Discrete mathematics

SEMESTER FIVESUBJECT CODE MA1256

V.SUNDARARAJANPROFESSOR

CSE

PROPOSITIONAL CALCULUSUnit - I

Unit I

• PROPOSITIONS• LOGICAL CONNECTIVES• COMPOUND PROPOSITIONS• CONDITIONAL & BI-CONDITIONAL

PROPOSITIONS @ TRUTH TABLES• TAUTOLOGY & CONTRADICTION • CONTRA+VE• LOGICAL EQUIVALENCE & IMPLICATION

Unit I

• DEMORGAN’S LAW• NORMAL FORMS• PRINCIPAL NORMAL FORMS @ CONJUCTIVE &

DISJUNCTIVE• RULES OF INFERENCE• ARGUMENTS• VALIDITY OF ARGUMENTS

Applications

• Construction of programmes

• Verification of Programmes

• Simplification of statements

• Study of traffic jam problems

PREDICATE CALCULUSUnit II

Unit II

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

• THEORY OF INFERENCE

• RULES OF UNIVERSAL SPECIFICATION & GENERALISATION

• VALIDITY OF ARGUMENTS

Applications

• Artificial intelligence

• Robotics

UNIT-III SET THEORY

Unit III

• BASIC & NOTATIONS• SUBSETS• ALGEBRA OF SETS• POWER SET • ORDERED PAIR & CARTESIAN PRODUCT• SET RELATIONS & PROPERTIES• RELATIONAL MATRIX & GRAPH OF

RELATION

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

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

UNIT-IV

FUNCTIONS

Unit IV

• DEFINITIONS• CLASSIFICATIONS• TYPES• EXAMPLES• COMPOSITIONS• INVERSE FUNCTIONS• BINARY & n-ARY OPERATIONS

• CHARECTERISTICS FUNCTIONS

• HASHING FUNCTIONS

• RECURSIVE FUNCTIONS

• PERMUTATION FUNCTIONS

Applications

•Animation in multimedia

•Image projection

•Image translation & shifting

•Image scaling

•Image reflection

•Special effect programes

UNIT-V

GROUPS

ALGEBRAIC SYSTEMSDEFINITIONSPROPERTIESSEMIGRROUPSMONOIDSHOMOMORPHISMSUB –SEMIGROUPSSUB-MONOIDS

LAGRANGE’S THEOREMNORMAL SUBGROUPSNORMAL ALGEBRAIC SYSTEM CODES & GROUP CODESBASIC NOTIONS FOR ERROR CORRECTIONERROR RECOVERY IN GROUP CODES

Applications

• Grouping the data & analysing

• Cryptography & crypto-analysis

• Encoding & decoding

TEACHING PLANUNIT NO. AS PER UNIVERSITY

ORDER (IN HOURS)AS PER TEACHING PLAN (IN HOURS)

1 9 + 3 11+3

2 9 + 3 11 + 3

3 9 + 3 14 +3

4 9 + 3 13+3

5 9 + 3 14+3

TOTAL 45+15 63+15

********* (+15) TUTORIAL HOURS

TEXT BOOKS

TREMBLY & MANOHAR-DISCRETE MATHEMATICAL STRUCTURES WITH COMPUTER APPLICATIONS – TMH Pub.Co.Ltd-2003

RALPH P. GRIMALDI- DISCRETE & COMBINATORIAL MATHEMATICS: AN APPLIED INTRODUCTION-4th EDITION ,PEARSON Education Asia-2002

REFERENCE BOOK

BERNARD KOLMAN, BUSBY R.C. AND SHARAN CUTLER ROSS-DISCRETE MATHEMATICAL STRUCTURES –4TH INDIAN REPRINT-PEARSON EDUCATION Pvt.Ltd.

KENNETH H.ROSEN-DISCRETE MATHEMATICAL AND ITS APPLICATIONS –5TH EDITION –TMH PUBLISHING COMPANY.

RICHARD JOHNSONBAUGH- DISCRETE MATHEMATICS - 5TH EDITION –PEARSON EDUCATION ASIA.

The End