## February 5, 2012

### MA 9265 DISCRETE MATHEMATICS REGULATIONS 2008 syllabus and question papers

MA 9265 DISCRETE MATHEMATICS
REGULATIONS 2008 syllabus and question papers
ANNA UNIVERSITY :: CHENNAI 600 025
REGULATIONS – 2008
CURRICULUM FOR B.E. COMPUTER SCIENCE AND ENGINEERING

AIM:
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.

OBJECTIVES:
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 output functions in computer science.
Be aware of the counting principles.
Be exposed to concepts and properties of algebraic structures such as semi groups, monoids and groups.

UNIT I LOGIC AND PROOFS 9
Propositional Logic – Propositional equivalences-Predicates and quantifiers – Nested Quantifiers – Rules of inference-introduction to proofs – proof methods and strategy.

UNIT II COMBINATORICS 9
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 and applications.

UNIT III GRAPHS 9

Graphs and graph models – Graph terminology and special types of graphs - presenting graphs and graph isomorphism – connectivity – Euler and Hamilton paths.

UNIT IV ALGEBRAIC STRUCTURES 9
Algebraic systems – Semi groups and monoids – Groups-Subgroups and homomorphisms – Cosets and Lagrange’s theorem – Ring & Fields.

UNIT V LATTICES AND BOOLEAN ALGEBRA 9
Partial ordering – Posets – Lattices as Posets – Properties of lattices-Lattices as algebraic systems – Sub lattices – direct product and Homomorphism – Some special
lattices – Boolean algebra

L: 45, T: 15, TOTAL = 60 PERIODS

TEXT BOOKS:
1. Kenneth H.Rosen, “Discrete Mathematics and its Applications”, 6th Edition, Special Indian edition , Tata McGraw – Hill Pub. Co. Ltd., New Delhi, (2007).
2. Trembly J.P. and Manohar R, “Discrete Mathematical Structures with Applications to Computer Science”, Tata McGraw–Hill Pub. Co. Ltd, New Delhi, 30th Re-print (2007).

REFERENCES
1. Ralph. P. Grimaldi, “Discrete and Combinatorial Mathematics: An Applied Introduction”, Fourth Edition, Pearson Education Asia, Delhi, (2002).
2. Thomas Koshy, ”Discrete Mathematics with Applications”, Elsevier Publications, (2006).
3. Seymour Lipschutz and Mark Lipson, ”Discrete Mathematics”, Schaum’s Outlines, Tata McGraw – Hill Pub. Co. Ltd., New Delhi, 2007,Second edition, Fifth reprint, (2007).