1. Discrete mathematics SEMESTERFIVE SUBJECT CODEMA1256 V.SUNDARARAJAN PROFESSOR CSE

2. PROPOSITIONAL CALCULUS Unit - I

3. Unit I PROPOSITIONS LOGICAL CONNECTIVES COMPOUND PROPOSITIONS CONDITIONAL & BI-CONDITIONAL PROPOSITIONS @ TRUTH TABLES TAUTOLOGY & CONTRADICTION CONTRA+VE LOGICAL EQUIVALENCE & IMPLICATION

4. Unit I DEMORGAN’S LAW NORMAL FORMS PRINCIPAL NORMAL FORMS @ CONJUCTIVE & DISJUNCTIVE RULES OF INFERENCE ARGUMENTS VALIDITY OF ARGUMENTS

5. Applications Construction of programmes Verification of Programmes Simplification of statements Study of traffic jam problems

6. PREDICATE CALCULUS Unit II

7. PREDICATES STATEMENT FUNCTION VARIABLES FREE & BOUND VARIABLES QUANTIFIERS UNIVERSE OF DISCOURSE LOGICAL EQUIVALENCE & IMPLICATION

8. THEORY OF INFERENCE RULES OF UNIVERSAL SPECIFICATION & GENERALISATION VALIDITY OF ARGUMENTS

9. Applications Artificial intelligence Robotics

10. UNIT-III SET THEORY

11. Unit III BASIC & NOTATIONS SUBSETS ALGEBRA OF SETS POWER SET ORDERED PAIR & CARTESIAN PRODUCT SET RELATIONS & PROPERTIES RELATIONAL MATRIX & GRAPH OF RELATION

12. PARTITIONS EQUIVALENCE RELATION PARTIAL ORDERING POSET HASSE DIAGRAM LATTICES SUBLATTICES BOOLEAN ALGEBRA HOMOMORPHISM

13. Applications Search-engine in the net Java & other Programmes Partitioning & analysing data Image transformation Image enhancement Image compression Image segmentation Image recognition Image morphology

14. UNIT-IV FUNCTIONS

15. Unit IV DEFINITIONS CLASSIFICATIONS TYPES EXAMPLES COMPOSITIONS INVERSE FUNCTIONS BINARY & n-ARY OPERATIONS

16. CHARECTERISTICS FUNCTIONS HASHING FUNCTIONS RECURSIVE FUNCTIONS PERMUTATION FUNCTIONS

17. Applications Animation in multimedia Image projection Image translation & shifting Image scaling Image reflection Special effect programes

18. UNIT-V GROUPS

19. ALGEBRAIC SYSTEMS DEFINITIONS PROPERTIES SEMIGRROUPS MONOIDS HOMOMORPHISM SUB –SEMIGROUPS SUB-MONOIDS

20. LAGRANGE’S THEOREM NORMAL SUBGROUPS NORMAL ALGEBRAIC SYSTEM CODES & GROUP CODES BASIC NOTIONS FOR ERROR CORRECTION ERROR RECOVERY IN GROUP CODES

21. Applications Grouping the data & analysing Cryptography & crypto-analysis Encoding & decoding

22. TEACHING PLAN UNIT NO. AS PER UNIVERSITY ORDER (IN HOURS) AS PER TEACHING PLAN (IN HOURS) 19 + 311+3 29 + 311 + 3 39 + 314 +3 49 + 313+3 59 + 314+3 TOTAL45+1563+15 *********(+15)  TUTORIAL HOURS

23. TEXT BOOKS TREMBLY & MANOHAR-DISCRETE MATHEMATICAL STRUCTURES WITH COMPUTER APPLICATIONS – TMH Pub.Co.Ltd- 2003 RALPH P. GRIMALDI- DISCRETE & COMBINATORIAL MATHEMATICS: AN APPLIED INTRODUCTION-4 th EDITION,PEARSON Education Asia-2002

24. REFERENCE BOOK BERNARD KOLMAN, BUSBY R.C. AND SHARAN CUTLER ROSS-DISCRETE MATHEMATICAL STRUCTURES –4 TH INDIAN REPRINT-PEARSON EDUCATION Pvt.Ltd. KENNETH H.ROSEN-DISCRETE MATHEMATICAL AND ITS APPLICATIONS –5 TH EDITION –TMH PUBLISHING COMPANY. RICHARD JOHNSONBAUGH- DISCRETE MATHEMATICS - 5 TH EDITION –PEARSON EDUCATION ASIA.

25. The End