Mathematics

10-hours course

This course reviews the mathematical foundations necessary to absorb the Body of Knowledge of the ARPM Certificate
Notation
Vector spaces
Linear transformations
Positive (semi)definite matrices
Inner product spaces
Matrix algebra
The spectral theorem
Differentiation
The Taylor expansion
Approximate derivatives
Integration
Monotone functions
Convexity
Many types of Fourier transform
Functional analysis perspective
Linear algebra perspective
Representations of a distribution
Marginalization
Conditioning
Normal distribution
Quadratic-normal distribution
Notable multivariate distributions
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