Unit 1 Probability fundamentals, Probability mass, density, and cumulative

7 lecture hours

• distribution functions
• Parametric families of distributions
• Expected value
• conditional expectation
• Applications of the univariate and multivariate Central Limit Theorem
• Probabilistic inequalities
• Markov chains

Unit 2 Random samples, sampling distributions of estimators, Methods of

• Moments and Maximum Likelihood 7 15

Unit 3 Statistical inference, Introduction to multivariate statistical models

8 lecture hours

• regression and classification problems
• principal components analysis
• The problem of overfitting model assessment

Unit 4 Graph Theory

9 lecture hours

• Planar graphs
• graph colouring
• Hamilton circuits and euler cycles
• Permutations and Combinations with and without repetition
• Specialized techniques to solve combinatorial enumeration problems

Unit 5 Computer science and engineering applications

9 lecture hours

• Data mining
• Network protocols
• analysis of Web traffic
• Computer security
• Software engineering
• Computer architecture
• operating systems
• distributed systems
• Machine learning

Unit 6 Recent Trends in various distribution functions in mathematical field of

5 lecture hours

• computer science for varying fields like bioinformatic
• soft computing, and computer vision