Online References, Resources, etc.

On this page, I am collecting links to various technical reference materials which I have found online. Mostly this will include talks and reference materials; I do not plan to keep a record of every paper which I have mentioned online. 

I do not maintain these links carefully; if any link has gone dead, then I apologise and encourage you to email me notifying me of this. I also do not claim expertise on all of the topics contained below; in many cases they have simply been recommended to me by somebody else.

Video Lectures

Courses

• Luke Postle - Probabilistic Methods - Videos for 12-week video graduate course on Probabilistic Methods.

• Yurii Nesterov - Modern Algorithmic Optimisation - Videos for a 10 x 1.5 hr course on Optimisation

• Caroline Uhler - Graphical Models: A Combinatorial and Geometric Perspective - Lecture 1, 2, 3

• Nick Trefethen - Approximation Theory and Approximation Practice 

• Philipp Hennig - Probabilistic Machine Learning 

Books, Lecture Notes

(n.b. many of these links point directly to the .pdf)

Books

• Robert Adler - Topological Complexity of Smooth Random Functions 

• Francis Bach - Learning Theory from First Principles 

• Christopher Bishop - Pattern Recognition and Machine Learning 

• Stephen Boyd, Lieven Vandenberghe - Convex Optimisation 

• S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein - Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers 

• Yann Brenier - Examples of Hidden Convexity in Nonlinear PDEs 

• Ariel Caticha - Entropic Physics 

• Luc Devroye - Non-Uniform Random Variate Generation 

• Luc Devroye, Laszlo Gyorfi - Nonparametric Density Estimation

• Lawrence C. Evans - Partial Differential Equations

• Christophe Giraud - Introduction to High-Dimensional Statistics

• Iain Johnstone - Gaussian Estimation: Sequence and Wavelet Models 

• Bas Klein - The Frequentist Theory of Bayesian Statistics  

• Shahar Mendelson - Geometric Aspects of Statistical Learning Theory 

• Frank Morgan - Geometric Measure Theory 

• Richard Nickl - Bayesian Non-Linear Statistical Inverse Problems 

• Art Owen - Monte Carlo Theory, Methods and Examples 

• Neal Parikh and Stephen Boyd - Proximal Algorithms

• James Rawlings, David Mayne, Moritz Diehl - Model Predictive Control

• David Ruelle - Thermodynamic Formalism 

• Sushant Sachdeva, Nisheeth K. Vishnoi - Faster Algorithms via Approximation Theory 

• Michael Unser, Pouya Tafti - An introduction to sparse stochastic processes 

Lecture Notes, Course Pages

• Ahmed El Alaoui - Topics in High-Dimensional Inference 

• Vesa Apaja - Quantum Monte Carlo 

• Stefanos Aretakis - General Relativity 

• Erwin Bolthausen - The Thouless-Anderson-Palmner Equation in Spin Glass Theory 

• Joan Andreu Lázaro Camí - Ergodic Theory

• Victor Batista - Statistical Methods and Thermodynamics 

• Rick Beatson, Leslie Greengard - Fast Multipole Methods 

• Pietro Caputo - Entropy and Markov Chains 

• Pierre Cardialaguet - Mean-Field Games 

• Keith Carne - Geometry and Groups

• Djalil Chafaï, Joseph Lehec - Logarithmic Sobolev Inequalities Essentials

• Xiaohui Chen - Geometric Flows for Applied Mathematicians 

• Ioana Cosma, Ludger Evers - Markov Chains and Monte Carlo Methods

• Mihalis Dafermos, Igor Rodnianski - Black Holes and Linear Waves 

• Fraser Daly - The Stein–Chen Method 

• Erik Demaine - Advanced Data Structures 

• Amir Dembo - Probability Theory

• Frank den Hollander - The Coupling Method 

• Partha Dey - Stein-Chen Method for Poisson Approximation

• Marcelo Disconzi - Recent Advances in Classical and Relativistic Fluids 

• John Duchi - Statistics and Information Theory 

• Daniel Dugger - A Primer on Homotopy Colimits

• Alina Ene - Adaptive Gradient Descent Algorithms 

• Lawrence Evans - Mathematical Optimal Control Theory 

• Carlos Fernandez-Granda - Optimization-Based Data Analysis 

• Charles Geyer - Markov Chain Monte Carlo

• Bill Gosper - Acceleration of Series 

• Craig Gross - Uncertainty Quantification 

• Ramon van Handel - Probability in High Dimension

• Nikolaos Kantas - Sequential Monte Carlo 

• Richard Kenyon - Lectures on Dimers

• Florent Krzakala - Statistical Physics for Optimisation and Learning 

• Joon Kwon - Regret Bounds 

• Rasmus Kyng - Advanced Graph Algorithms and Optimization 

• Daniel Lacker - Mean-Field Games and Interacting Particle Systems

• Daniel Lacker - Probabilistic Compactification Methods for Stochastic Optimal Control and Mean-Field Games 

• Sanjay Lall - Linear Control Systems 2

• Yin Tat Lee - Interplay between Convex Optimization and Geometry 

• Nicolas Macris, Rüdiger Urbanke - Statistical Physics for Communications, Signal Processing, and Computer Science 

• Song Mei - Mean Field Asymptotics in Statistical Learning

• Richard Nickl - Statistical Theory 

• Ryan O'Donnell - Analysis of Boolean Functions 

• Francesco Orabona - Online Learning

• Johannes Pausch - Non-Equilibrium Statistical Field Theory 

• Kaare Brandt Petersen, Michael Syskind Peterson - The Matrix Cookbook 

• Gabriel Peyré - Computational Optimal Transport

• Amit Rajaraman - High-Dimensional Convex Geometry  

• Mark Rudelson - Non-Asymptotic Theory of Random Matrices 

• Gonçalo dos Reis, David Šiška - Stochastic Control and Dynamic Asset Allocation

• Gian-Carlo Rota - Probability 

• Aaron Roth - Modern Topics in Uncertainty Quantification 

• Tim Roughgarden - Communication Complexity (for Algorithm Designers)

• Christian Schmeiser - Entropy Methods 

• Thomas B. Schön, Fredrik Lindsten - Learning of Dynamical Systems

• Cosma Shalizi - Stochastic Processes

• Daniel Spielman - Spectral and Algebraic Graph Theory 

• Jacob Steinhardt - Robust Statistics 

• Suhasini Subba Rao - A Course in Time Series Analysis 

• Alain-Sol Sznitman - Topics in Propagation of Chaos 

• Terence Tao - Fourier Analysis Part 1, Part 2

• John Thickstun - Generative Models 

• UIUC - Statistics 

• Richard Weber - Optimisation and Control 

• Yihong Wu - Information-Theoretic Methods for High-Dimensional Statistics  

Slides

• Oscar Mauricio Agudelo Mañozca, Bart de Moor - Introduction to Model Predictive Control 

• Anthony Atkinson, Marco Riani - Introduction to Robust Statistics 

• Rina Foyle Barber - Conformal Prediction 

• Luca Bortolussi - Fluid and Mean-Field Approximations

• Arieh Iserles - A Tale of Two Matrices 

• Toni Karvonen - Why Not To Use The Gaussian Kernel 

• Jason Lee - Provable Representation Learning 

• Lek-Heng Lim - Numerical Multilinear Algebra 

• Ulysse Marteau-Ferey - Finding Global Minima via Kernel Approximations 

• Michael Mascagni - Monte Carlo Methods for Partial Differential Equations 

• Yurii Nesterov - Relative Smoothness - A New Paradigm in Convex Optimisation 

• Art Owen - A Robust Hybrid of Ridge and Lasso 

• Art Owen - Monte Carlo and Quasi-Monte Carlo for Image Synthesis 

• Art Owen - Quasi-Monte Carlo Tutorial 

• Cosma Shalizi - So, You Think You Have a Power Law, Do You? Well Isn't That Special? 

• Adrien Taylor - Computer-Aided Analyses of First-Order Methods via Semidefinite Programming 

• Nick Trefethen - Six Myths of Polynomial Interpolation and Quadrature 

• Nick Trefethen - Who Invented The Great Numerical Algorithms? 

Static Websites

Collections of Materials

• Anton Bovier - Lecture Notes 

• Dexter Chua - Lecture Notes

• Keith Conrad - Blurbs 

• Richard Feynman - Lecture Notes 

• Roger Grosse - Course Pages 

• Martin Hairer - Lecture Notes

• Universität Potsdam - Lecture Notes

• Annie Liang - Lecture Notes

• James Milne - Lecture Notes 

• David Tong - Lecture Notes 

• Random Services - Teaching Notes 

Blog Posts by Others

• Francis Bach - The Many Faces of Integration by Parts - Randomised Smoothing and Score Functions 

• Terence Tao - Li-Yau-Hamilton Harnack Inequalities and Kappa-Solutions 

• Terence Tao - Comparison Geometry, The High-Dimensional Limit, and Perelman Reduced Volume 

• Terence Tao - The Varopoulos-Carne Bound 

MathOverflow (and similar) Posts

• Simple Proof of Prékopa's Inequality

• 'Permutation Coupling' for Markov Chains 

• A Strange Variant of the Gaussian Log-Sobolev Inequality 

• Convergence of Metric Spaces of Increasing Dimension