematics Magazine 76 (2003) 129-135. pdf.
• Robert B. Ash and Richard L. Bishop, Monopoly as a Markov Process. pdf.
• Linguistics
• Dmitri V. Khmelev and Fiona J. Tweedie, Using Markov Chains for Identification of Writers, Literary and Linguistic Computing, 2001, vol. 16, no. 4, 299-307. pdf.
• Chapter 8 (Probabilistic Language Models) from Michael Hammond, Introduction to the Mathematics of Language (unpublished?).pdf.
• Tony Fischetti, How to fake a sophisticated knowledge of wine with Markov chains. blog post.
• Music
• Wikipedia page.
• Roman Klinger and Gunter Rudolph, Automatic Composition of Music with Methods of Computational Intelligence, WSEAS TRANS. on INFORMATION SCIENCE & APPLICATIONS Issue 3, Volume 4, March 2007. pdf.
• Monte Carlo simulation
• Charles J. Mode (editor), Applications Of Monte Carlo Methods In Biology, Medicine And Other Fields Of Science, Intech. link.
• Shaul Mordechai (editor), Applications of Monte Carlo Method in Science and Engineering, Intech. link.
• Blog post regarding monte carlo simulation and fantasy football leagues. blog.
• Jiri Lahvicka, Using Monte Carlo simulation to calculate match importance: the case of English Premier League. link.
• Multidimensional scaling (MDS)
• General reading
• Gale Young and A. S. Householder, Discussion of a set of points in terms of their mutual distances, Psychometrika, Vol. 3, No. 1, March 1938. pdf.
• Applications
• Psychology
• Megan H. Papesh and Stephen D. Goldinger, A multidimensional scaling analysis of own- and cross-race face space, Cognition, Volume 116, Issue 2, August 2010, Pages 283-288.link.
• Marta L. Axelson, et al, An Analysis of the Four Food Groups Using Multidimensional Scaling, Journal of Nutrition Education, Vol 18 Issue 6, Dec. 1986, pp. 265-273.link.
• Marc L. Carter, et al, Perception of Sports Photographs: A Multidimensional Scaling Analysis, Perceptual and Motor Skills, 2001, 92, 643-652. pdf.
• Food
• (Blog post) Seeing India through Food - An Experiment in Multidimensional Scaling. blog post.
• Timbre
• Paul Iverson and Carol L. Krumhansl, Isolating the dynamic attributes of musical timbre, J. Acoust. Soc. Am. 94 (5), November 1993.pdf.
• John M. Grey, Multidimensional perceptual scaling of musical timbres, J. Acoust. Soc. Am. 61 (5), May 1977. pdf.