MATH590: Approximation in ${ℝ}^d$ (NUM)

Module overview

Concepts from mathematical analysis are introduced and reinterpreted as data analysis procedures, with a particular focus on the structure of the real numbers.

• Number systems: $\mathbb{N},\mathbb{Z},\mathbb{Q},ℝ,{\mathbb{Q}}_p$

• Rigid body motion, data sets

• Approximation in $ℝ$: interpolation, least-squares, min-max

• Approximation in ${ℝ}^d$, $d\in \mathbb{N}$

• Data transformations: interpolation, integration, differentiation

• Data reduction: least-squares, min-max

• Data representation: functional analysis