M.C.A. Semester I : Discrete Mathematics

DISCRETE MATHEMATICS 1. Number Systems   Decimal Number Systems   Binary Number Systems   Hexadecimal Number Systems   Octal Number Systems   o Binary Arithmetic 2. Propositions and Logical Operations · Notation, Connections, Normal forms, Truth Tables   Equivalence and Implications   · Theory of inference for statement calculus, Predicate calculus   Rules of Logic </li> </ul> o Mathematical Induction and Quantifiers 3. Sets, Relations and Diagraphs   Review of set concepts </li>  Relations and digraphs </li>  Properties of relations </li>  Equivalence relations </li> </ul> · Computer representation of relations and digraphs   Manipulation of relations </li>  Partially Ordered sets (Posets) </li> </ul> 4. Recurrence Relations 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   Monoids, semi groups </li> </ul> · Product and quotients of algebraic structures · Isomorphism, homomorphism, automorphism · Normal subgroups, Codes and group codes 6. Classification of Languages 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. “Discrete Mathematics and its application” – Rosen 7. “Discrete Mathematical Structure” : G. Shankar Rao New Age 8. Fundamental Approach to “Discrete Mathematics Acharjaya D. P. Sreekumar New Age. 9. “Computer Fundamentals” – P. K. Sinha 10. “Computer Fundamentals” - B. Ram (4th Edition) New Age International Publishers. 11. Fundamentals of computer - V. Rajaraman (4th Edition) Preritice HallIndia. 12. “Digital Computer Fundamental - (6th Edition) - Thomas Bartec (Tata McGraw Hill) 13. Computer Fundamentals - D. P). Nagpal (S. Chand)   14. Computer Fundamentals - A. B. Patil, d. Ravichandran, (for MSBTE) - Tata McGraw Hill.

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