Propositional Logic – Propositional equivalences – Predicates and Quantifiers – Nested Quantifiers – Rules of inference – Introduction to proofs – Proof methods and strategy.
Mathematical induction – Strong induction and well ordering – 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.
Algebraic systems – Semi groups and monoids – Groups – Subgroups – Homomorphism’s – Normal subgroup and cosets – Lagrange’s theorem.
Partial ordering – Posets – Lattices as posets – Properties of lattices – Lattices as algebraic systems – Sub lattices – Direct product and homomorphism – Some special lattices – Boolean algebra.
Reference Book:
1.Ralph.P. Grimaldi, “Discrete and Combinatorial Mathematics: An Applied Introduction”,5th Edition, Pearson Education Asia, Delhi, 2014. (Unit I, II and III) 2.Thomas Koshy, “Discrete Mathematics with Applications”, Elsevier Publications, 2006. (Unit III) 3.Seymour Lipschutz and Marc Lipson, “Discrete Mathematics”, Schaum’s Outlines, Tata McGraw Hill Pub. Co. Ltd., New Delhi, 3rd Edition, 2010. (Unit IV and V). 4.Balakrishnan, V.K.,” Introductory Discrete Mathematics”, Dover Publications Inc, New York, 2010. (Unit II and III). 5.Norman L Biggs, ”Discrete Mathematics”, Oxford University press, Oxford, 2nd Edition, 2003. (Unit I, II ,III , IV and V)
Text Book:
1.Kenneth H. Rosen, "Discrete Mathematics and its Applications", 7th Edition, Tata Mc Graw Hill Pub. Co. Ltd., New Delhi, Special Indian Edition, 2011. (Unit I, II and III). 2.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. (Unit IV and V).
