Related papers: The Maslov dequantization, idempotent and tropical…
This is a survey paper on applications of mathematics of semirings to numerical analysis and computing. Concepts of universal algorithm and generic program are discussed. Relations between these concepts and mathematics of semirings are…
A unifying approach to software and hardware design generated by ideas of Idempotent Mathematics is discussed. The so-called idempotent correspondence principle for algorithms, programs and hardware units is described. A software project…
These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is…
This is a very gentle introductory course on quantum mechanics aimed at the first years of the undergraduate level. The basic concepts are introduced, with many applications and illustrations. Contains 12 short chapters of equal length,…
We do not present any original or new material. This is a tutorial addressed to students who need to study the microscopic derivation of the quantum-mechanical master equation encountered in many practical physical situations.
In which a review of the concept of countability is done in mathematics, subjecting review some of the theorems so far accepted, showing their inconsistency and also taking concrete elements on the countability of all the powers of the set…
These notes are an introduction to the theory of quantum symmetries of finite and infinite sets, graphs, and locally compact spaces.
A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.
Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.
This is an expository article on the techniques of quantization as they are applied to Gromov-Witten theory and related areas.
Invited contribution to the Encyclopedia of Mathematical Physics (2nd edition), providing an overview over some main ideas and results in quantum cosmology. Key points: Canonical quantisation of homogeneous, isotropic cosmology; discussion…
This is a brief overview of some turning points in the history of infinitesimals.
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
These lectures are a brief introduction to supersymmetry.
This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…
In this paper, we introduce and develop the concept of \emph{ramification} in a given modulus. We study some properties in relation to this concept and it's connection to some important problems in mathematics, particularly the Goldbach…
This is a short introduction to quantum computers, quantum algorithms and quantum error correcting codes. Familiarity with the principles of quantum theory is assumed. Emphasis is put on a concise presentation of the principles avoiding…
This basic introduction to tropical geometry is hopefully accessible to a first years student in mathematics. The topics discussed here are basic tropical algebra, tropical plane curves, some tropical intersections, and Viro's patchworking.…
Short review article on quantum computation accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM
This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.