Related papers: Alcune Note di Analisi Matematica
We develop a graphical notation to introduce classical Lie algebras. Although this paper deals with well-known results, our pictorial point of view is slightly different to the traditional one. Our graphical notation is fairly elementary…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…
The paper examines the construction of a course in mathematical analysis at a pedagogical university, aimed at developing the ability of future mathematics teachers to detect and solve problems related to finding proofs. Key words: teaching…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
In this article we give a short and informal overview of some aspects of the theory of C*- and von Neumann algebras. We also mention some classical results and applications of these families of operator algebras.
My purpose is to examine some concepts of mathematical logic, which have been studied by Carlo Cellucci. Today the aim of classical mathematical logic is not to guarantee the certainty of mathematics, but I will argue that logic can help us…
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…
This set of notes re-proves known results on weighted automata (over a field, also known as multiplicity automata). The text offers a unified view on theorems and proofs that have appeared in the literature over decades and were written in…
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…
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,…
These are the notes from my courses on the arithmetic of quadratic forms.
We collect some classical results related to analysis on the Riemann surfaces. The notes may serve as an introduction to the field: we suppose that the reader is familiar only with the basic facts from topology and complex analysis. the…
In this article, we will showcase some analytical concepts that can be used to tackle Functional Equations (FE) in the positive real numbers domain. Such concepts and related techniques have occasionally appeared in recent High School Math…
These are some basic notes concerning Holder and Lipschitz classes on metric spaces.
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
This book contains a large number of exercises related to different stochastic disciplines. Difficulty of the problems varies from the basic level in the first chapter up to the analysis of articles in Probability, Statistics and Computer…
This book is based on notes compiled over the many years I have been teaching the course "Applied Functional Analysis" in the first year of the Master programme at Delft University of Technology, for students with previous exposure to the…
It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…
These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…