Propositional Logic – Propositional equivalences – Predicates and Quantifiers – Nested Quantifiers – Rules of inference.
Mathematical induction – Strong induction– The basics of counting – The pigeonhole principle – Permutations and combinations – Recurrence relations – Solving linear recurrence relations – Generating functions – Inclusion and exclusion principle and its applications.
Graphs and graph models – Graph terminology and special types of graphs – Matrix representation of graphs and graph isomorphism – Connectivity – Euler and Hamilton paths, circuits-Planar graphs, Introduction to trees, application of trees.
Groups – Subgroups – Homomorphism’s , Isomorphism - Normal subgroup and cosets – Lagrange’s theorem –Cayley’s Theorem-Fundamental Theorem of group homomorphism- Definition and examples of Rings, Integral domains and Fields.
Relations and their properties-Partial ordering – Posets – Lattices as Posets – Properties of lattices – Lattices as algebraic systems – Sub lattices – Direct product and homomorphism –– Boolean algebra.
Reference Book:
Grimaldi.R.P., “Discrete and Combinatorial Mathematics: An Applied Introductionâ€,5th Edition, Pearson Education Asia, Delhi, 2014. Eric Lehman, F Tom Leighton, Albert R Meyer, “Mathematics for Computer Scienceâ€, Samurai Media Limited, 2017 Lipschutz.S and Mark Lipson, “Discrete Mathematicsâ€, Schaum’s Outlines, Tata McGraw Hill Pub. Co. Ltd., New Delhi, 3rd Edition,2010 Koshy.T, “Discrete Mathematics with Applicationsâ€, Elsevier Publications, 2006. Balakrishnan, V.K.,†Introductory Discrete Mathematicsâ€, Dover Publications Inc, New York, 2010. Norman L Biggs, â€Discrete Mathematicsâ€, Oxford University press, Oxford, 2nd Edition, 2003.
Text Book:
Kenneth H Rosen, “Discrete Mathematics and its Applicationsâ€, 7th Edition, Special Indian edition, Tata McGraw Hill, New Delhi, 2017. Tremblay J.P. and Manohar.R, "Discrete Mathematical Structures with Applications to Computer Science", Tata Mc Graw Hill Pub. Co. Ltd, New Delhi, 30th Reprint, 2011.
