# 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

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” : 1^{st} 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 (4^{th} Edition) New Age International Publishers.

11. Fundamentals of computer - V. Rajaraman (4^{th} Edition) Preritice HallIndia.

12. “Digital Computer Fundamental - (6^{th} 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.