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MMA603 MATHEMATICAL FOUNDATION FOR
COMPUTER SCIENCE 3 1 0 4
1. LOGIC 9 3 0
Statements - Connectives - Truth Tables - Normal forms - Predicate calculus - Inference - Theory for
Statement Calculus and Predicate Calculus - automata theorem proving. SETS
Sets - Relations – Graphs – Functions. COMBINATORICS: Review of Permutation and Combination -
Mathematical Induction - Pigeonhole principle - Principle of Inclusion and Exclusion - generating function -
Recurrence relations
2. ALGEBRAIC STRUCTURES 9 3 0
Semi group - Monoid – Groups (Definition and Examples only) Cyclic group - Permutation group (Sn and
Dn) - Substructures - Homomorphism of semi group, monoid and groups - Cosets and Lagrange Theorem –
Normal Subgroups - Rings and Fields (Definition and examples only)
3. RECURSIVE FUNCTIONS 9 3 0
recursive functions – primitive recursive functions – computable and non computable functions.
LATTICES: Partial order relation – poset – Hasse Diagram – Boolean algebra.
4. FINITE AUTOMATA AND REGULAR LANGAUGES 9 3 0
Finite automata and regular languages-Regular expressions and regular languages-Memory required to
recognize a language-Non Determinism and Kleene’s Theorem-Pumping Lemma-Decision Problems
5. PUSH DOWN AUTOMATA AND CONTEXT FREE LANGUAGES 9 3 0
Push down Automata and Context free languages-context free grammars-definition –examples-operationsderivation
trees-Ambiguity-PDA and CFG Context free and non –context free languages.
References:
1. J. P. Trembley, Manohar, Discrete Mathematical Structures with Applications to Computer
Science, TMH
2. K.H. Rosen, “Discrete Mathematics and its Applications”, McGraw - Hill Book Company,
1999.
3. John. C. Martin, “Introduction to Languages and Theory of Computation”, II edition,
McGraw Hill 1997.
4. Hop craft and Ulman ,Introduction to automata, languages and computation,Narosa
Publishers 1986.
5. Mott, Kandel & Baker, Discrete Mathematics for Computer Scientists & Mathematics 2nd
Edition, PHI 2002
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| Author: India 17 Dec 2007 | Member Level: Diamond Points : 1 |
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