MAT302 Discrete Mathematics
This course introduces some of the basic ideas of discrete mathematics, including graph theory, algorithms and their complexity, languages and grammars, and finite state machines. The course assumes familiarity with the foundational concepts of logic and sets, numbers and counting, relations and functions, probability and combinatorics, which have been covered in other courses. The objective is to solidify a foundation for understanding the mathematics of digital computing.
Online or Downloadable References for the Course:
- General Discrete Mathematics
- Chen, WWL. Discrete Mathematics (Compiled Notes). Sydney: Macquarie University, 2008.
- Cooper, Christopher. DMTH137 Discrete Mathematics. Sydney: Macquarie University, 2010.
- Lerma, Miguel A. Notes on Discrete Mathematics. Chicago: Northwestern University, 2005.
- Graph Theory
- Bondy, John Adrian and U.S. R. Murty. Graph Theory with Applications. North Holland, 1976.
- Diestel, Reinhard. Graph Theory, 4th electronic edition (free preview). Springer, 2010.
- See Ch 6-7 in Cooper DMTH137, 2010 and Ch 17-19 in Chen, 2008.
- Tutorials and demonstrations
- Caldwell, Chris K. Graph Theory Tutorials. University of Tennesse Martin.
- Fredricks, Gary. Collection of Small Simple Graphs.
- Demonstration of Djikstra’s shortest path algorithm.
- Graph theory glossary is a good Wikipedia list of annoted graph theory terminology
- Algorithms and their complexity
- Wilf, Herbert S. Algorithms and Complexity, 1st Ed. Philadelphia: Herbert S. Wilf, 1994.
- “Big O notation,” Wikipedia, The Free Encyclopedia, (accessed January 23, 2012).
- “Analysis of algorithms,” Wikipedia, The Free Encyclopedia, (accessed January 23, 2012).
- Stanford University Lecture Video: http://www.academicearth.org/lectures/algorithm-analysis
- Modeling Computation
- Cooper, Christopher. DMTH237 Languages and Machines. Sydney: Macquarie University, 2009.
- See Chapters 5-7 in Chen, 2008.
General Discrete Math References
- Rosen, Kenneth H., Discrete Mathematics and Its Applications, 5th Ed., McGraw-Hill, NY, 2003.
- Sarkar, Swapan K., A Textbook of Discrete Mathematics, S. Chand & Co. Ltd., New Delhi, 2003.
- Johnsonbaugh, Richard, Discrete Mathematics, 5th Ed., Pearson Education Asia, New Delhi, 2001.
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