JNTUH B.Tech 2nd Year 1 sem Computer Science & Technology (2-1) Mathematical Foundations of Computer Science Engineering R13.

JNTUH B.Tech 2nd year Mathematical Foundations of Computer Science gives you detail information about Mathematical Foundations of Computer Science Engineering R13 year subject. It will be help full you to understand you complete curriculum of the year.

Objectives

• To explain with examples the basic terminology of functions, relations, and sets.
• To perform the operations associated with sets, functions, and relations.
• To relate practical examples to the appropriate set, function, or relation model, and interpret the associated operations and terminology in context.
• To describe the importance and limitations of predicate logic.
• To relate the ideas of mathematical induction to recursion and recursively defined structures.
• To use Graph Theory for solving problems

UNIT-I

Mathematical Logic : Statements and notations, Connectives, Well formed formulas, Truth Tables, tautology, equivalence implication, Normal forms, Quantifiers, universal quantifiers. Predicates: Predicative logic, Free & Bound variables, Rules of inference, Consistency, proof of contradiction, Automatic Theorem Proving.

UNIT-II

Relations: Properties of Binary Relations, equivalence, transitive closure, compatibility and partial ordering relations, Lattices, Hasse diagram. Functions: Inverse Function Composition of functions, recursive Functions, Lattice and its Properties, Algebraic structures : Algebraic systems Examples and general properties, Semi groups and monads, groups sub groups’ homomorphism, Isomorphism.

UNIT-III

Elementary Combinatorics: Basis of counting, Combinations & Permutations, with repetitions, Constrained repetitions, Binomial Coefficients, Binomial Multinomial theorems, the principles of Inclusion – Exclusion. Pigeon hole principles and its application.

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TEXT BOOKS

1. Elements of DISCRETE MATHEMATICS- A computer Oriented Approach- C L Liu, D P Mohapatra. Third Edition, Tata McGraw Hill.
2. Discrete Mathematics for Computer Scientists & Mathematicians, J.L. Mott, A. Kandel, T.P. Baker, PHI.

REFERENCE BOOKS

1. Discrete Mathematics and its Applications, Kenneth H. Rosen, Fifth Edition.TMH.
2. Discrete Mathematical structures Theory and application-Malik & Sen, Cengage.
3. Discrete Mathematics with Applications, Thomas Koshy, Elsevier
4. Logic and Discrete Mathematics, Grass Man & Trembley, Pearson Education.

Outcomes

• Ability to Illustrate by examples the basic terminology of functions, relations, and sets and demonstrate knowledge of their associated operations.
• Ability to Demonstrate in practical applications the use of basic counting principles of permutations, combinations, inclusion/exclusion principle and the pigeonhole methodology.
• Ability to represent and Apply Graph theory in solving computer science problems

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