# MA8351 DISCRETE MATHEMATICS NOTES 2017 REGULATION

__MA8351 DISCRETE MATHEMATICS NOTES 2017 REGULATION __

In this post we have posted some notes on

**MA8351 DISCRETE MATHEMATICS**of**BASIC SCIENCES**for**ANNA UNIVERSITY AFFILIATED COLLEGES STUDENTS.**Here We have listed the the notes whichever we could collect for

**MA8351 DISCRETE MATHEMATICS**subject, We think that it will be helpful for your exam preparation.#### OBJECTIVES:

π To extend studentβs logical and mathematical maturity and ability to deal with abstraction.

π To introduce most of the basic terminologies used in computer science courses and application of ideas to solve practical problems.

π To understand the basic concepts of combinatorics and graph theory.

π To familiarize the applications of algebraic structures.

π To understand the concepts and significance of lattices and boolean algebra which are widely used in computer science and engineering.

__UNIT I LOGIC AND PROOFS__

Propositional logic β Propositional equivalences – Predicates and quantifiers β Nested quantifiers β Rules of inference – Introduction to proofs β Proof methods and strategy.

__UNIT II COMBINATORICS__

Mathematical induction β Strong induction and well ordering β The basics of counting β The pigeonhole principle β Permutations and combinations β Recurrence relations β Solving linear recurrence relations β Generating functions β Inclusion and exclusion principle and its applications

__UNIT III GRAPHS __

Graphs and graph models β Graph terminology and special types of graphs β Matrix representation of graphs and graph isomorphism β Connectivity β Euler and Hamilton paths.

__UNIT IV ALGEBRAIC STRUCTURES__

Algebraic systems β Semi groups and monoids – Groups β Subgroups β Homomorphismβs β Normal subgroup and cosets β Lagrangeβs theorem β Definitions and examples of Rings and Fields.

__UNIT V LATTICES AND BOOLEAN ALGEBRA__

Partial ordering β Posets β Lattices as posets β Properties of lattices – Lattices as algebraic systems β Sub lattices β Direct product and homomorphism β Some special lattices β Boolean algebra.

#### TOTAL: 60 PERIODS

**:**

__OUTCOMES__At the end of the course, students would:

π Have knowledge of the concepts needed to test the logic of a program.

π Have an understanding in identifying structures on many levels.

π Be aware of a class of functions which transform a finite set into another finite set which relates to input and output functions in computer science.

π Be aware of the counting principles.

π Be exposed to concepts and properties of algebraic structures such as groups, rings and

fields.

__TEXTBOOKS__:

1. Rosen, K.H., “Discrete Mathematics and its Applications”, 7th Edition, Tata McGraw

Hill Pub. Co. Ltd., New Delhi, Special Indian Edition, 2011.

2. Tremblay, J.P. and Manohar.R, ” Discrete Mathematical Structures with Applications to Computer Science”, Tata McGraw Hill Pub. Co. Ltd, New Delhi, 30th Reprint, 2011.

__REFERENCES__:

1. Grimaldi, R.P. “Discrete and Combinatorial Mathematics: An Applied Introduction”, 4th Edition,

Pearson Education Asia, Delhi, 2007.

2. Lipschutz, S. and Mark Lipson., “Discrete Mathematics”, Schaumβs Outlines, Tata McGraw Hill Pub. Co. Ltd., New Delhi, 3rd Edition, 2010.

3. Koshy, T. “Discrete Mathematics with Applications”, Elsevier Publications, 2006.

__MA8351 DISCRETE MATHEMATICS NOTES __

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