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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

• Introduction to the General Linear Model.

• p values from cumulative distribution functions;

• The argument in “Why most published research findings are false”;

• Exploring the R formula;

• Finding the least-squares line.

Imaging

• Coordinate systems and affine transforms;

• Slice timing.

• Optimizing space

• 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.

General Computing

• The curious coder’s guide to git;

• Points on floats;

• Floating point error.

Python background

• Brisk introduction to Python

• Inserting values into strings;

• “for” and “while”, “break” and “else:”;

• Functions are objects;

• Global and local scope of Python variables.