MA7151 MATHEMATICAL FOUNDATIONS FOR COMPUTER APPLICATIONS NOTES ANNA UNIVERSITY

MATHEMATICAL FOUNDATIONS FOR COMPUTER APPLICATIONS NOTES MA7151 ANNA UNIVERSITY

MATHEMATICAL FOUNDATIONS FOR COMPUTER APPLICATIONS NOTES MA7151 FOR ANNA UNIVERSITY

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

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