Unit 1: Sets, subsets, and their respective properties. Relations and their properties, functions, bijective function, inverse functions, domain, and range.
Unit 2: Matrix Theory: Basic Matrix algebra, determinant of a matrix, inverse of a matrix, finding solution of a linear system, geometry representation of matrices, Subspace, Vector Space, Solution Space of a Matrix, Null- Space, Basis, Linear independent, Spanning set.
Unit 3: Probability Theory: Permutations and combinations, basic probability theory, probability threes, conditional probability, Independence, Bayes Theorem, Random variable definition, discrete random variables and their properties, Bernoulli, Binomial, Uniform, probability mass function, Cumulative distribution function, expectation and Variance.
Unit 4: Continuous random variables, normal distribution, exponential, geometric, PDF, CDF, Marginal distribution, Independent Random Variables, Joint Random Variable.
Unit 5: Random process: general concept, power spectrum, discrete-time processes, random walks and other applications, Markov chains, transition probabilities.Unit 6: Introduction to Game Theory, basic game theory games and their application to Cyber Security