Ma2265 Discrete Mathematics Important Question With Answers

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

1. Obsah osnovy správy o činnosti organizácie sav za rok 2010

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   ... publikáciách neregistrovaných v citačných indexoch (3, 4) 72 10 ... . Nominácie na cenu Krištáľové krídlo sú už známe / ... of rings. In DISCRETE MATHEMATICS. ISSN 0012-365X, SEP 6 2009, vol. ... Notes in Computer Science, vol. 2265. - SRN : Springer, 2001, s. ...

2. Obsah osnovy správy o činnosti organizácie sav za rok 2009 (3)

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   ... S.: s-maps in von Neumann algebras, Quantum Structure 2009, ... Duchoň, DrSc., MÚ SAV Téma dizert. práce: Matematicko ... cutwidth linear arrangements of abelian Cayley graphs. In DISCRETE MATHEMATICS ... in Computer Science, vol. 2265. - SRN : Springer, ...

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   ... Analysis: Discrete Inverse ... , C. Hofer, C. Teichert, M.A. Nino, J. Camarero, J.J. de Miguel, ... G. Schonhense, Sub-nanosecond resolution x- ... , and G. Chouteau, Revised magnetic properties ... A 57 Ma Pacific plate ... Mathematical ... 71 (16), 2265-7, 1997. Yao, ...

4. Ma, T.Y., and , Influence of substrate temperature on the structural and electrical properties of al

   Документ

   ... Analysis: Discrete Inverse ... , C. Hofer, C. Teichert, M.A. Nino, J. Camarero, J.J. de Miguel, ... G. Schonhense, Sub-nanosecond resolution x- ... , and G. Chouteau, Revised magnetic properties ... A 57 Ma Pacific plate ... Mathematical ... 71 (16), 2265-7, 1997. Yao, ...

5. Graph parameters and semigroup functions

   Документ

   ... Newman I, Wigderson A Search Problems IN The Decision Tree Model SIAM J DISCRETE ... Sebő A Polyhedral Combinatorics, DIMACS Series in Discrete Mathematics ... 1163 Bednarska Ma lgorzataet al ... Chen CYet al APPLIED MATHEMATICS ... David Discrete Math.308: 2265-2268 ...

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Ma2265 Discrete Mathematics Important Question With Answers

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