The Structure Of The Real Line
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The Structure Of The Real Line
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Author : Lev Bukovský
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-02
The Structure Of The Real Line written by Lev Bukovský and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-02 with Mathematics categories.
The rapid development of set theory in the last fifty years, mainly by obtaining plenty of independence results, strongly influenced an understanding of the structure of the real line. This book is devoted to the study of the real line and its subsets taking into account the recent results of set theory. Whenever possible the presentation is done without the full axiom of choice. Since the book is intended to be self-contained, all necessary results of set theory, topology, measure theory, and descriptive set theory are revisited with the purpose of eliminating superfluous use of an axiom of choice. The duality of measure and category is studied in a detailed manner. Several statements pertaining to properties of the real line are shown to be undecidable in set theory. The metamathematics behind set theory is shortly explained in the appendix. Each section contains a series of exercises with additional results.
Set Theory
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Author : Tomek Bartoszynski
language : en
Publisher: A K Peters/CRC Press
Release Date : 1995-08-15
Set Theory written by Tomek Bartoszynski and has been published by A K Peters/CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-08-15 with Mathematics categories.
This research level monograph reflects the current state of the field and provides a reference for graduate students entering the field as well as for established researchers.
Set Theory
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Author : Tomek Bartoszynski
language : en
Publisher: CRC Press
Release Date : 1995-08-15
Set Theory written by Tomek Bartoszynski and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-08-15 with Mathematics categories.
This research level monograph reflects the current state of the field and provides a reference for graduate students entering the field as well as for established researchers.
Rods Sets And Arrows
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Author : Dirk De Bock
language : en
Publisher: Springer Nature
Release Date : 2019-12-10
Rods Sets And Arrows written by Dirk De Bock and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-10 with Education categories.
For anyone interested in the history and effects of the introduction of so-called “Modern Mathematics” (or “Mathématique Moderne,” or “New Mathematics,” etc.) this book, by Dirk De Bock and Geert Vanpaemel, is essential reading. The two authors are experienced and highly qualified Belgian scholars and the book looks carefully at events relating to school mathematics for the period from the end of World War II to 2010. Initially the book focuses on events which helped to define the modern mathematics revolution in Belgium before and during the 1960s. The book does much more than that, however, for it traces the influence of these events on national and international debates during the early phases of the reform. By providing readers with translations into English of relevant sections of key Continental documents outlining the major ideas of leading Continental scholars who contributed to the “Mathématique Moderne” movement, this book makes available to a wide readership, the theoretical, social, and political backdrops of Continental new mathematics reforms. In particular, the book focuses on the contributions made by Belgians such as Paul Libois, Willy Servais, Frédérique Lenger, and Georges Papy. The influence of modern mathematics fell away rapidly in the 1970s, however, and the authors trace the rise and fall, from that time into the 21st century, of a number of other approaches to school mathematics—in Belgium, in other Western European nations, and in North America. In summary, this is an outstanding, landmark publication displaying the fruits of deep scholarship and careful research based on extensive analyses of primary sources.
The Mystery Of The Aleph
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Author : Amir D. Aczel
language : en
Publisher: Simon and Schuster
Release Date : 2001-08-28
The Mystery Of The Aleph written by Amir D. Aczel and has been published by Simon and Schuster this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-28 with Mathematics categories.
A compelling narrative that blends the story of infinity with the tragic tale of a tormented and brilliant mathematician.
Elements Of The Theory Of Functions And Functional Analysis
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Author : Andre? Nikolaevich Kolmogorov
language : en
Publisher: Courier Corporation
Release Date : 1999-01-01
Elements Of The Theory Of Functions And Functional Analysis written by Andre? Nikolaevich Kolmogorov and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-01 with Mathematics categories.
Advanced-level text, now available in a single volume, discusses metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque intervals, Hilbert space, more. Exercises. 1957 edition.
The Foundations Of Mathematics
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Author : Ian Stewart
language : en
Publisher: OUP Oxford
Release Date : 2015-03-12
The Foundations Of Mathematics written by Ian Stewart and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-12 with Mathematics categories.
The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas. This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups. While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward. This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.
Michael Atiyah Collected Works
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Author : Michael Atiyah
language : en
Publisher: Oxford University Press
Release Date : 1988-04-28
Michael Atiyah Collected Works written by Michael Atiyah and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-04-28 with Biography & Autobiography categories.
This is a collection of the works of Michael Atiyah, a well-established mathematician and winner of the Fields Medal. It is thematically divided into volumes; this one discusses gauge theory, a current topic of research.
Structuralism And Structures
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Author : Charles E Rickart
language : en
Publisher: World Scientific
Release Date : 1995-02-20
Structuralism And Structures written by Charles E Rickart and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-02-20 with Mathematics categories.
This book is devoted to an analysis of the way that structures must enter into a serious study of any subject, and the term “structuralism” refers to the general method of approaching a subject from the viewpoint of structure. A proper appreciation of this approach requires a deeper understanding of the concept of structure than is provided by the simple intuitive notion of structures that everyone posseses to some degree. Therefore, a large part of the discussion is devoted directly or indirectly to a study of the nature of structures themselves. A formal definition of a structure, plus some basic general properties and examples, is given early in the discussion. Also, in order to clarify the general notions and to see how they are used, the later chapters are devoted to an examination of how structures enter into some special fields, including linguistics, mental phenomena, mathematics (and its applications), and biology (especially in the theory of evolution). Because the author is a mathematician, certain mathematical ideas have influenced greatly the choice and approach to the material covered. In general, however, the mathematical influence is not on a technical level and is often only implicit. Even the chapter on mathematical structures is nontechnical and is about rather than on mathematics. Only in the last chapter and earlier in three short sections does one find any of the expected “formal” mathematics. In other words, the great bulk of the material is accessible to someone without a mathematical background.
Time And Space
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Author : Barry Dainton
language : en
Publisher: Routledge
Release Date : 2016-04-15
Time And Space written by Barry Dainton and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-15 with Philosophy categories.
The first edition (2001) of this title quickly established itself on courses on the philosophy of time and space. This fully revised and expanded new edition sees the addition of chapters on Zeno's paradoxes, speculative contemporary developments in physics, and dynamic time, making the second edition, once again, unrivalled in its breadth of coverage. Surveying both historical debates and the ideas of modern physics, Barry Dainton evaluates the central arguments in a clear and unintimidating way and is careful to keep the conceptual issues throughout comprehensible to students with little scientific or mathematical training. The book makes the philosophy of space and time accessible for anyone trying to come to grips with the complexities of this challenging subject. With over 100 original line illustrations and a full glossary of terms, the book has the requirements of students firmly in sight and will continue to serve as an essential textbook for philosophy of time and space courses.