相关论文: Randomness in Arithmetic and The Decline and Fall …

Lecture given Wednesday 27 October 1993 at a Physics -- Computer Science Colloquium at the University of New Mexico. The lecture was videotaped; this is an edited transcript. It also incorporates remarks made at the Limits to Scientific…

These lectures give a brief introduction to the Computer Algebra systems Reduce and Maple. The aim is to provide a systematic survey of most important commands and concepts. In particular, this includes a discussion of simplification…

These are notes from a three-lecture mini-course on free probability given at MSRI in the Fall of 2010 and repeated a year later at Harvard. The lectures were aimed at mathematicians and mathematical physicists working in combinatorics,…

Recently delivered lectures on Self-Referential Mathematics, [2], at the Department of Mathematics and Applied Mathematics, University of Pretoria, are briefly presented. Comments follow on the subject, as well as on Inconsistent…

These are lecture notes that are based on the lectures from a class I taught on the topic of Randomized Linear Algebra (RLA) at UC Berkeley during the Fall 2013 semester.

Random matrix theory has played a major role in several areas of pure and applied mathematics, as well as statistics, physics, and computer science. This lecture aims to describe the intrinsic freeness phenomenon and how it provides new…

This is the transcript of a lecture given at UMass-Lowell in which I compare and contrast the work of Godel and of Turing and my own work on incompleteness. I also discuss randomness in physics vs randomness in pure mathematics.

Transcript of G.J. Chaitin's 2 March 2000 Carnegie Mellon University School of Computer Science Distinguished Lecture. The notion of randomness is taken from physics and applied to pure mathematics in order to shed light on the…

Lecture given Friday 7 April 1995 at the Santa Fe Institute, Santa Fe, New Mexico. The lecture was videotaped; this is an edited transcript.

Brief lecture notes for a course about random matrices given at the University of Cambridge.

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.

Some Goedel centenary reflections on whether incompleteness is really serious, and whether mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information. [Enriques lecture given…

This chapter is based on lectures on Randomized Numerical Linear Algebra from the 2016 Park City Mathematics Institute summer school on The Mathematics of Data.

These are notes from my lecture at 4ECM in Stockholm (June 2004).

In my book "Algorithmic Information Theory" I explain how I constructed a million-character equation that proves that there is randomness in arithmetic. My book only includes a few pages from the monster equation, and omits the software…

My first paper exclusively about ridge regression was published in Technometrics and chosen for invited presentation at the 1975 Joint Statistical Meetings in Atlanta. Unfortunately, that paper contained a wide range of assorted details and…

Those notes rest on the Samuel Eilenberg Lectures I gave at Columbia University, NY, in the fall 2022. I thank all the mathematicians who participated in their elaboration, directly or indirectly. They are meant to be published as a…

This is the text of my report presented at the 29th Solvay Conference on Physics on `The Structure and Dynamics of Disordered Systems' held in Bruxelles from October 19 to 21, 2023. I consider the problem of minimizing a random energy…

This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…

These lecture notes provide an introduction to free probability theory, with a focus on tools and techniques useful in the study of large random matrices. Topics include freeness, free cumulants, additive and multiplicative free…