Course Syllabus | Department Of Mathematics

Probability and Random Processes / Discrete Mathematics

Code: MA2151 / MA1221 | L-T-P-C: 3-1-0-8

The batch joind in July 2025 will do MA1221 Discrete Mathematics (3-0-0-6) in place of MA2151 Probability and Random Processes (3-1-0-8)

MA1221 Discrete Mathematics

Set theory: Sets, relations, equivalence relations, partially ordered sets, functions, countability, lattices and Boolean algebras. Logic: Well-formed formula, interpretations, propositional logic, predicate logic, theory of inference for propositional logic and predicate logic. Combinatorics: Permutations, combinations, recurrences, generating functions, partitions, special numbers like Fibonacci, Stirling and Catalan numbers. Graph Theory: Graphs and digraphs, special types of graphs, isomorphism, connectedness, Euler and Hamilton graphs, planar graphs, graph colouring, trees, matching.

Texts:

J. P. Tremblay and R. Manohar, Discrete Mathematics with Applications to Computer Science, Tata McGraw-Hill, 1997
K. H. Rosen, Discrete Mathematics & its Applications, Sixth Edition, Tata McGraw-Hill, 2007.

References:

A. Shen and N. K. Vereshchagin, Basic Set Theory, American Mathematical Society, 2002
A. Kumar, S. Kumaresan and B. K. Sarma, A Foundation Course in Mathematics, Narosa, 2018.
M. Huth and M. Ryan, Logic in Computer Science, Cambridge University Press, 2004.
V. K. Balakrishnan, Theory and Problems of Combinatorics, Schaum's Series, McGraw-Hill, 1995.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Second Edition, Addison-Wesley, 1994.
A. Tucker, Applied Combinatorics, Sixth Edition, Wiley, 2012.
R. Balakrishnan and K. Ranganathan, A Text Book of Graph Theory, Springer, 2000.

MA2151 Probability and Random Processes

Probability spaces, independence, conditional probability, and basic formulae; Random variables, distribution functions, probability mass/density functions, functions of random variables; Standard univariate discrete and continuous distributions and their properties; Mathematical expectations, moments, moment generating functions, characteristic functions; Random vectors, multivariate distributions, marginal and conditional distributions, conditional expectations; Modes of convergence of sequences of random variables, laws of large numbers, central limit theorem; Definition and classification of random processes, discrete-time Markov chains, classification of states, limiting and stationary distributions, Poisson process, continuous-time Markov chains.

Texts:

P. G. Hoel, S. C. Port and C. J. Stone, Introduction to Probability Theory, Universal Book Stall, 2000.
G. R. Grimmett and D. R. Stirzaker, Probability and Random Processes, Fourth Edition, Oxford University Press, 2020.

References:

S. M. Ross, Introduction to Probability Models, Thirteenth Edition, Academic Press, 2023.
H. Pishro-Nik, Introduction to Probability, Statistics, and Random Processes, Available at https://www.probabilitycourse.com, Kappa Research LLC, 2014.
J. Medhi, Stochastic Processes, Third Edition, New Age International, 2009.
W. Feller, An Introduction to Probability Theory and its Applications, Volume I, Third Edition, Wiley, 1968.
K. S. Trivedi, Probability and Statistics with Reliability, Queuing, and Computer Science Applications, Second Edition, Wiley, 2001.
C. M. Grinstead and J. L. Snell, Introduction to Probability, Second Edition, Universities Press India, 2009.