CSE301

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Mathematical Analysis for Computer Science

3 Credit Hour Course

Intended For Level 3 Term 1 Students

Prerequisite:

Advanced counting and discrete probability: recurrences and sums, binomial coefficients, special numbers, generating functions, probability generating function; Random variables: discrete and continuous random variables, multivariate distributions, moment generating functions; Conditional probability and conditional expectation; Probability bounds: Markov and Chebyshev inequalities, Chernoff bound, Cauchy-Schwarz and Jensen inequalities; Convergence of random variables: law of large numbers, central limit theorem; Statistical inference: parametric and nonparametric models, point estimation, confidence intervals, bootstrapping; Parametric inference: maximum likelihood estimation; Bayesian inference: maximum a posteriori estimation; Hypothesis testing: permutation test, likelihood ratio test, multiple testing; Stochastic processes: Poisson process, Gaussian process; Markov chains: discrete-time, continuous-time, birth-death process; Queuing theory: exponential models, open and closed queuing network, applications of queuing models.