Related papers: Some Notes on Standard Borel and Related Spaces
The goal of this note is to provide a constructive version of the proof of local structure of etale algebras.
In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.
We prove a general result on irregularities of distribution for Borel sets intersected with bounded measurable sets or affine half-spaces.
These are notes from a basic course in Several Complex Variables
A number of topics in analysis are discussed, with emphasis on basic principles. There is some overlap with "Elements of linear and real analysis" (arXiv:math/0108030), with numerous changes in content and presentation since then.
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…
These are notes for a graduate-level introductory course on singularity categories.
These notes provide an introduction to a number of those topics in Classical Mechanics that are useful for field theory.
The validity of non-perturbative methods is questioned. The concept of relative space is introduced.
The cut pseudo-metric on the space of graph limits induces an equivalence relation. The quotient space obtained by collapsing each equivalence class to a point is a metric space with appealing analytic properties. We show that the…
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…
These Course Notes provide an introduction to mathematical proofs for undergraduate students transitioning from computational calculus to abstract mathematics. Topics include propositional logic, proof techniques, mathematical induction,…
The purpose of this article is to present, in a simple way, an analytic approach to special numbers and polynomials. The approach is based on the derivative polynomials. The paper is, to some extent, a review article, although it contains…
The purpose of this text is to set up a few basic notions concerning quantum graphs, to indicate some areas addressed in the quantum graph research, and to provide some pointers to the literature. The pointers in many cases are secondary,…
Algebraic basics on Temperley-Lieb algebras are proved in an elementary and straightforward way with the help of tensor categories behind them.
This review aims to provide a very short and pedestrian introduction to some of the basics of extra-dimensional physics. The hope is to facilitate access and to be, in some respects, complementary to the many already existing reviews on…
We give a short introduction to the theory of modular metric spaces. This is a corrected version of the paper [1], which had some errors. We are grateful to V. V. Chistyakov for bringing these to our attention.
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…
An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut
These notes are a brief introduction to the RSA algorithm and modular arithmetic. They are intended for an undergraduate audience.