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LP-CS-MA2265

LP Rev. No: 01

Date:12.04.2011

Page 1 of 6
###### Sub Code & Name : MA 2265 DISCRETE MATHEMATICS

Unit: I Branch: CS Semester : V

Unit syllabus:

UNIT I LOGIC AND PROOFS

Propositional Logic – Propositional equivalences-Predicates and quantifiers-Nested

Quantifiers-Rules of inference-introduction to Proofs-Proof Methods and strategy

Objective: To enable the students to have knowledge of the concepts needed to test the logic of a program.

 Session No Topics to be covered Time Ref Teaching Method 1 Introduction to logic 50 1,3,4 Black Board and Chalk 2 Propositional Logic-Prepositions. 50 3 Conditional and Bi-conditional statements. 50 4,5 Propositional Equivalences, Tautological implications. 100 6,7 Theory of Inference- Rules of inference. 100 8,9 Normal forms- p.c.n.f, p.d.n.f. 100 10 Predicate Calculus, quantifiers 50 11 Inference theory of predicate calculus 50 12 Validity of arguments 50 13 Validity of arguments 50 14 Introduction to proofs 50 15 Proof methods and strategy. 50 16 Proof methods and strategy. 50

LP-CS-MA2265

LP Rev. No: 01

Date:12.04.2011

Page 2 of 6
###### Sub Code & Name : MA 2265 DISCRETE MATHEMATICS

Unit: II Branch: CS Semester : V

Unit syllabus:

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.

Objective: To enable the students to be aware of the counting principles

 Session No Topics to be covered Time Ref Teaching Method 17 Introduction to Mathematical Induction 50 1,3,4 Black Board and Chalk 18 Strong and weak induction; principles of counting. 50 19 Pigeonhole principle; generalized pigeonhole principle 50 20 Permutations; circular permutations 50 21 Combinations; combinations with repetitions 50 22 Recursion; recurrence relations. 23 Recursion; recurrence relations. 50 24 Solution of finite order homogeneous relations. 50 25 Solution of non-homogeneous relations. 50 26 Generating functions 50 27 Problems 50 28 Principles of Inclusion and Exclusion 29 Revision 50 30 CAT I 75

LP-CS-MA2265

LP Rev. No: 01

Date:12.04.2011

Page 3 of 6
###### Sub Code & Name : MA 2265 DISCRETE MATHEMATICS

Unit: III Branch: CS Semester : V

Unit syllabus:

UNIT III GRAPHS

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

Objective:

To enable the students to have an understanding in identifying structures on many levels.

 Session No Topics to be covered Time Ref Teaching Method 31 Introduction to graphs and Graph mafels. 50 1,3,4 Black Board and Chalk 32 Graph terminology and special types of graphs 50 33 Bipartite graphs and applications of special types of graphs 50 34 Representation of graphs 50 35 Graph isomorphism 50 36 Connectivity and paths 50 37 Connectedness in undirected graphs 50 38 Connectedness in directed graphs 50 39 Euler path and circuits 50 40 Hamilton paths and circuits 50 41 Problems 42 Revision 50

LP-CS-MA 2265

LP Rev. No: 01

Date:12.04.2011

Page 4 of 6
###### Sub Code & Name : MA 2265 DISCRETE MATHEMATICS

Unit: IV Branch: CS Semester : V

Unit syllabus:

UNIT IV ALGEBRAIC STRUCTURES Algebraic systems-Semi groups and monoids-Groups-Subgroups and homomorphisms-

Cosets and Lagrange’s theorem- Ring & Fields (Definitions and examples)

Objective:

To be exposed to concepts and properties of algebraic structures such as semi groups,

monoids and groups

 Session No Topics to be covered Time Ref Teaching Method 43 Introduction to algebraic systems; definitions and examples. 50 2,4,5 Black Board and Chalk 44 Properties of algebraic system - homomorphism, automorphism, congruence relations. 50 45 Sub algebra, semi groups, monoids 50 46 Cyclic monoids, homomorphism of semi groups and monoids 50 47 Sub semi groups and sub monoids 50 48 Groups- definition and properties; sub groups – examples and results 50 49,50 Normal sub groups, cosets and Lagrange’s theorem 100 51 Rings and fields, Integral domains 50 52 Revision 50 53 CAT II 75

LP-CS-MA2265

LP Rev. No: 01

Date:12.04.2011

Page 5 of 6
###### Sub Code & Name : MA 2265 DISCRETE MATHEMATICS

Unit: V Branch: CS Semester : V

Unit 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

Objective:

To enable the students to 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.

 Session No Topics to be covered Time Ref Teaching Method 54 Partial ordering, posets and lattices- definitions and examples 50 2,4,5 Black Board and Chalk 55 Properties of Lattices; lattices as algebraic systems 50 56 Sub lattices, direct product and homomorphisms 50 57 Some Special lattices 50 58 Complete, complement and distributive lattices and chains 50 59 Boolean Algebra – Definitions and examples 50 60 Properties, Problems 50 61 Revision 62 Cat III 75

LP-CS-MA2265

LP Rev. No: 01

Date:12.04.2011

Page 6 of 6
###### Sub Code & Name : MA 2265 DISCRETE MATHEMATICS

Unit: Branch: CS Semester : V

Course Delivery Plan:

 Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 I II I II I II I II I II I II I II I II I II I II I II I II I II I II I II Units CAT I CAT II CAT III

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, 8.1 to 8.5)

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 2-3.8 & 2-3.9,3-1,3-2 & 3-5, 4-1 & 4-2)

REFERENCES:

3. Ralph. P. Grimaldi, “Discrete and Combinatorial Mathematics: An Applied

Introduction”, Fourth Edition, Pearson Education Asia, Delhi, (2002).

4. Thomas Koshy, ”Discrete Mathematics with Applications”, Elsevier Publications,

(2006).

5. Seymour Lipschutz and Mark Lipson, ”Discrete Mathematics”, Schaum’s Outlines,

Tata McGraw-Hill Pub. Co. Ltd., New Delhi, Second edition, (2007).

 Prepared by Approved by Signature Name Dr. B. Thilaka Dr. R. Muthucumarasamy Designation Associate Professor HOD,AM Date 12.04.2011 12.04.2011

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