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2010
AI
This volume serves as a memorial to the influential mathematician Paul Richard Halmos, known for his contributions to operator theory and his role as an educator and community member. It includes tributes, a review of Halmos's influential article on mathematical writing, a list of his publications, and a collection of expository articles by notable operator theorists. These contributions provide insight into Halmos's impact on the field of mathematics and the development of concepts in Hilbert space operators.
The Bulletin of Symbolic Logic, 2009
The Princeton Companion to Mathematics combines cultural, philosophical and historical perspectives on mathematics with substantial accounts of current mathematical subject areas. These accounts are written in enough detail to enable a reader with some universitylevel mathematics to obtain a sense of the character and leading problems of each subject area. The volume is divided into seven parts: nature of mathematics (Part I), historical origins (Part II), mathematical concepts, branches and results (Parts III, IV, V), biographies
For those already familiar with the philosophy of Franklin Merrell-Wolff, this essay elucidates the mathematical allusions in his lectures and writings, and helps one to understand why Dr. Wolff regarded pure mathematics as one of the great achievements of the West, with spiritual implications. This paper presumes no knowledge of math on the part of the reader, beyond high-school geometry and algebra.
Historia Mathematica, 1998
Bulletin of The American Mathematical Society, 1981
Entropy 26, 989., 2024
The argument of this article is threefold. First, the article argues that from its rise in the sixteenth century to our own time, the advancement of modern physics as mathematical-experimental science has been defined by the invention of new mathematical structures. Second, the article argues that quantum theory, especially following quantum mechanics, gives this thesis a radically new meaning by virtue of the following two features: on the one hand, quantum phenomena are defined as essentially different from those found in all previous physics by purely physical features; and on the other, quantum mechanics and quantum field theory are defined by purely mathematical postulates, which connect them to quantum phenomena strictly in terms of probabilities, without, as in all previous physics, representing or otherwise relating to how these phenomena physically come about. While these two features may appear discordant, if not inconsistent, I argue that they are in accord with each other, at least in certain interpretations (including the one adopted here), designated as “reality without realism”, RWR, interpretations. This argument also allows this article to offer a new perspective on a thorny problem of the relationships between continuity and discontinuity in quantum physics. In particular, rather than being concerned only with the discreteness and continuity of quantum objects or phenomena, quantum mechanics and quantum field theory relate their continuous mathematics to the irreducibly discrete quantum phenomena in terms of probabilistic predictions while, at least in RWR interpretations, precluding a representation or even conception of how these phenomena come about. This subject is rarely, if ever, discussed apart from previous work by the present author. It is, however, given a new dimension in this article which introduces, as one of its main contributions, a new principle: the mathematical complexity principle.
Annals of Communications in Mathematics, 2025
Annals of Communications in Mathematics, ISSN 2582-0818 (online), is an international journal publishing original scientific papers and invited survey articles from all fields of Pure and Applied Mathematics. Editorial office e-mail: [email protected] Papers submitted to Annals of Communications in Mathematics are screened for plagiarism using Similarity Check / iThenticate plagiarism detection tools. There is no page charge for papers.
Annals of Communications in Mathematics, 2023
Annals of Communications in Mathematics, ISSN 2582-0818 (online), is an international journal publishing original scientific papers and invited survey articles from all fields of Pure and Applied Mathematics. Editorial office e-mail: [email protected] Papers submitted to Annals of Communications in Mathematics are screened for plagiarism using Similarity Check / iThenticate plagiarism detection tools. There is no page charge for papers.
Linear Algebra and its Applications, 1983
This unusual little book, which is intended to serve both as a text and as a reference, is a survey of a broad portion of the theory of linear spaces, with particular attention to the solution of linear equations. The book is in four chapters, entitled "Nontopological linear space theory," "Finite systems of linear algebraic equations and their generaliTations," "Topological linear spaces: some comparisons," and "Current research problems." It differs from other brief books on these subjects in two principle ways. First, the author takes a very broad view, putting into 168 pages the beginnings or the essentials of a wide variety of topics, including the general theory of linear spaces, systems of linear equations, integral operators and integral equations, compact operators, the Fredholm theorems and the theories of Banach spaces, of Hflbert spaces, and of topological vector spaces. Second, the book is built on a very systematic and explicit comparison of the finite and infinite dimensional theories. In much of the book, this comparison is undertaken on a theorem by theorem basis and most results are presented in two different versions, with comments on their differences. Where no reasonable generalization to the infinite dimensional case exists, the book generally provides relevant examples in considerable detail. The author's goal seems to have been that of illuminating a large area of mathematics by means of this systematic comparison. Generalizing a theorem is usually an excellent way of coming to a firm understanding of it, so Professor Jfi_rvinen's approach has much to recommend it. Moreover, this book contains an accessible compilation of a large number of results, from different but related areas, which otherwise would not be easy to find in a single source. Unfortunately, no treatment of so much in so short a space can possibly be complete. Professor Jfi_rvinen is thus obliged to replace most of the proofs by references, and to limit himself largely to supplying a context and to describing the flow of the results in his subjects. This approach poses the danger that the exposition can easily turn into a loosely connected list of definitions and results. On the other hand, it makes for a very clear view of broad outlines, and it places on the reader the burden of supplying or
Springer eBooks, 2016
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
Journal of Symbolic Logic, 1983
I am not the autor, it is a collection of essays edited by Hilary Putnam and Paul Benacerraf. The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.
2014
It surely goes without saying that Charles Parsons is one of the most important philosophers of mathematics in our generation. Through his many publications and his teaching and lecturing, he has spawned and influenced a large body of historically sensitive work in the philosophy of mathematics and an equally large body of philosophically sensitive work in the history of the philosophy of mathematics. This is Parsons' fourth book. It and From Kant to Husserl (Harvard University Press, 2012) collect together most of his essays on other philosophers, with the exception of those essays reprinted in his earlier collection, Mathematics in Philosophy (Ithaca, New York, Cornell University Press, 1983). As indicated by its title, the essays in the present book are on philosophers whose work appeared primarily, or entirely, in the twentieth century. All but one of the essays have been published elsewhere. It is good to have them collected here, for at least two reasons. First, some of the essays appear in collections that are not readily available, including volumes honoring some of the authors discussed, which are sources that are notoriously hard to acquire. Second, and more important, it is interesting and helpful to see similar ideas and themes developed in different contexts. Four of the essays have new postscripts.
Annals of Communications in Mathematics, 2024
Annals of Communications in Mathematics, ISSN 2582-0818 (online), is an international journal publishing original scientific papers and invited survey articles from all fields of Pure and Applied Mathematics. Editorial office e-mail: [email protected] Papers submitted to Annals of Communications in Mathematics are screened for plagiarism using Similarity Check / iThenticate plagiarism detection tools. There is no page charge for papers.
Annals of Communications in Mathematics, 2022
Annals of Communications in Mathematics, ISSN 2582-0818 (online), is an international journal publishing original scientific papers and invited survey articles from all fields of Pure and Applied Mathematics. Editorial office e-mail: [email protected] Papers submitted to Annals of Communications in Mathematics are screened for plagiarism using Similarity Check / iThenticate plagiarism detection tools. There is no page charge for papers.
arXiv: Functional Analysis, 2014
Over the decades, Functional Analysis has been enriched and inspired on account of demands from neighboring fields, within mathematics, harmonic analysis (wavelets and signal processing), numerical analysis (finite element methods, discretization), PDEs (diffusion equations, scattering theory), representation theory; iterated function systems (fractals, Julia sets, chaotic dynamical systems), ergodic theory, operator algebras, and many more. And neighboring areas, probability/statistics (for example stochastic processes, Ito and Malliavin calculus), physics (representation of Lie groups, quantum field theory), and spectral theory for Schr\"odinger operators. We have strived for a more accessible book, and yet aimed squarely at applications; -- we have been serious about motivation: Rather than beginning with the four big theorems in Functional Analysis, our point of departure is an initial choice of topics from applications. And we have aimed for flexibility of use; acknowledgi...
Annals of Communications in Mathematics, 2024
Annals of Communications in Mathematics, ISSN 2582-0818 (online), is an international journal publishing original scientific papers and invited survey articles from all fields of Pure and Applied Mathematics. Editorial office e-mail: [email protected] Papers submitted to Annals of Communications in Mathematics are screened for plagiarism using Similarity Check / iThenticate plagiarism detection tools. There is no page charge for papers.
Annals of Communications in Mathematics, 2024
Annals of Communications in Mathematics, ISSN 2582-0818 (online), is an international journal publishing original scientific papers and invited survey articles from all fields of Pure and Applied Mathematics. Editorial office e-mail: [email protected] Papers submitted to Annals of Communications in Mathematics are screened for plagiarism using Similarity Check / iThenticate plagiarism detection tools. There is no page charge for papers.
Annals of Communications in Mathematics, 2022
Annals of Communications in Mathematics, ISSN 2582-0818 (online), is an international journal publishing original scientific papers and invited survey articles from all fields of Pure and Applied Mathematics. Editorial office e-mail: [email protected] Papers submitted to Annals of Communications in Mathematics are screened for plagiarism using Similarity Check / iThenticate plagiarism detection tools. There is no page charge for papers.
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