Syllabus for MCA First Year Semester – I (with effect from the academic year 2007-2008)
DISCRETE MATHEMATICS
Lecture : 4 Hrs/week Practical : 1 Hr/week
One paper: 100 marks / 3 Hrs duration Practical exam: 25 marks
1. Number Systems 5 Hrs
•Decimal Number Systems
•Binary Number Systems
•Hexadecimal Number Systems
•Octal Number Systems
o Binary arithmetic
2. Propositions and Logical Operations 8 Hrs
•Notation, Connections, Normal forms, Truth tables
•Equivalence and Implications
•Theory of inference for statement calculus, Predicate calculus
•Rules of Logic
o Mathematical Induction and Quantifiers
3. Sets, Relations and Diagraphs 8 Hrs
•Review of set concepts
•Relations and digraphs
•Properties of relations
•Equivalence relations
•Computer representation of relations and digraphs
•Manipulation of relations
•Partially Ordered Sets (Posets)
4. Recurrence Relations 8 Hrs
Towers of Hanoi, Iterations, Homogeneous linear equations with constant coefficients, particular solution, difference table, finite order differences,
Line in a plane in general position
5. Groups and applications 8 Hrs
•Monoids, semi groups
•Product and quotients of algebraic structures
•Isomorphism, homomorphism, automorphism
•Normal subgroups, Codes and group codes
6. Classification of Languages 8 Hrs
Overview of Formal Languages:
Representation of regular languages and grammars, finite state machines
Term work/Practical : Each candidate will submit a journal /assignments in which at least 10 assignments based on the above syllabus and the internal test paper. Test graded for 10 marks and Practical graded for 15 marks.
References :
1. “Discrete Mathematical Structures” : Tremblay and Manohar, Tata McGraw Hill
2. “Discrete Mathematics”: 1st edition by Maggard, Thomson
3. “Discrete Mathematics” : Semyour Lipschutz, Varsha Patil IInd Edition Schaum’s Series TMH
4. “Discrete Mathematical Structures” : Kolman, Busby and Ross, Prentice Hall India, Edition 3
5. “Elements of Discrete Structures” : C.L.Liu
6. “Computer Fundamentals” – P.K.Sinha
7. “Discrete Mathematics and its application” – Rosen
8. “Discrete Mathematical Structure” : G. Shankar Rao New Age
9. Fundamental Approach to “Discrete Mathematics Acharjaya D.P. Sreekumar New Age
