Matrices, Rank of Matrix, Solving System of Equations-Eigen Values and Eigen Vectors- Inverse of a Matrix - Cayley Hamilton Theorem
Basic Definitions - Venn Diagrams and set operations - Laws of set theory - Principle of inclusion and exclusion - partitions- Permutation and Combination - Relations- Properties of relations - Matrices of relations - Closure operations on relations - Functions - injective, surjective and bijective functions.
Propositions and logical operators - Truth table - Propositions generated by a set, Equivalence and implication - Basic laws- Some more connectives - Functionally complete set of connectives- Normal forms - Proofs in Propositional calculus - Predicate calculus
Languages and Grammars-Phrase Structure Grammar-Classification of Grammars-Pumping Lemma for Regular Languages – Context Free Languages
Finite State Automata-Deterministic Finite State Automata(DFA), Non Deterministic Finite State Automata (NFA)- Graph Theory – Basic Definitions – Paths, Reachability and Connectedness – Matrix Representation of Graphs – Trees
Reference Book:
1.Jean Paul Tremblay, Rampurkar Manohar, “Discrete Mathematical Structures with Applications to Computer Science”, Tata McGraw Hill, 1997. (Unit V) 2. M.K.Venkataraman “Engineering Mathematics”, Volume II, National Publishing Company, Second Edition,1989. (Unit I) 3. A.Tamilarasi & A.M.Natarajan, “Discrete Mathematics and its Application”, Khanna Publishers, Second Edition, 2005. (Unit I, II & III)
Text Book:
1 Kenneth H.Rosen, “ Discrete Mathematics and Its Applications”, Tata McGraw Hill, Fourth Edition, 2002. (Unit I, II & III) Hopcroft and Ullman, “Introduction to Automata Theory, Languages and Computation”, Narosa Publishing House, Delhi, 2002. ( Unit IV & V)
