JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Pre-Requisites

UG level course in Discrete Mathematics/ Mathematical Foundations of Computer

Science

Course Objectives:

• To understand the mathematical fundamentals that is prerequisites for a variety of courses like Data mining, Network protocols, analysis of Web traffic, Computer security, Software engineering, Computer architecture, operating systems, distributed systems, Bioinformatics, Machine learning.
• To develop the understanding of the mathematical and logical basis to many modern techniques in information technology like machine learning, programming language design, and concurrency.
• To study various sampling and classification problems.

Course Outcomes

After completion of course, students would be able to:

• To understand the basic notions of discrete and continuous probability.
• To understand the methods of statistical inference, and the role that sampling distributions play in those methods.
• To be able to perform correct and meaningful statistical analyses of simple to moderate complexity.

UNIT - I

Probability mass, density, and cumulative distribution functions, Parametric families of distributions, Expected value, variance, conditional expectation, Applications of the univariate and multivariate Central Limit Theorem, Probabilistic inequalities, Markov chains

UNIT - II

Random samples, sampling distributions of estimators, Methods of Moments and Maximum Likelihood,

UNIT - III

Statistical inference, Introduction to multivariate statistical models: regression and classification problems, principal components analysis, The problem of over fitting model assessment.

UNIT - IV

Graph Theory: Isomorphism, Planar graphs, graph colouring, Hamilton circuits and Euler cycles. Permutations and Combinations with and without repetition. Specialized techniques to solve combinatorial enumeration problems

UNIT - V

Computer science and engineering applications Data mining, Network protocols, analysis of Web traffic, Computer security, Software engineering, Computer architecture, operating systems, distributed systems, Bioinformatics, Machine learning.

Recent Trends in various distribution functions in mathematical field of computer science for varying fields like bio-informatics, soft computing, and computer vision.

Page 3 of 55

R19 M.TECH. CSE/CS

Text Book:

John Vince, Foundation Mathematics for Computer Science, Springer.

References:

• 1. K. Trivedi. Probability and Statistics with Reliability, Queuing, and Computer Science Applications. Wiley.
• 2. M. Mitzenmacher and E. Upfal. Probability and Computing: Randomized Algorithms and Probabilistic Analysis.
• 3. Alan Tucker, Applied Combinatorics, Wiley Page 4 of 55 R19 M.TECH. CSE/CS M. Tech - CSE/CS – I Year – I Semester Common to CSE and CS Syllabus