Subject Details
Dept     : AIML
Sem      : 5
Regul    : 2019
Faculty : S.Sindhuja
phone  : NIL
E-mail  : sindhuja.171@gmail.com
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Syllabus

UNIT
1
LOGIC AND PROOFS

Propositional Logic – Propositional equivalences – Predicates and Quantifiers – Nested Quantifiers – Rules of inference – Introduction to proofs – Proof methods and strategy.

UNIT
2
COMBINATORICS

Mathematical induction – 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 principle and its applications.

UNIT
3
GRAPHS

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

UNIT
4
ALGEBRAIC STRUCTURES

Algebraic systems – Semi groups and monoids – Groups – Subgroups – Homomorphism’s – Normal subgroup and cosets – Lagrange’s theorem.

UNIT
5
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.

Reference Book:

1.Grimaldi.R.P., “Discrete and Combinatorial Mathematics: An Applied Introduction”,5th Edition, Pearson Education Asia, Delhi, 2014. 2. Lipschutz.S and Mark Lipson, “Discrete Mathematics”, Schaum’s Outlines, Tata McGraw Hill Pub. Co. Ltd., New Delhi, Revised 3rd Edition,2017 3. Koshy.T, “Discrete Mathematics with Applications”, Elsevier Publications, 2006. 4. Balakrishnan, V.K.,” Introductory Discrete Mathematics”, Dover Publications Inc, New York,2010. 5. Narsingh Deo, Graph theory with Application to Engineering and computer science, Prentice Hall India, First Edition, 2016.

Text Book:

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.