Related papers: Some Fundamental Theorems in Mathematics
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
This is an introduction to small divisors problems. The material treated in this book was brought together for a PhD course I tought at the University of Pisa in the spring of 1999. Here is a Table of Contents: Part I One Dimensional Small…
Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
Optics, aka functional references, are classes of tools that allow composable access into compound data structures. Usually defined as programming language libraries, they provide combinators to manipulate different shapes of data such as…
Logical and mathematical aspects of the basic concepts of thermodynamics are considered.
In this paper, we generalize the fundamental theorems of functional analysis to the framework of bicomplex topological modules.
At two examples dealt with in methodologically different ways it will be pointed out how the concept of an empirical theory (in the sense of the Structuralists) can be useful to specify contents relevant to maths didactics.
This survey aims to provide a guide to the literature on topological 4-manifolds. Foundational theorems on 4-manifolds are stated, especially in the topological category. Precise references are given, with indications of the strategies…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Summer term 2001, to undergraduate Mathematics and Physics students. It covers a few selected topics from perturbation theory at an introductory…
This is the logical foundation for for Relativity Theory, Probability Theory, and for Quantum Theory. Contents is the following: 1 Introduction. 2 Classical logic. 3 Time and space. 3.1 Recorders. 3.2 Time. 3.3 Space. 3.4 Relativity. 4.…
This note is intended to be a friendly introduction to virtual classes. We review virtual classes and we give a number of properties and applications. We also include a new virtual push-forward theorem and many computations of virtual…
This is an expository article for Elsevier's Encyclopedia of Mathematical Physics on the subject in the title. Comments/corrections welcome.
In this paper, we give the explicit bounds for the data of objects involved in some basic theorems of Singularity theory: the Inverse, Implicit and Rank Theorems for Lipschitz mappings, Splitting Lemma and Morse Lemma, the density and…
When talking to secondary school students, first impressions are crucial. Accidentally say something that sounds boring and you'll lose them in seconds. A physical demonstration can be an eye-catching way to begin an activity or spark off a…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
We present mathematical details of several cosmological models, whereby the topological and the geometrical background will be emphasized.
These notes, connected to a "potpourri" topics class currently underway, discuss some basic topics in analysis and connections with other areas of mathematics.
This is an explanation and defense of "mathematical conceptualism" for a general mathematical and philosophical audience. I make a case that it is cogent, rigorous, attractive, and better suited to ordinary mathematical practice than all…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.