MA4113 Algebra and Probability Syllabus:

MA4113 Algebra and Probability Syllabus – Anna University PG Syllabus Regulation 2021

COURSE OBJECTIVES:

 To understand the basics of random variables with emphasis on the standard discrete and continuous distributions.
 To make students understand the notion of a Markov chain, and how simple ideas of conditional probability and matrices can be used to give a thorough and effective account of discrete – time Markov chains.
 To apply the small / large sample tests through Tests of hypothesis.
 To introduce the basic notions of groups, rings, fields which will then be used to solve related problems.
 To introduce and apply the concepts of rings, finite fields and polynomials.

UNIT I RANDOM VARIABLES

Random variables – Moments – Binomial, Biometric, Poisson, Uniform, Exponential and Normal distributions – Joint distributions – Marginal – Correlation – Linear Regression distributions.

UNIT II RANDOM PROCESSES

Classification – Stationary random process – Markov process – Markov chain – Poisson process – Gaussian process – Autocorrelation – Cross correlation.

UNIT III TESTING OF HYPOTHESIS

Sampling distributions – Type I and Type II errors – Small and large samples – Tests based on Normal, t, Chi square and F distributions for testing of mean, variance and proportions, Tests for independence of attributes and goodness of fit.

UNIT IV GROUPS AND RINGS

Groups: Definition – Properties – Homomorphism – Isomorphism – Cyclic groups – Cosets – Lagrange’s theorem. Rings: Definition – Sub rings – Integral domain – Field – Integer modulo n – Ring homomorphism.

UNIT V FINITE FIELDS AND POLYNOMIALS

Rings – Polynomial rings – Irreducible polynomials over finite fields – Factorizations of polynomials over finite fields.

TOTAL : 60 PERIODS

COURSE OUTCOMES:

At the end of the course, students will be able to
 analyze the performance in terms of probabilities and distributions achieved by the determined solutions.
 classify various random processes and solve problems involving stochastic processes.
 apply the basic principles underlying statistical inference (estimation and hypothesis testing).
 apply the basic notions of groups, rings, fields which will then be used to solve related problems.
 explain the fundamental concepts of advanced algebra and their role in modern mathematics and applied contexts.

REFERENCES:

1. Devore J.L.,” Probability and Statistics for Engineering and sciences”, Cengage learning, 9th Edition, Boston,2017.
2. Grimaldi R. P. and Ramana B.V., “Discrete and Combinatorial Mathematics”, Pearson Education, 5th Edition, New Delhi, 2007.
3. Johnson R. A. and Gupta C.B., “Miller and Freund’s Probability and Statistics for Engineers”, Pearson India Education, Asia, 9th Edition, New Delhi, 2017.
4. Ibe. O.C., “ Fundamentals of Applied Probability and Random Processes”, Elsevier U.P., 1st Indian Reprint, 2007.