Review Of Saunders Maclane S Mathematics Form And Function
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Mathematics Form And Function
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Author : Saunders MacLane
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematics Form And Function written by Saunders MacLane 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 2012-12-06 with Mathematics categories.
This book records my efforts over the past four years to capture in words a description of the form and function of Mathematics, as a background for the Philosophy of Mathematics. My efforts have been encouraged by lec tures that I have given at Heidelberg under the auspices of the Alexander von Humboldt Stiftung, at the University of Chicago, and at the University of Minnesota, the latter under the auspices of the Institute for Mathematics and Its Applications. Jean Benabou has carefully read the entire manuscript and has offered incisive comments. George Glauberman, Car los Kenig, Christopher Mulvey, R. Narasimhan, and Dieter Puppe have provided similar comments on chosen chapters. Fred Linton has pointed out places requiring a more exact choice of wording. Many conversations with George Mackey have given me important insights on the nature of Mathematics. I have had similar help from Alfred Aeppli, John Gray, Jay Goldman, Peter Johnstone, Bill Lawvere, and Roger Lyndon. Over the years, I have profited from discussions of general issues with my colleagues Felix Browder and Melvin Rothenberg. Ideas from Tammo Tom Dieck, Albrecht Dold, Richard Lashof, and Ib Madsen have assisted in my study of geometry. Jerry Bona and B.L. Foster have helped with my examina tion of mechanics. My observations about logic have been subject to con structive scrutiny by Gert Miiller, Marian Boykan Pour-El, Ted Slaman, R. Voreadou, Volker Weispfennig, and Hugh Woodin.
Review Of Saunders Maclane S Mathematics Form And Function
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Author : H. A. Pogorzelski
language : en
Publisher:
Release Date : 2010
Review Of Saunders Maclane S Mathematics Form And Function written by H. A. Pogorzelski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Arithmetic categories.
Algebra
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Author : Saunders Mac Lane
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Algebra written by Saunders Mac Lane and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Algebra categories.
Presents modern algebra from first principles. This title combines standard materials and necessary algebraic manipulations with general concepts that clarify meaning and importance. It presents a conceptual approach to algebra that starts with a description of algebraic structures by means of axioms chosen to suit the examples.
Categories For The Working Mathematician
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Author : Saunders Mac Lane
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Categories For The Working Mathematician written by Saunders Mac Lane 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 2013-04-17 with Mathematics categories.
An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.
Algebra
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Author : Saunders Mac Lane
language : en
Publisher: American Mathematical Society
Release Date : 2023-10-10
Algebra written by Saunders Mac Lane and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-10 with Mathematics categories.
This book presents modern algebra from first principles and is accessible to undergraduates or graduates. It combines standard materials and necessary algebraic manipulations with general concepts that clarify meaning and importance. This conceptual approach to algebra starts with a description of algebraic structures by means of axioms chosen to suit the examples, for instance, axioms for groups, rings, fields, lattices, and vector spaces. This axiomatic approach—emphasized by Hilbert and developed in Germany by Noether, Artin, Van der Waerden, et al., in the 1920s—was popularized for the graduate level in the 1940s and 1950s to some degree by the authors' publication of A Survey of Modern Algebra. The present book presents the developments from that time to the first printing of this book. This third edition includes corrections made by the authors.
Foundations Of Mathematics
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Author : Andrés Eduardo Caicedo
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-05-12
Foundations Of Mathematics written by Andrés Eduardo Caicedo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-12 with Continuum hypothesis categories.
This volume contains the proceedings of the Logic at Harvard conference in honor of W. Hugh Woodin's 60th birthday, held March 27–29, 2015, at Harvard University. It presents a collection of papers related to the work of Woodin, who has been one of the leading figures in set theory since the early 1980s. The topics cover many of the areas central to Woodin's work, including large cardinals, determinacy, descriptive set theory and the continuum problem, as well as connections between set theory and Banach spaces, recursion theory, and philosophy, each reflecting a period of Woodin's career. Other topics covered are forcing axioms, inner model theory, the partition calculus, and the theory of ultrafilters. This volume should make a suitable introduction to Woodin's work and the concerns which motivate it. The papers should be of interest to graduate students and researchers in both mathematics and philosophy of mathematics, particularly in set theory, foundations and related areas.
Vita Mathematica
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Author : Ronald Calinger
language : en
Publisher: Cambridge University Press
Release Date : 1996
Vita Mathematica written by Ronald Calinger and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
Enables teachers to learn the history of mathematics and then incorporate it in undergraduate teaching.
Saunders Mac Lane
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Author : Saunders Mac Lane
language : en
Publisher: CRC Press
Release Date : 2005-05-25
Saunders Mac Lane written by Saunders Mac Lane and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-25 with Mathematics categories.
Saunders Mac Lane was an extraordinary mathematician, a dedicated teacher, and a good citizen who cared deeply about the values of science and education. In his autobiography, he gives us a glimpse of his "life and times," mixing the highly personal with professional observations. His recollections bring to life a century of extraordinary accomplis
Women In The History Of Analytic Philosophy
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Author : Jeanne Peijnenburg
language : en
Publisher: Springer Nature
Release Date : 2023-01-01
Women In The History Of Analytic Philosophy written by Jeanne Peijnenburg and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Philosophy categories.
This book contains a selection of papers from the workshop Women in the History of Analytic Philosophy held in October 2019 in Tilburg, the Netherlands. It is the first volume devoted to the role of women in early analytic philosophy. It discusses the ideas of ten female philosophers and covers a period of over a hundred years, beginning with the contribution to the Significs Movement by Victoria, Lady Welby in the second half of the nineteenth century, and ending with Ruth Barcan Marcus’s celebrated version of quantified modal logic after the Second World War. The book makes clear that women contributed substantially to the development of analytic philosophy in all areas of philosophy, from logic, epistemology, and philosophy of science, to ethics, metaphysics, and philosophy of language. It illustrates that although women's voices were no different from men's as regards their scope and versatility, they had a much harder time being heard. The book is aimed at historians of philosophy and scholars in gender studies
Categories For The Working Mathematician
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Author : Saunders Mac Lane
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-09-25
Categories For The Working Mathematician written by Saunders Mac Lane 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 1998-09-25 with Mathematics categories.
Categories for the Working Mathematician provides an array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. The book then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterized by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including two new chapters on topics of active interest. One is on symmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into prominence. The bibliography has also been expanded to cover some of the many other recent advances concerning categories.