Syllabus B Tech Computer Science Third Semester Discrete Structure CS302

The concepts developed in this course will aid in quantification of several concepts in Computer Science Engineering that have been introduced at the Engineering courses. Technology is being increasingly based on the latest Syllabus B Tech Computer Science Third Semester Discrete Structure CS302 is given here.

The objective of this course “Syllabus B Tech Computer Science Third Semester Discrete Structure CS302“ is to develop ability and gain insight into the process of problem-solving, with emphasis on thermodynamics. Specially in following manner: Apply conservation principles (mass and energy) to evaluate the performance of simple engineering systems and cycles. Evaluate thermodynamic properties of simple homogeneous substances. Analyze processes and cycles using the second law of thermodynamics to determine maximum efficiency and performance. Discuss the physical relevance of the numerical values for the solutions to specific engineering problems and the physical relevance of the problems in general and Critically evaluate the validity of the numerical solutions for specific engineering problems. More precisely, the objectives are:

To enable young technocrats to acquire mathematical knowledge to understand Laplace transformation, Inverse Laplace transformation and Fourier Transform which are used in various branches of engineering.
To introduce effective mathematical tools for the Numerical Solutions algebraic and transcendental equations.
To acquaint the student with mathematical tools available in Statistics needed in various field of science and engineering.

CS 302 – Discrete Structure

Unit 1

Set Theory, Relation, Function, Theorem Proving Techniques : Set Theory: Definition of sets, countable and uncountable sets, Venn Diagrams, proofs of some general identities on sets Relation: Definition, types of relation, composition of relations, Pictorial representation of relation, Equivalence relation, Partial ordering relation, Job-Scheduling problem Function: Definition, type of functions, one to one, into and onto function, inverse function, composition of functions, recursively defined functions, pigeonhole principle. Theorem proving Techniques: Mathematical induction, Proof by contradiction.

Unit 2

Algebraic Structures: Definition, Properties, types: Semi Groups, Monoid, Groups, Abelian group, properties of groups, Subgroup, cyclic groups, Cosets, factor group, Permutation groups, Normal
subgroup, Homomorphism and isomorphism of Groups, example and standard results, Rings and Fields: definition and standard results.

Unit 3

Propositional Logic: Proposition, First order logic, Basic logical operation, truth tables, tautologies, Contradictions, Algebra of Proposition, logical implications, logical equivalence, predicates, Normal Forms, Universal and existential quantifiers. Introduction to finite state machine Finite state machines as models of physical system equivalence machines, Finite state machines as language recognizers.

Unit 4

Graph Theory: Introduction and basic terminology of graphs, Planer graphs, Multigraphs and weighted graphs, Isomorphic graphs, Paths, Cycles and connectivity, Shortest path in weighted graph, Introduction to Eulerian paths and circuits, Hamiltonian paths and circuits, Graph coloring, chromatic number, Isomorphism and Homomorphism of graphs.

Unit 5

Posets, Hasse Diagram and Lattices: Introduction, ordered set, Hasse diagram of partially, ordered set, isomorphic ordered set, well ordered set, properties of Lattices, bounded and complemented lattices. Combinatorics: Introduction, Permutation and combination, Binomial Theorem, Multimonial Coefficients Recurrence Relation and Generating Function: Introduction to Recurrence Relation and Recursive algorithms , Linear recurrence relations with constant coefficients, Homogeneous solutions, Particular solutions, Total solutions , Generating functions , Solution by method of generating functions.

Books Recommended

1. C.L.Liu, “Elements of Discrete Mathematics” Tata Mc Graw-Hill Edition.
2. Trembley, J.P & Manohar; “Discrete Mathematical Structure with Application CS”, McGraw Hill.
3. Kenneth H. Rosen, “Discrete Mathematics and its applications”, McGraw Hill.
4. Bisht, “Discrete Mathematics”,Oxford University Press
5. Biswal,”Discrete Mathematics & Graph Theory”, PHI.

Syllabus B Tech Computer Science Third Semester Discrete Structure CS302

CS 302 – Discrete Structure

Books Recommended

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