Connected successfully Syllabus || SNS Courseware
Subject Details
Dept     : AIDS
Sem      : 3
Regul    : 2023
Faculty : R.Nivetha
phone  : 7305524252
E-mail  : nivetha.r.math@snsce.ac.in
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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 – Definition and examples of Rings and Fields

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, 3rd Edition,2010 3.Koshy.T, “Discrete Mathematics with Applications”, Elsevier Publications, 2006. 4.Balakrishnan, V.K.,” Introductory Discrete Mathematics”, Dover Publications Inc, New York, 2010. 5.Norman L Biggs, ”Discrete Mathematics”, Oxford University press, Oxford, 2nd Edition, 2003

Text Book:

1.Kenneth H Rosen ,"Discrete Mathematics and its applications",seventh Edition ,special Indian edition ,TataMc GrawHill,Newdelhi,2017. 2.Tremblay J.P. and Manohar, R, "Discrete Mathematical Structures with Applications to Computer Science", Tata Mc Graw Hill Pub. Co. Ltd, New Delhi, 30th Reprint, 2011