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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 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.

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.