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# MA6566 Discrete Mathematics Syllabus

## OBJECTIVES: MA6566 Discrete Mathematics Syllabus

To extend student‟s Logical and Mathematical maturity and ability to deal with abstraction and to introduce most of the basic terminologies used in computer science courses and application of ideas to solve practical problems.

### UNIT I LOGIC AND PROOFS MA6566 Discrete Mathematics Syllabus

Propositional Logic – Propositional equivalences – Predicates and Quantifiers – Nested Quantifiers – Rules of inference – Introduction to proofs – Proof methods and strategy.

#### UNIT II COMBINATORICS MA6566 Discrete Mathematics Syllabus

Mathematical induction – Strong induction and well ordering – The basics of counting – The pigeonhole principle – Permutations and combinations – Recurrence relations – Solving linear recurrence relations – Generating functions – Inclusion and exclusion principle and its applications.

##### UNIT III GRAPHS MA6566 Syllabus Discrete Mathematics

Graphs and graph models – Graph terminology and special types of graphs – Matrix representation of graphs and graph isomorphism – Connectivity – Euler and Hamilton paths.

###### UNIT IV ALGEBRAIC STRUCTURES MA6566 Syllabus Discrete Mathematics

Algebraic systems – Semi groups and monoids – Groups – Subgroups – Homomorphism‟s – Normal subgroup and cosets – Lagrange‟s theorem – Definitions and examples of Rings and Fields.

###### UNIT V LATTICES AND BOOLEAN ALGEBRA MA6566 Discrete Mathematics Syllabus

Partial ordering – Posets – Lattices as posets – Properties of lattices – Lattices as algebraic systems – Sub lattices – Direct product and homomorphism – Some special lattices – Boolean algebra.

OUTCOMES: MA6566 Discrete Mathematics Syllabus

At the end of the course, students would:
 Have knowledge of the concepts needed to test the logic of a program.
 Have an understanding in identifying structures on many levels.
 Be aware of a class of functions which transform a finite set into another finite set which relates to input and output functions in computer science.
 Be aware of the counting principles.
 Be exposed to concepts and properties of algebraic structures such as groups, rings and fields.

 Subject Name Discrete Mathematics Subject code MA6566 Regulation 2013