M.C.A. Semester I : Discrete Mathematics

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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

o Mathematical Induction and Quantifiers

3. Sets, Relations and Diagraphs

  • 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

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

· 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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