| Course Code: CS1115 Course Name: Discrete Mathematics Prerequisites: Nil Syllabus: Set theory: sets, relations, functions, equivalence relations, partial orders, Hasse diagrams; Logic: propositional and predicate logic, truth tables, logical equivalence, inference rules, proof techniques, satisfiability; Combinatorics: counting, permutations, combinations, inclusion-exclusion, pigeonhole principle, recurrence relations, generating functions; Elementary number theory: divisibility, primes, GCD, Euclidean algorithm, modular arithmetic, Fermat`s Little Theorem, Eule`s theorem, Chinese Remainder Theorem, RSA cryptography; Algebra: Definitions and examples of groups, rings, fields, coding theory applications. Texts: 1. E. Lehman, F. T. Leighton, and A. R. Meyer, Mathematics for Computer Science. MIT OpenCourseWare, 2017. Available online: https://courses.csail.mit.edu/6.042/julie/ 2. K. H. Rosen, Discrete Mathematics and Its Applications, 7th Edition. McGraw-Hill Education, 2012. ISBN: 9780073383095. References: 1. R. Johnsonbaugh, Discrete Mathematics, 7th Edition, Pearson, 2008. 2. R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics: A Foundation for Computer Science, 2nd Edition. Addison-Wesley, 1994 3. V. Shoup, A Computational Introduction to Number Theory and Algebra, 2nd Edition. Cambridge University Press, 2009. ISBN: 9780521516440. Available online: https://shoup.net/ntb/ |