The Foundations Of Mathematics
DOWNLOAD
Download The Foundations Of Mathematics PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Foundations Of Mathematics book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
The Foundations Of Mathematics
DOWNLOAD
Author : Ian Stewart
language : en
Publisher: Oxford University Press, USA
Release Date : 2015
The Foundations Of Mathematics written by Ian Stewart and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 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.
The Foundations Of Mathematics
DOWNLOAD
Author : Thomas Q. Sibley
language : en
Publisher: John Wiley & Sons
Release Date : 2008-04-07
The Foundations Of Mathematics written by Thomas Q. Sibley and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-07 with Mathematics categories.
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
Introduction To The Foundations Of Mathematics
DOWNLOAD
Author : Raymond L. Wilder
language : en
Publisher: Courier Corporation
Release Date : 2013-09-26
Introduction To The Foundations Of Mathematics written by Raymond L. Wilder and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-26 with Mathematics categories.
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.
Essays On The Foundations Of Mathematics And Logic
DOWNLOAD
Author : Giandomenico Sica
language : en
Publisher: Polimetrica s.a.s.
Release Date : 2005
Essays On The Foundations Of Mathematics And Logic written by Giandomenico Sica and has been published by Polimetrica s.a.s. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
The Foundations Of Mathematics
DOWNLOAD
Author : Paul Carus
language : en
Publisher: Cosimo, Inc.
Release Date : 2004-01-01
The Foundations Of Mathematics written by Paul Carus and has been published by Cosimo, Inc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Mathematics categories.
In this brief treatise, Carus traces the roots of his belief in the philosophical basis for mathematics and analyzes that basis after a historical overview of Euclid and his successors. He then examines his base argument and proceeds to a study of different geometrical systems, all pulled together in his epilogue, which examines matter, mathematics, and, ultimately, the nature of God.
The Foundations Of Mathematics Updated Edition
DOWNLOAD
Author : Michael Bradley
language : en
Publisher: Infobase Holdings, Inc
Release Date : 2019-11-01
The Foundations Of Mathematics Updated Edition written by Michael Bradley and has been published by Infobase Holdings, Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-01 with Mathematics categories.
Praise for the previous edition: “…ample information for reports.”—School Library Journal During the 16th and 17th centuries, mathematicians developed a wealth of new ideas but had not carefully employed accurate definitions, proofs, or procedures to document and implement them. However, in the early 19th century, mathematicians began to recognize the need to precisely define their terms, to logically prove even obvious principles, and to use rigorous methods of manipulation. The Foundations of Mathematics, Updated Edition presents the lives and accomplishments of 10 mathematicians who contributed to one or more of the four major initiatives that characterized the rapid growth of mathematics during the 19th century: the introduction of rigor, the investigation of the structure of mathematical systems, the development of new branches of mathematics, and the spread of mathematical activity throughout Europe. This updated edition communicates the importance and impact of the work of the pioneers who redefined this area of study. Each unit contains information on the person's research, discoveries, and contributions to the field and concludes with a list of print and Internet references specific to that individual.
The Foundations Of Mathematics
DOWNLOAD
Author : Michael J. Bradley
language : en
Publisher: Infobase Publishing
Release Date : 2006
The Foundations Of Mathematics written by Michael J. Bradley and has been published by Infobase Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Juvenile Nonfiction categories.
During the 16th and 17th centuries, mathematicians developed a wealth of new ideas but had not carefully employed accurate definitions, proofs, or procedures to document and implement them. However, in the early 19th century, mathematicians began to recognize the need to precisely define their terms, to logically prove even obvious principles, and to use rigorous methods of manipulation. The Foundations of Mathematics presents the lives and accomplishments of 10 mathematicians who lived between CE 1800 and 1900 and contributed to one or more of the four major initiatives that characterized the rapid growth of mathematics during the 19th century: the introduction of rigor, the investigation of the structure of mathematical systems, the development of new branches of mathematics, and the spread of mathematical activity throughout Europe. This readable new volume communicates the importance and impact of the work of the pioneers who redefined this area of study.
Wittgenstein S Lectures On The Foundations Of Mathematics Cambridge 1939
DOWNLOAD
Author : Ludwig Wittgenstein
language : en
Publisher:
Release Date : 1976
Wittgenstein S Lectures On The Foundations Of Mathematics Cambridge 1939 written by Ludwig Wittgenstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
Foundations Of Mathematics And Other Logical Essays
DOWNLOAD
Author : Frank Plumpton Ramsey
language : en
Publisher: Routledge
Release Date : 2013-10-15
Foundations Of Mathematics And Other Logical Essays written by Frank Plumpton Ramsey and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-15 with Philosophy categories.
This is Volume V in a series of eight on the Philosophy of Logic and Mathematics. Originally published in 1931, this study offers a collection of logical essays around the topic of the foundations of mathematics. Though mathematical teaching was Ramsey's profession, philosophy was his vocation. Reared on the logic of Principia Mathematica, he was early to see the importance of Dr. Wittgenstein's work (in the translation of which he assisted); and his own published papers were largely based on this. But the previously unprinted essays and notes collected in this volume show him moving towards a kind of pragmatism, and the general treatise on logic upon which at various times he had been engaged was to have treated truth and knowledge as purely natural phenomena to be explained psychologically without recourse to distinctively logical relations.
Reflections On The Foundations Of Mathematics
DOWNLOAD
Author : Stefania Centrone
language : en
Publisher: Springer Nature
Release Date : 2019-11-11
Reflections On The Foundations Of Mathematics written by Stefania Centrone and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-11 with Mathematics categories.
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.