\(\newcommand{L}[1]{\| #1 \|}\newcommand{VL}[1]{\L{ \vec{#1} }}\newcommand{R}[1]{\operatorname{Re}\,(#1)}\newcommand{I}[1]{\operatorname{Im}\, (#1)}\)

# Tutorials on imaging, computing and mathematics¶

## Mathematics¶

- Notation;
- Some algebra with summation;
- The angle sum rule;
- Formula for rotating a vector in 2D;
- Sum of sines and cosines;
- Sums of sinusoids;
- Vectors and dot products;
- Vector projection;
- Angles between vectors;
- Correlation and projection;
- Matrix rank;
- Inverse of a diagonal matrix;
- Refresher on complex numbers;
- Fourier without the ei;
- Introducing principal component analysis;
- Linear interpolation.

## Statistics¶

## Imaging¶

- Coordinate systems and affine transforms;
- Slice timing correction;
- Calculating transformations between images;
- Mutual information as an image matching metric;
- An introduction to smoothing;
- Convolution;
- Smoothing as convolution;
- Correlated regressors;
- Notes on the Bonferroni threshold;
- Thresholding with false discovery rate;
- Thresholding with random field theory.