These are lectures on some fundamental mathematics underlying many approaches and algorithms in machine learning. They are not about particular learning algorithms; they are about the basic concepts and tools upon which such algorithms are built. Often students feel intimidated by such material: there is a vast amount of "classical mathematics", and it can be hard to find the wood for the trees. The main topics of these lectures are Lagrange multipliers, functional analysis, some notes on matrix analysis, and convex optimization. I’ve concentrated on things that are often not dwelt on in typical CS coursework. Lots of examples are given; if it's green, it's a puzzle for the student to think about. These lectures are far from complete: perhaps the most significant omissions are probability theory, statistics for learning, information theory, and graph theory. I hope eventually to turn all this into a series of short tutorials. Please let me know of any errors, etc. ; :from Chris Burges homepage : Lecture contains: Lagrange multipliers: * Lagrange the Mathematician * Lagrange multipliers: an indirect approach can be easier * Multiple Equality Constraints * Multiple Inequality Constraints * Two points on a d-sphere * The Largest Parallelogram * Resource allocation * A convex combination of numbers is maximized by choosing the largest * The Isoperimetric problem * For fixed mean and variance, which univariate distribution has maximum entropy? * An exact solution for an SVM living on a simplex Notes on some Basic Statistics * Probabilities can be Counter-Intuitive (Simpson's paradox; the Monty Hall puzzle) * IID-ness: Measurement Error decreases as 1/sqrt{n} * Correlation versus Independence * The Ubiquitous Gaussian: Product of Gaussians is Gaussian Convolution of two Gaussians is a Gaussian Projection of a Gaussian is a Gaussian Sum of Gaussian random variables is a Gaussian random variables Uncorrelated Gaussian variable...