Thursday, April 21, 2011

MA2311 DISCRETE MATHEMATICS FIVTH ANNA UNIVERSITY CHENNAI SYLLABUS


                                                                                                                           
                                                                                                                          
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                                                                          
Propositional Logic – Propositional equivalences-Predicates and quantifiers-Nested Quantifiers-Rules of inference-introduction to Proofs-Proof Methods and strategy

UNIT II                        COMBINATORICS                                                                               
Mathematical inductions-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                                                                                                 Graphs and graph models-Graph terminology and special types of graphs-Representing graphs and graph isomorphism -connectivity-Euler and Hamilton paths    
                                                            
UNIT IV           ALGEBRAIC STRUCTURES                                                                         
Algebraic systems-Semi groups and monoids-Groups-Subgroups and homomorphisms-Cosets and Lagrange’s theorem- Ring & Fields (Definitions and examples)                                                              
UNIT V             LATTICES AND BOOLEAN ALGEBRA                                            
Partial ordering-Posets-Lattices as Posets- Properties of lattices-Lattices as Algebraic systems –Sub lattices –direct product and Homomorphism-Some Special lattices-Boolean Algebra
       
LECTURES :45                             TUTORIAL :15                                     TOTAL: 60

TEXT BOOKS:
  1. Kenneth H.Rosen, “Discrete Mathematics and its Applications”, Special Indian edition, Tata McGraw-Hill Pub. Co. Ltd., New Delhi, (2007).  (For the units 1 to 3, Sections 1.1 to 1.7 , 4.1 & 4.2, 5.1 to 5.3, 6.1, 6.2, 6.4 to 6.6, .1 to .5)
  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).(For units  4 & 5 , Sections 2-3. & 2-3.,3-1,3-2 & 3-5, 4-1  & 4-2)

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, Second edition, (2007).

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