MA4105 Applied Mathematics for Pervasive Computing Syllabus:

MA4105 Applied Mathematics for Pervasive Computing Syllabus – Anna University PG Syllabus Regulation 2021

COURSE OBJECTIVES:

This course will held the student to
 study the methods of solving a system of linear equations using matrix theory.
 learn the mathematical aspects of graph, colouring, various graph theoretic algorithms which are applicable to computer languages.
 study the linear programming models and Transportation models and various techniques to solve them.
 determination of probability and moments, distributions of discrete and continuous random variables and random processes.
 study the characteristics of queueing models and discrete Markov chains, applications of them.

UNIT I MATRIX METHODS

Introduction to vector spaces – Basic vector analysis methods – Matrix norms – Jordan canonical form – Generalized eigenvectors – Singular value decomposition – Pseudo inverse – Least square approximations – QR decomposition method.

UNIT II GRAPH THEORY

Introduction to paths, trees, vector spaces – Matrix coloring and directed graphs – Some basic algorithms – Shortest path algorithms – Depth – First search on a graph – Isomorphism – Other Graph – Theoretic algorithms – Performance of graph theoretic algorithms – Graph theoretic computer languages.

UNIT III OPTIMIZATION TECHNIQUES

Linear programming – Basic concepts – Graphical and simplex methods – Big M method – Two phase simplex method – Revised simplex method – Transportation problems – Assignment problems.

UNIT IV PROBABILITY AND RANDOM VARIABLES

Probability – Axioms of probability – Conditional probability – Bayes theorem – Random variables – Probability function – Moments – Moment generating functions and their properties – Binomial, Poisson, Exponential, Normal distributions – Two dimensional random variables – Poisson process.

UNIT V QUEUEING THEORY

Single and multiple servers – Markovian queuing models – Finite and infinite capacity queues – Finite source model – Queuing applications.

TOTAL: 60 PERIODS

COURSE OUTCOMES :

At the end of the course, students will be able to
 apply various methods in matrix theory to solve system of linear equations.
 mathematical concepts on graph theory and various graph related algorithms.
 could develop a fundamental understanding of linear programming models, able to develop a linear programming model from problem description, apply the simplex method for solving linear programming problems.
 computation of probability and moments, standard distributions of discrete and continuous random variables and functions of a random variable.
 exposing the basic characteristic features of a queuing system and acquire skills in analyzing queuing models, using discrete time Markov chains to model computer systems.

REFERENCES :

1. Bronson, R. “Matrix Operations”, Schaum’s outline series, 2nd Edition, McGraw Hill, 2011.
2. Lewis, D.W. “Matrix Theory”, Allied Publishers, Chennai, 1995.
3. Narasingh Deo, “Graph Theory with Applications to Engineering and Computer Science”, Prentice Hall India, 1997.
4. Rao, S. S. “Engineering Optimization, Theory and Practice”, 4th Edition, John Wiley and Sons, 2009.
5. Taha H .A. “Operations Research: An Introduction”, 10th Edition, Pearson Education Asia, New Delhi, 2017.
6. Walpole R.E., Myer R.H., Myer S.L., and Ye, K., “Probability and Statistics for Engineers and Scientists “, 9th Edition, Pearson Education, Delhi, 2012.