course structure - DSpace at CUSAT

CAS 2104 - Discrete Mathematical Structures
(Revised July 2010)
Unit 1
Foundations: Sets, Logic and Algorithms – Sets, Mathematical Logic, Validity of
Arguments. Quantifiers and First – Order Logic, Proof Techniques, Algorithms,
Integers and Mathematical Induction, Linear Diophantine Equations, Relations,
Equivalence relations, Equivalence Classes and Partitions, closures, Partially ordered
sets, Lattices.
Unit 2
Matrices and Closures of Relations, Matrices, The Matrix of a Relation and Closures,
Binary Operations, Counting Principles, Basic Counting Principle, Pigeon hole Principle,
Permutations, Combinations, Generalized Permutations and Combinations.
Unit 3
Recurrence Relations. Sequences and Recurrence Relations, Linear Homogeneous
Recurrence Relations. Linear Non homogeneous Recurrence Relations.
Unit 4
Boolean Algebra and Combinatorial Circuits. Two-element Boolean Algebra, Boolean
Algebra, Logical Gates and Combinatorial Circuits, Karnaugh Maps and Minimization
of Boolean Expressions.
Unit 5
Finite Automata and Languages – Finite Automata and Regular Languages,
Deterministic Finite Automata, Pumping Lemma, Nondeterministic Finite Automata,
Grammars and Languages.
Text Book:
D.S.Malik & M.K Sen, ‘Discrete Mathematical Structures: Theory and
Applications, Cengage Learning, 2008.
References:
1. Ralph P.Grimaldi & B.V.Ramana, ‘Discrete and Combinatorial Mathematics’,5 th
Ed. Pearson, 2008.
2. Trembley J.P. & Manohar R.P, ‘Discrete Mathematical Structures with
Application to Computer Science’, Mc.Graw Hill, 2007.
3. John E.Hopcroft & Jeffery D.Ullman, ‘Introduction to Automata Theory,
Languages and Computation’, Narosa Publishing House, 2008.
4. John Truss, ‘Discrete Mathematics for Computer Scientists’, 2 nd Ed. Pearson,
2001.
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