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DOC/LP/01/28.02.02


L ESSON PLAN

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






LESSON PLAN

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





LESSON PLAN

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





LESSON PLAN

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





LESSON PLAN

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





LESSON PLAN

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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