### MA2265 Discrete Mathematics Syllabus and formula Material

MA2265 DISCRETE MATHEMATICS
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.

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

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

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:

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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