Related papers: Lecture Notes on Randomized Linear Algebra
We mark up a corpus of LaTeX lecture notes semantically and expose them as Linked Data in XHTML+MathML+RDFa. Our application makes the resulting documents interactively browsable for students. Our ontology helps to answer queries from…
These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.
This article was prepared in connection with the 2009 Barnett lecture at the University of Cincinnati, and deals with various classes of fractal sets and analysis on them.
These lecture notes provide an introduction to logarithmic geometry with a view towards recent applications in the desingularization theory.
The first version of these lecture notes is based on the hand-written notes I prepared for the cosmology course taught to graduate students of PPGFis and PPGCosmo at the Federal University of Esp\'irito Santo (UFES), starting in 2014. The…
This paper presents an extended version of lecture notes for an introductory course on Berkovich analytic spaces that I gave in 2010 at Summer School "Berkovich spaces" at Institut de Mathmatiques de Jussieu.
These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.
These are lecture notes from author's mini-course during Session 1: "Vertex algebras, W-algebras, and application" of INdAM Intensive research period "Perspectives in Lie Theory", at the Centro di Ricerca Matematica Ennio De Giorgi, Pisa,…
These are course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, "Shapes of Polyhedra". A…
This paper outlines our ideas on how to teach linear algebra in a mechanized mathematical environment, and discusses some of our reasons for thinking that this is a better way to teach linear algebra than the ``old fashioned way''. We…
These are lecture notes from my talks at the "Current Developments in Mathematics" conference (Harvard, 2006). They cover a variety of topics involving symplectic cohomology. In particular, a discussion of (algorithmic) classification…
We develop a random model for relation algebras. We prove some preliminary results and pose questions that lay out a new direction of research.
This article consists of six lectures on the categorification of the Burau representation and on link homology groups which categorify the Jones and the HOMFLY-PT polynomial. The notes are based on the lecture course at the PCMI 2006 summer…
These lecture notes concern information-theoretic notions of entropy. They are intended for, and have been successfully taught to, undergraduate students interested inresearch careers. Besides basic notions of analysis related to…
These are yet another lecture notes on Seiberg-Witten invariants, where no claim of originality is made, they contain a discussion of some related results from the recent literature.
These are the lecture notes (in Italian) of a course held in Perugia, Italy, during the summer 2002. They concern the basic facts on the iterative solution of linear systems. The course is self-contained and requires only basic knowledge of…
Recent progress on the understanding of the Random Conductance Model is reviewed and commented. A particular emphasis is on the results on the scaling limit of the random walk among random conductances for almost every realization of the…
This is the draft of lecture notes for Phd students in Sichuan University. In this notes we expand Li-Ruan's paper with much more detailed explanations and calculations.
These are lecture notes based on the first part of a course on 'Mathematical Data Science', which I taught to final year BSc students in the UK in 2019-2020. Topics include: concentration of measure in high dimensions; Gaussian random…
Algorithmic information theory roots the concept of information in computation rather than probability. These lecture notes were constructed in conjunction with the graduate course I taught at Universit\`a della Svizzera italiana in the…