Statistics & Probability
Descriptive statistics, sampling, estimation, confidence intervals,
hypothesis testing, regression, and ANOVA. Probability axioms, conditional
probability, named distributions, joint and marginal distributions,
expectation, variance, and the central limit theorem.
Calculus & Linear Algebra
Single and multivariable calculus: limits, derivatives, integration
techniques, sequences and series, partial derivatives, and multiple
integrals. Linear algebra: vector spaces, matrices, determinants,
eigenvalues, and linear transformations.
Discrete Mathematics
Combinatorics and graph theory: counting principles, generating
functions, recurrence relations, binary strings, plane trees, graph
colourings, matchings, connectivity, and planarity.