Engineering Tutorials

CSE-203 F Discrete Structures

Section A: Set Theory and Propositional Calculus:

Introduction to set theory, Set operations, Algebra of sets, Duality, Finite and Infinite sets, Classes of sets, Power Sets, Multi sets, Cartesian Product, Representation of relations, Types of relation, Equivalence relations and partitions , Partial ordering relations and lattices Function and its types, Composition of function and relations, Cardinality and inverse relations

Introduction to propositional Calculus: Basic operations: AND(^), OR(v), NOT(~), Truth value of a compound statement, propositions, tautologies, contradictions.

Section B: Techniques of Counting and Recursion and recurrence Relation:

Permutations with and without repetition, Combination.Polynomials and their evaluation, Sequences, Introduction to AP, GP and AG series, partial fractions, linear recurrence relation with constant coefficients, Homogeneous solutions, Particular solutions, Total solution of a recurrence relation using generating functions.

Section C: Algebric Structures

Definition and examples of a monoid, Semigroup, Groups and rings, Homomorphism, Isomorphism and Automorphism, Subgroups and Normal subgroups, Cyclic groups, Integral domain and fields, Cosets, Lagrange’s theorem

Section D: Section Graphs and Trees:

Introduction to graphs, Directed and Undirected graphs, Homomorphic and Isomorphic graphs, Subgraphs, Cut points and Bridges, Multigraph and Weighted graph, Paths and circuits, Shortest path in weighted graphs, Eurelian path and circuits, Hamilton paths and circuits, Planar graphs, Euler’s formula, Trees, Spanning trees, Binary trees and its traversals

Text Book:

• Elements of Discrete Mathematics,C.L Liu, 1985, McGraw Hill

Reference Books:

Discrete Mathematics by Johnson Bough R., 5 Edition, PEA, 2001..

• Concrete Mathematics: A Foundation for Computer Science, Ronald Graham, Donald Knuth and Oren Patashik, 1989, Addison-Wesley.

• Mathematical Structures for Computer Science, Judith L. Gersting, 1993, Computer Science Press.

• Applied Discrete Structures for Computer Science, Doerr and Levasseur, (Chicago: 1985,SRA

• Discrete Mathematics by A. Chtewynd and P. Diggle (Modular Mathematics series), 1995, Edward Arnold, London,

• Schaums Outline series: Theory and problems of Probability by S. Lipshutz, 1982, McGraw-Hill Singapore

• Discrete Mathematical Structures, B. Kolman and R.C. Busby, 1996, PHI

• Discrete Mathematical Structures with Applications to Computers by Tembley & Manohar, 1995, Mc Graw Hill.

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