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Author : Errett Bishop,Henry Cheng
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 50,5 Mb
Release : 1972
Category : Constructive mathematics
ISBN : 9780821818169
Author : Vladimir I. Bogachev
Publisher : Springer Science & Business Media
Page : 1075 pages
File Size : 45,6 Mb
Release : 2007-01-15
Category : Mathematics
ISBN : 9783540345145
This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.
Author : Yuen-Kwok Chan
Publisher : Cambridge University Press
Page : 627 pages
File Size : 46,9 Mb
Release : 2021-05-27
Category : Mathematics
ISBN : 9781108835435
This book provides a systematic and general theory of probability within the framework of constructive mathematics.
Author : S. Barry Cooper
Publisher : Springer Science & Business Media
Page : 842 pages
File Size : 54,8 Mb
Release : 2007-06-11
Category : Computers
ISBN : 9783540730002
This book constitutes the refereed proceedings of the Third International Conference on Computability in Europe, CiE 2007, held in Sienna, Italy, in June 2007. The 50 revised full papers presented together with 36 invited papers were carefully reviewed and selected from 167 submissions.
Author : M.J. Beeson
Publisher : Springer Science & Business Media
Page : 484 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642689529
This book is about some recent work in a subject usually considered part of "logic" and the" foundations of mathematics", but also having close connec tions with philosophy and computer science. Namely, the creation and study of "formal systems for constructive mathematics". The general organization of the book is described in the" User's Manual" which follows this introduction, and the contents of the book are described in more detail in the introductions to Part One, Part Two, Part Three, and Part Four. This introduction has a different purpose; it is intended to provide the reader with a general view of the subject. This requires, to begin with, an elucidation of both the concepts mentioned in the phrase, "formal systems for constructive mathematics". "Con structive mathematics" refers to mathematics in which, when you prove that l a thing exists (having certain desired properties) you show how to find it. Proof by contradiction is the most common way of proving something exists without showing how to find it - one assumes that nothing exists with the desired properties, and derives a contradiction. It was only in the last two decades of the nineteenth century that mathematicians began to exploit this method of proof in ways that nobody had previously done; that was partly made possible by the creation and development of set theory by Georg Cantor and Richard Dedekind.
Author : Johanna N. Y. Franklin,Christopher P. Porter
Publisher : Cambridge University Press
Page : 370 pages
File Size : 48,9 Mb
Release : 2020-05-07
Category : Computers
ISBN : 9781108478984
Surveys on recent developments in the theory of algorithmic randomness and its interactions with other areas of mathematics.
Author : Errett Bishop
Publisher : Ishi Press
Page : 404 pages
File Size : 41,6 Mb
Release : 2012-07
Category : Mathematics
ISBN : 4871877140
This book, Foundations of Constructive Analysis, founded the field of constructive analysis because it proved most of the important theorems in real analysis by constructive methods. The author, Errett Albert Bishop, born July 10, 1928, was an American mathematician known for his work on analysis. In the later part of his life Bishop was seen as the leading mathematician in the area of Constructive mathematics. From 1965 until his death, he was professor at the University of California at San Diego.
Author : Gregory J. Chaitin
Publisher : World Scientific
Page : 332 pages
File Size : 47,6 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 9810201710
This book contains in easily accessible form all the main ideas of the creator and principal architect of algorithmic information theory. This expanded second edition has added thirteen abstracts, a 1988 Scientific American Article, a transcript of a EUROPALIA 89 lecture, an essay on biology, and an extensive bibliography. Its new larger format makes it easier to read. Chaitin's ideas are a fundamental extension of those of Gdel and Turning and have exploded some basic assumptions of mathematics and thrown new light on the scientific method, epistemology, probability theory, and of course computer science and information theory.
Author : Douglas Bridges,Hajime Ishihara,Michael Rathjen,Helmut Schwichtenberg
Publisher : Cambridge University Press
Page : 864 pages
File Size : 48,8 Mb
Release : 2023-03-31
Category : Mathematics
ISBN : 9781009041416
Constructive mathematics – mathematics in which 'there exists' always means 'we can construct' – is enjoying a renaissance. fifty years on from Bishop's groundbreaking account of constructive analysis, constructive mathematics has spread out to touch almost all areas of mathematics and to have profound influence in theoretical computer science. This handbook gives the most complete overview of modern constructive mathematics, with contributions from leading specialists surveying the subject's myriad aspects. Major themes include: constructive algebra and geometry, constructive analysis, constructive topology, constructive logic and foundations of mathematics, and computational aspects of constructive mathematics. A series of introductory chapters provides graduate students and other newcomers to the subject with foundations for the surveys that follow. Edited by four of the most eminent experts in the field, this is an indispensable reference for constructive mathematicians and a fascinating vista of modern constructivism for the increasing number of researchers interested in constructive approaches.
Author : Sheldon Axler
Publisher : Springer Nature
Page : 430 pages
File Size : 49,7 Mb
Release : 2019-11-29
Category : Mathematics
ISBN : 9783030331436
This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online. For errata and updates, visit https://measure.axler.net/
Author : Jess Drake
Publisher : Scientific e-Resources
Page : 324 pages
File Size : 44,6 Mb
Release : 2018-05-30
Category : Electronic
ISBN : 9781839474217
Logic originally meaning "e;the word"e; or "e;what is spoken"e; is generally held to consist of the systematic study of the form of arguments. A valid argument is one where there is a specific relation of logical support between the assumptions of the argument and its conclusion. There is no universal agreement as to the exact scope and subject matter of logic, but it has traditionally included the classification of arguments, the systematic exposition of the 'logical form' common to all valid arguments, the study of inference, including fallacies, and the study of semantics, including paradoxes. Historically, logic has been studied in philosophy and mathematics and recently logic has been studied in computer science, linguistics, psychology, and other fields. The book is about the logic and talks about various aspects of it such as general character of the enquiry, argument from analogy, mathematical reasoning, etc. This book will prove to be very useful for the people interested in logic as well as the students of logic.
Author : Giandomenico Sica
Publisher : Polimetrica s.a.s.
Page : 122 pages
File Size : 53,8 Mb
Release : 2005
Category : Mathematics
ISBN : 9788876990212
Author : W. Scheppach,M. Scheurlen
Publisher : Springer Science & Business Media
Page : 698 pages
File Size : 43,9 Mb
Release : 2003-01-31
Category : Medical
ISBN : 0792387805
This book is the proceedings of Falk Symposium 128, held in Würzburg, Germany, on May 2-3, 2002, and dedicated to the important issue of colonic carcinogenesis and its underlying genetic and environmental factors. Colorectal cancer is one of the leading causes of cancer-related death in industrialized countries. It has been recognized to be the consequence of a dynamic process leading from hyperproliferative epithelium through different classes of adenomas to invasive carcinoma. This adenoma-carcinoma sequence has been characterized on a molecular basis. Modern molecular biology has also helped to clarify the clustering of colorectal cancer within families, a phenomenon that has been known to clinicians for a long time. Thus, the pathogenesis of the two distinct familial colon cancer syndromes FAP (familial adenomatous polyposis) and HNPCC (hereditary non-polyposis colorectal cancer) is increasingly being understood. Thereby, an identification of affected people has become possible before the disease has manifested. There is also convincing evidence that the pathogenesis of sporadic colonic cancer is modulated by environmental, mainly nutritional, factors. Carcinogens seem to be far less important than the components of the `normal' human diet. It is likely that the interplay between protective and noxious dietary compounds determines the progression of the adenoma-carcinoma sequence. Additionally, a broad spectrum of drugs has been shown to affect colonic tumorigenesis, which provides the rationale for chemoprevention strategies. These issues set the scene for discussions on how genetic and environmental factors may interact in the pathogenesis of colonic cancer, contributing fresh ideas to the prevention of this most prevalent malignancy in the industrialized world.
Author : G. E. Shilov,B. L. Gurevich
Publisher : Courier Corporation
Page : 258 pages
File Size : 43,6 Mb
Release : 2013-05-13
Category : Mathematics
ISBN : 9780486165615
This treatment examines the general theory of the integral, Lebesque integral in n-space, the Riemann-Stieltjes integral, and more. "The exposition is fresh and sophisticated, and will engage the interest of accomplished mathematicians." — Sci-Tech Book News. 1966 edition.
Author : Lev D. Beklemishev
Publisher : Elsevier
Page : 416 pages
File Size : 44,9 Mb
Release : 2000-04-01
Category : Mathematics
ISBN : 0080955029
Provability, Computability and Reflection