3rd semester Engineering Mathematics-II study materials

SYLLABUS

EN010301 B Engineering Mathematics II

Teaching scheme Credits: 4


MODULE 1 Mathematical logic (12 hours)

Basic concept of statement , logical connectives, Tautology and logical equivalence – Laws of algebra of propositions – equivalence formulas – Tautological implications (proof not expected for the above laws , formulas and implications). Theory of inference for statements – Predicate calculus – quantifiers – valid formulas and equivalences – free and bound variables – inference theory of predicate calculus.

MODULE 2 Number theory and functions (12 hours)

Fundamental concepts – Divisibility – Prime numbers- relatively prime numbers – fundamental theorem of arithmetic – g.c.d - Euclidean algorithm - properties of gcd (no proof) – l cm – Modular Arithmetic – congruence – properties – congruence class modulo n – Fermat’s theorem – Euler’s Totient functions - Euler’s theorem - Discrete logarithm Function – types of functions – composite functions – inverse of a function – pigeon hole principles.

MODULE 3 Relations (10 hours)

Relations – binary relation – types of relations – equivalence relation –partition – equivalence classes – partial ordering relation – Hasse diagram - poset.

MODULE 4 Lattice (14 hours)

Lattice as a poset – some properties of lattice (no proof) – Algebraic system – general properties – lattice as algebraic system – sublattices – complete lattice – Bounded Lattice - complemented Lattice – distributive lattice – homomorphism - direct product.

MODULE 5 Graph Theory (12 hours)

Basic concept of graph – simple graph – multigraph – directed graph- Basic theorems (no proof) . Definition of complete graph , regular graph, Bipartite graph, weighted graph – subgraph – Isomorphic graph –path – cycles – connected graph.- Basic concept of Eulergraph and Hamiltonian circuit – trees – properties of tree (no proof) - length of tree – spanning three – sub tree – Minimal spanning tree (Basic ideas only . Proof not excepted for theorems)


Click on the below links to download:

1.Discrete mathematics –Schaum’s outlines – Mc Graw Hill-S.Lipschutz, M.L.Lipson

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2.Discrete mathematics & its Application - Mc Graw Hill-Kenneth H Rosen

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