Download Full eBooks in PDF
Conceptions Of Set And The Foundations Of Mathematics Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Conceptions Of Set And The Foundations Of Mathematics book. This book definitely worth reading, it is an incredibly well-written.
Author : Luca Incurvati
Publisher : Cambridge University Press
Page : 255 pages
File Size : 47,7 Mb
Release : 2020-01-23
Category : History
ISBN : 9781108497824
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Author : John P. Mayberry
Publisher : Cambridge University Press
Page : 454 pages
File Size : 40,9 Mb
Release : 2000
Category : Mathematics
ISBN : 0521770343
This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.
Author : A.A. Fraenkel,Y. Bar-Hillel,A. Levy
Publisher : Elsevier
Page : 415 pages
File Size : 45,8 Mb
Release : 1973-12-01
Category : Computers
ISBN : 9780080887050
Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of the antinomies that led to the reconstruction of set theory as it was known before. It then moves to the axiomatic foundations of set theory, including a discussion of the basic notions of equality and extensionality and axioms of comprehension and infinity. The next chapters discuss type-theoretical approaches, including the ideal calculus, the theory of types, and Quine's mathematical logic and new foundations; intuitionistic conceptions of mathematics and its constructive character; and metamathematical and semantical approaches, such as the Hilbert program. This book will be of interest to mathematicians, logicians, and statisticians.
Author : Thomas Q. Sibley
Publisher : John Wiley & Sons
Page : 817 pages
File Size : 45,5 Mb
Release : 2008-04-07
Category : Mathematics
ISBN : 9780470085011
The Foundations of Mathematics provides a careful introduction to proofs in mathematics, along with basic concepts of logic, set theory and other broadly used areas of mathematics. The concepts are introduced in a pedagogically effective manner without compromising mathematical accuracy and completeness. Thus, in Part I students explore concepts before they use them in proofs. The exercises range from reading comprehension questions and many standard exercises to proving more challenging statements, formulating conjectures and critiquing a variety of false and questionable proofs. The discussion of metamathematics, including Gödel’s Theorems, and philosophy of mathematics provides an unusual and valuable addition compared to other similar texts
Author : Abraham Adolf Fraenkel
Publisher : Unknown
Page : 297 pages
File Size : 50,9 Mb
Release : 1968
Category : Electronic
ISBN : OCLC:803151895
Author : Howard Eves
Publisher : Courier Corporation
Page : 370 pages
File Size : 49,9 Mb
Release : 2012-04-10
Category : Mathematics
ISBN : 9780486132204
Third edition of popular undergraduate-level text offers historic overview, readable treatment of mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, sets, more. Problems, some with solutions. Bibliography.
Author : Joel David Hamkins
Publisher : MIT Press
Page : 350 pages
File Size : 55,5 Mb
Release : 2021-03-09
Category : Mathematics
ISBN : 9780262542234
An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.
Author : Ian Stewart,David Orme Tall
Publisher : Oxford University Press, USA
Page : 409 pages
File Size : 50,9 Mb
Release : 2015
Category : Mathematics
ISBN : 9780198706434
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.
Author : Alfred North Whitehead,Bertrand Russell
Publisher : Cambridge University Press
Page : 524 pages
File Size : 53,9 Mb
Release : 1927
Category : Mathematics
ISBN : 052106791X
The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.
Author : Garret Sobczyk
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 52,7 Mb
Release : 2012-10-26
Category : Mathematics
ISBN : 9780817683856
The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.
Author : Sean Morris
Publisher : Cambridge University Press
Page : 221 pages
File Size : 53,6 Mb
Release : 2018-12-13
Category : History
ISBN : 9781107152502
Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.
Author : Robert R. Stoll
Publisher : Courier Corporation
Page : 512 pages
File Size : 45,6 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486139647
Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.
Author : Raymond L. Wilder
Publisher : Courier Corporation
Page : 352 pages
File Size : 45,6 Mb
Release : 2013-09-26
Category : Mathematics
ISBN : 9780486276205
Classic undergraduate text acquaints students with fundamental concepts and methods of mathematics. Topics include axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and much more. 1965 second edition.
Author : Kenneth Kunen
Publisher : Unknown
Page : 251 pages
File Size : 52,7 Mb
Release : 2009
Category : Mathematics
ISBN : 1904987141
Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.
Author : Stefania Centrone,Deborah Kant,Deniz Sarikaya
Publisher : Springer Nature
Page : 511 pages
File Size : 53,7 Mb
Release : 2019-11-11
Category : Mathematics
ISBN : 9783030156558
This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The volume is divided into three sections, the first two of which focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, which has widely been assumed to serve as a framework for foundational issues, as well as new material elaborating on the univalent foundations, considering an approach based on homotopy type theory (HoTT). The third section then builds on this and is centred on philosophical questions connected to the foundations of mathematics. Here, the authors contribute to discussions on foundational criteria with more general thoughts on the foundations of mathematics which are not connected to particular theories. This book shares the work of some of the most important scholars in the fields of set theory (S. Friedman), non-classical logic (G. Priest) and the philosophy of mathematics (P. Maddy). The reader will become aware of the advantages of each theory and objections to it as a foundation, following the latest and best work across the disciplines and it is therefore a valuable read for anyone working on the foundations of mathematics or in the philosophy of mathematics.
