Here are some topics. Are they
considered relevant to
data science?
Matrix row rank and column rank are equal.
In matrix theory, the polar decomposition.
Each Hermitian matrix
has an orthogonal basis of
eigenvectors.
Weak law of large numbers.
Strong law of large numbers.
The Radon-Nikodym theorem and
conditional expectation.
Sample mean and variance are
sufficient statistics for independent,
identically distributed samples from
a univariate Gaussian distribution.
The Neyman-Pearson lemma.
The Cramer-Rao lower bound.
The margingale convergence theorem.
Convergence results of
Markov chains.
Markov processes in continuous time.
The law of the iterated logarithm.
The Lindeberg-Feller version of the
central limit theorem.
The normal equations of linear
regression analysis.
Non-parametric statistical hypothesis
tests.
Power spectral estimation
of second order, stationary
stochastic processes.
Resampling plans.
Unbiased estimation.
Minimum variance estimation.
Maximum likelihood estimation.
Uniform minimum variance unbiased estimation.
Wiener filtering.
Kalman filtering.
Autoregressive moving average (ARMA) processes.
Rank statistics are always sufficient.
Farkas lemma.
Minimum spanning trees on directed
graphs.
The simplex algorithm of linear
programming.
Column generation in linear programming
(Gilmore-Gomory).
The simplex algorithm for
min cost capacitated network flows.
conjugate gradients.
The Kuhn-Tucker conditions.
Constraint qualifications for the
Kuhn-Tucker conditions.
Fourier series.
The Fourier transform.
Hilbert space.
Banach space.
Quasi-Newton iteration and
updates, e.g., Broyden-Fletcher-Goldfarb-Shanno.
Orthogonal polynomials for
numerically stable polynomial
curve fitting.
Lagrange multipliers.
The Pontryagin maximum principle.
Quadratic programming.
Convex programming.
Multi-objective programming.
Integer linear programming.
Deterministic dynamic programming.
Stochastic dynamic programming.
The linear-quadratic-Gaussian
case of dynamic programming.