Related papers: Lecture Notes on Quadratic Forms and their Arithme…

These are notes from a lecture course on symmetric spaces by the second author given at the University of Pittsburgh in the fall of 2010.

These lecture notes are based on a set of six lectures that I gave in Edinburgh in 2008/2009 and they cover some topics in the interface between Geometry and Physics. They involve some unsolved problems and conjectures and I hope they may…

This is a set of lecture notes suitable for a Master's course on quantum computation and information from the perspective of theoretical computer science. The first version was written in 2011, with many extensions and improvements in…

Work in progress concerning alternative formalizations of arithmetic.

Notes to lectures on the epsilon calculus, covering axioms, semantics, completeness, and the first epsilon theorem.

These lecture notes are based on an introductory course given by the author at the summer school "Noncommutative Algebraic Geometry" at MSRI in June 2012. The emphasis throughout is on examples to illustrate the many different facets of…

These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.

This article discusses some important applications of the quadratic function with the aim of highlighting the importance of cuadr\'aticas.- forms are also intended to show how a simple function covers virtually all areas of knowledge are…

There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.

These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.

In this paper we consider certain quaternary quadratic forms and octonary quadratic forms and by using the theory of modular forms, we find formulae for the number of representations of a positive integer by these quadratic forms.

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,…

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

In this paper, we will first summarize known results concerning continued fractions. Then we will limit our consideration to continued fractions of quadratic numbers. The second author described periods and sometimes precise form of…

In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.

Lecture notes on quantum machine learning for computer scientists.

These lecture notes provide an introduction to quantum information and quantum computation, which are strongly related disciplines and subject of intense research. The lecture notes contain only a small selection of topics in these…

These are lecture notes on string theory at Fudan University.

These are some basic notes concerning Holder and Lipschitz classes on metric spaces.

The purpose of this short note is to collect a set of formulas pertaining to momentum kinematics for higher spin light-front vertices. At least one of the formulas seems to be previously unknown.