Related papers: Lecture Notes on Randomized Linear Algebra

This is a lecture note for the course DS-GA 3001 <Natural Language Understanding with Distributed Representation> at the Center for Data Science , New York University in Fall, 2015. As the name of the course suggests, this lecture note…

These are notes for a graduate-level introductory course on singularity categories.

These are the extended lecture notes of my lecture about ``Linear Operators on Polynomials, $K$-Positivity Preserver, and their Generators''. The lecture was given at the University of Konstanz in the winter semester 2025/26.

These are the lecture notes for the introductory course on Whitehead, Reidemeister and Ray-Singer torsions, given by the author at the University of Zurich in Spring semester 2014.

These notes are from a 4-lecture mini-course taught by the author at the conference on von Neumann algebras as part of the ``Geometrie non commutative en mathematiques et physique'' month at CIRM in 2004.

These notes were originally prepared as additional material for the lessons I have given at the summer school Gamma-ray Astrophysics and Multifrequency: Data analysis and astroparticle problems, organized by the Department of Physics of the…

Lecture notes of a master course given at Orsay between 2019-2024. Topics covered include Part I: One-dimensional random walks, cycle lemma and Bienaym\'e--Galton--Watson random trees. Part II: Erd\"os--R\'enyi random graphs, three proofs…

This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incomplete, but due to recent requests from…

These are lecture notes for lectures at the Park City Math Institute, summer 2007. We cover aspects of the dimer model on planar, periodic bipartite graphs, including local statistics, limit shapes and fluctuations.

These lecture notes cover the theory of convex optimization, with a particular emphasis on first-order methods.

This is a lecture notes for a mini-course in Department of Mathematics, Ghent University, 14 Mar.-25 Mar. 2023.

These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…

These notes are for the author's lectures, "Integral Reduction and Applied Algebraic Geometry Techniques" in the School and Workshop on Amplitudes in Beijing 2016. I introduce the applications of algebraic geometry methods on multi-loop…

These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous…

These lecture notes were written for the course 18.657, High Dimensional Statistics at MIT. They build on a set of notes that was prepared at Princeton University in 2013-14 that was modified (and hopefully improved) over the years.

These notes represent approximately one semester's worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications:…

This is a self-contained set of lecture notes covering various aspects of the theory of open quantum system, at a level appropriate for a one-semester graduate course. The main emphasis is on completely positive maps and master equations,…

These lecture notes have been developed for the course Computational Social Choice of the Artificial Intelligence MSc programme at the University of Groningen. They cover mathematical and algorithmic aspects of voting theory.

A series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required. Based primarily on…

The past decade has witnessed two important new developments in the study of linear series on algebraic varieties. First, vector bundles have emerged as powerful tools for analyzing linear series on curves and surfaces. More recently, the…