| Course Code: CS514 Course Name: Mathematics for Computer Science Prerequisites: Nil Syllabus: Review of sets, functions, relations; Logic: formulae, interpretations, methods of proof in propositional and predicate logic; Number theory: division algorithm, Euclid's algorithm, fundamental theorem of arithmetic, Chinese remainder theorem; Combinatorics: permutations, combinations, partitions, recurrences, generating functions; Graph Theory: isomorphism, complete graphs, bipartite graphs, matchings, colourability, planarity; Probability: conditional probability, random variables, probability distributions, tail inequalities. Texts: 1. Lehman E. and Leighton, F. T. and Meyer, A. R., Mathematics for Computer Science, Creative Commons, 2011. 2. Rosen, K. H., Discrete Mathematics and its Applications, 7/e, McGraw Hill Education, 2011. References: 1. Graham, R. L., Knuth, D. E., and Patashnik, O., Concrete Mathematics, 2/e, Addison-Wesley, 1994. 2. Burton, D. M., Elementary Number Theory, 7/e, McGraw-Hill Higher Education, 2010. 3. Diestel, R., Graph Theory, 4/e, Springer, 2010. 4. Feller, W., An introduction to probability theory and its Applications Vol. 1, 3/e, Wiley, 2008. 5. Ross, S. M., A First Course in Probability, 9/e, Pearson, 2012. |