**MA7151 MATHEMATICAL FOUNDATIONS FOR COMPUTER APPLICATIONS L T P C**

**3 1 0 4**

**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.

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