Related papers: Lecture notes on complexity of quantifier eliminat…
We give a method to transform into programs, classical proofs using a well ordering of the reals. The technics uses a generalization of Cohen's forcing and the theory of classical realizability introduced by the author.
In this note we report on an implementation of discovery-oriented problems in courses on Real Analysis and Differential Equations. We explain a type of task-design that gives students the opportunity to conjecture, refute and prove. What is…
This article contains ideas and their elaboration for quantifiers, which appeared after checking in practice the experimental language of the formal knowledge representation YAFOLL [1]: - looking at for_all and exists quantifiers as…
We reformulate Special Relativity by a quaternionic algebra on reals. Using {\em real linear quaternions}, we show that previous difficulties, concerning the appropriate transformations on the $3+1$ space-time, may be overcome. This implies…
We consider the Quantifier Elimination (QE) problem for propositional CNF formulas with existential quantifiers. QE plays a key role in formal verification. Earlier, we presented an approach based on the following observation. To perform…
These notes are based on the course given at the School of Geometry, University Kasdi Merbah (Ouargla) 2012. The aim of the course was the deformation quantization of Poisson Lie groups. In these notes we only review Kontsevich's formality…
Researchers are often perplexed when their machine learning algorithms are required to deal with complex number. Various strategies are commonly employed to project complex number into real number, although it is frequently sacrificing the…
In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to…
We begin by surveying the historical positions in different attempts to understand the material world since the rise of modern science, with specific focus on the role of Cartesian primary qualities in explanatory conceptualisation.…
This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems…
These lecture notes endeavour to collect in one place the mathematical background required to understand the properties of kernels in general and the Random Fourier Features approximation of Rahimi and Recht (NIPS 2007) in particular. We…
This is a kind of introduction to some basic topics in analysis, some of which would be covered in standard graduate courses, and some not. However, an important difference is that not much in the way of prerequisites are needed, beyond…
I developed the lecture notes based on my ``Linear Model'' course at the University of California, Berkeley over the past ten years. This book provides an intermediate-level introduction to the linear model. It balances rigorous proofs and…
These are the notes for a 5-lecture-course given at ESSLLI 2006 in Malaga, Spain. The URL of the school is http://esslli2006.lcc.uma.es/ . This version slightly differs from the one which has been distributed at the school because typos…
This is a note accompanying "CS 410/510: INTRO TO QUANTUM COMPUTING" I taught at Portland State University in Spring 2017. It is a review and summary of some early results related to Grover's quantum search algorithm in a consistent way. I…
These are expanded notes of a two-semester course on Lie groups and Lie algebras given by the author at MIT.
The education system for students in physics suffers (worldwide) from the absence of a deep course in probability and randomness. This is the real problem for students interested in quantum information theory, quantum optics, and quantum…
This material is a rewriting and expansion of notes for beginning graduate students in seminars in combinatorics (Department of Mathematics, University of California San Diego). Solid skills in linear and multilinear algebra were required…
This document collects the lecture notes from my course "Communication Complexity (for Algorithm Designers),'' taught at Stanford in the winter quarter of 2015. The two primary goals of the course are: 1. Learn several canonical problems…
This is a set of lecture notes that developed out of courses on the lambda calculus that I taught at the University of Ottawa in 2001 and at Dalhousie University in 2007 and 2013. Topics covered in these notes include the untyped lambda…