Linear Algebra, Probability, and Statistics

- Linear algebra [vectors and scalars, inner product, vector projection, linear dependence and independence, matrix, determinant, matrix inverse, system of linear equations, matrix equation, Gaussian elimination, Cramer's rule, matrix rank, eigenvalue, eigenvector, matrix diagonalization, positive, negative and semi-definiteness, and their applications]
- Elementary complex variables [arithmetics of complex numbers, representations of complex numbers, De Moivre's theorem, roots of unity, complex functions, and their applications]
- Basic probability theory [axioms of probability, conditional probability, Bayes' theorem, the total probability formula, random variable, (joint) probability distribution, expectation, variance, independence, and their applications]
- Commonly used distributions [Bernoulli, Binomial, Geometric, Negative Binomial, Exponential, Poisson and Normal distribution, and their applications]
- Basic statistics [point estimates, sample mean, sample variance with known or unknown mean, confidence interval for a population mean with known or unknown population variances, inference for proportion, and their applications]