MA7151 MATHEMATICAL FOUNDATIONS FOR COMPUTER APPLICATIONS Syllabus
COURSE OBJECTIVES:
To understand the concepts and operations of matrix algebra needed for computing graphics modeling
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.
To impart discrete knowledge in computer engineering through finite automata and Context free grammars
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, subjective and objective 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
COURSE OUTCOMES:
Acquire the basic knowledge of matrix, set theory, functions and relations concepts needed for designing and solving problems
Acquire the knowledge of logical operations and predicate calculus needed for computing skill
Able to design and solve Boolean functions for defined problems
Apply the acquired knowledge of formal languages to the engineering areas like Compiler Design
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 Company, 2 nd 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.
COURSE OBJECTIVES:
To understand the concepts and operations of matrix algebra needed for computing graphics modeling
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.
To impart discrete knowledge in computer engineering through finite automata and Context free grammars
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, subjective and objective 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
COURSE OUTCOMES:
Acquire the basic knowledge of matrix, set theory, functions and relations concepts needed for designing and solving problems
Acquire the knowledge of logical operations and predicate calculus needed for computing skill
Able to design and solve Boolean functions for defined problems
Apply the acquired knowledge of formal languages to the engineering areas like Compiler Design
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 Company, 2 nd 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.