MA7151 Syllabus - MATHEMATICAL FOUNDATIONS FOR COMPUTER APPLICATIONS

MA7151 MATHEMATICAL FOUNDATIONS FOR COMPUTER APPLICATIONS   L T P C

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COURSE OBJECTIVES:

1.To understand the concepts and operations of matrix algebra needed for computing graphics

modeling

2. To understand and apply the class of functions which transform a finite set into another finite set which relates to input output functions in computer science.

3. To impart discrete knowledge in computer engineering through finite automata and Context free grammars

UNIT I MATRIX ALGEBRA                                                                                                   9

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                                                                                              9

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, subjective and objective functions.

UNIT III MATHEMATICAL LOGIC                                                                                        9

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                                                                                          9

Languages and Grammars-Phrase Structure Grammar-Classification of Grammars-Pumping Lemma

For Regular Languages-Context Free Languages.

UNIT V FINITE STATE AUTOMATA                                                                                    9

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

Automa ta (NFA )-Equiv alence of DFA and NFA-Equivalence of NFA and Regular Languages

TOTAL: 45+15= 60 PERIODS COURSE OUTCOMES:

1. Acquire the basic knowledge of matrix, set theory, functions and relations concepts needed for designing and solving problems

2. Acquire the knowledge of logical operations and predicate calculus needed for computing skill

3. Able to design and solve Boolean functions for defined problems

4. Apply the acquired knowledge of formal languages to the engineering areas like Compiler Design

5. Apply the acquired knowledge of finite automata theory and design discrete problems to solve by computers.

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 ompany, 2nd

Edition,1989.

5. Juraj Hromkovic, “Theoretical Computer Science”, Springer Indian Reprint, 2010.

6. David Makinson, “Sets, Logic and Maths for Computing”, Springer Indian Reprint, 2011.