**MA9221 MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE**

**UNIT I MATRIX ALGEBRA**

**Matrices, Rank of Matrix, Solving System of Equations-Eigen Values and Eigen Vectors-**

**Inverse of a Matrix - Cayley Hamilton Theorem**

**UNIT II BASIC SET THEORY**

**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.**

**UNIT III MATHEMATICAL LOGIC**

**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.**

**UNIT IV FORMAL LANGUAGES**

**Languages and Grammars-Phrase Structure Grammar-Classification of Grammars-**

**Pumping Lemma For Regular Languages-Context Free Languages.**

**UNIT V FINITE STATE AUTOMATA**

**Finite State Automata-Deterministic Finite State Automata(DFA), Non Deterministic**

**Finite State Automata (NFA)-Equivalence of DFA and NFA-Equivalence of NFA and**

**Regular Languages.**

**REFERENCES:**

**1. Kenneth H.Rosen, “ Discrete Mathematics and Its Applications”, Tata McGraw Hill,**

**Fourth Edition, 2002 (Unit 1,2 & 3).**

**2. Hopcroft and Ullman, “Introduction to Automata Theory, Languages and**

**Computation”, Narosa Publishing House, Delhi, 2002. ( Unit 4,5)**

**3. A.Tamilarasi & A.M.Natarajan, “Discrete Mathematics and its Application”, Khanna**

**Publishers, 2nd Edition 2005.**

**4. M.K.Venkataraman “Engineering Mathematics”, Volume II, National Publishing**

**Company, 2nd Edition,1989.**