DISCRETE MATHEMATICAL STRUCTURE & GRAPH THEORY, CODE- 211505 L-T-P: 3-1-0 Credit : 4 SNo. Chapter Topics Lectures 1 Mathematical Statement and Notation, Negation, Conjunction, Disjunction, 8 Logic and Set Tautologies, Truth tables, Basic concepts of set theory, Theory Inclusion and equality of sets, power set, ordered pairs and n-tuples. 2 Relations and Relation and ordering, Properties of Binary Relations in a set 8 Functions Relation Matrix and the Graphs a Relation, Partition and Covering of a set. Equivalence relation, Partial ordering, Partially ordered set, Functions (definition and introduction), Composition of functions, Inverse functions, Characteristics function of a set. 3 Group Theory Semigroups and Monoids(defininitions and examples), 8 Homomorphism of semigroups and monomoids, Subsemi groups and submonoids, Groups(definitions and examples) Subgroups and Homomorphisms, Cosets and Lanranges theorem, Normal subgroups, Codes and group codes. 4 Rings(Definition Integral domains, ring, homomorphisms, Ideas of Ring 4 and Examples) polynomial. 5 Graph Theory Basic concepts of Graph Theory, Basic definitions, Paths 12 and circuits. Rechability and connectedness, Matrix representation of graphs, Trees and their representation and operations, Rooted trees, Path lengths in rooted trees, Multi graphs and weighted graphs, Shortest paths in weighted graphs. Text Books : Discrete Mathematics Structures with application to Computer Science by J. P.Tremblay & R. Manohar. Discrete Maths for Computer Scientists & Mathematicians. (Chapter 2, 5, by J. L. Mott, A. Kandel, T. P. Baker References : Elements of Discrete Mathematics by C. L. Liu. Discrete Mathematics by Lipschutz Discrete Mathematics by R.Johnsonbaugh.
DISCRETE MATHEMATICAL STRUCTURE & GRAPH THEORY, CODE- 211505 L-T-P: 3-1-0 Credit : 4 SNo. Chapter Topics Lectures 1 Mathematical Logic and Set Theory Statement and Notation, Negation, Conjunction, Disjunction, Tautologies, Truth tables, Basic concepts of set theory, Inclusion and equality of sets, power set, ordered pairs and n-tuples. 8 2 Relations and Functions Relation and ordering, Properties of Binary Relations in a set Relation Matrix and the Graphs a Relation, Partition and Covering of a set. Equivalence relation, Partial ordering, Partially ordered set, Functions (definition and introduction), Composition of functions, Inverse functions, Characteristics function of a set. 8 3 Group Theory Semigroups and Monoids(defininitions and examples), Homomorphism of semigroups and monomoids, Subsemi groups and submonoids, Groups(definitions and examples) Subgroups and Homomorphisms, Cosets and Lanranges theorem, Normal subgroups, Codes and group codes. 8 4 Rings(Definition and Examples) Integral domains, ring, homomorphisms, Ideas of Ring polynomial. 4 5 Graph Theory Basic concepts of Graph Theory, Basic definitions, Paths and circuits. Rechability and connectedness, Matrix representation of graphs, Trees and their representation and operations, Rooted trees, Path lengths in rooted trees, Multi graphs and weighted graphs, Shortest paths in weighted graphs. 12 Text Books : Discrete Mathematics Structures with application to Computer Science by J. P.Tremblay & R. Manohar. Discrete Maths for Computer Scientists & Mathematicians. (Chapter 2, 5, by J. L. Mott, A. Kandel, T. P. Baker References : Elements of Discrete Mathematics by C. L. Liu. Discrete Mathematics by Lipschutz Discrete Mathematics by R.Johnsonbaugh.