Categories for the Working Mathematician PDF Download

Author: Saunders Mac Lane
Publisher: Springer Science & Business Media
ISBN: 1475747217
Category : Mathematics
Languages : en
Pages : 320

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Book Description
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.

Author: George Shoobridge Carr
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages :

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Book Description

Author: Henri Poincaré
Publisher: Cosimo, Inc.
ISBN: 1616402547
Category : Science
Languages : en
Pages : 294

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Book Description
Henri Poincare's Science and Method is an examination of the process scientists go through when determining which of the countless facts before them will be most useful in advancing scientific knowledge. In this highly readable text-first published in 1908 and here presented in a 1914 translation by Francis Maitland-Poincare investigates mathematics, logic, physics, mechanics, and astronomy and discusses how the methods of selection differ with each field. Topics discussed include: [ the selection of facts [ the future of mathematics [ chance [ the relativity of space [ mathematics and logic [ mechanics and radium [ mechanics and optics [ the new mechanics and astronomy [ the Milky Way and the theory of gases [ and much more.

Author: Francis Su
Publisher: Yale University Press
ISBN: 0300237138
Category : Mathematics
Languages : en
Pages : 287

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Book Description
"The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.

Author: Shiing-Shen Chern
Publisher: World Scientific
ISBN: 9789810223854
Category : Mathematics
Languages : en
Pages : 734

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Book Description
This volume is about the life and work of Shiing-Shen Chern (1911-), one of the leading mathematicians of this century. The book contains personal accounts by some friends, together with a summary of the mathematical works by Chern himself. Besides a selection of the mathematical papers the book also contains all his papers published after 1988.

Author: William Dunham
Publisher: American Mathematical Society
ISBN: 147046618X
Category : Mathematics
Languages : en
Pages : 185

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Book Description
Leonhard Euler was one of the most prolific mathematicians that have ever lived. This book examines the huge scope of mathematical areas explored and developed by Euler, which includes number theory, combinatorics, geometry, complex variables and many more. The information known to Euler over 300 years ago is discussed, and many of his advances are reconstructed. Readers will be left in no doubt about the brilliance and pervasive influence of Euler's work.

Author: Cédric Villani
Publisher: Macmillan + ORM
ISBN: 0374710236
Category : Biography & Autobiography
Languages : en
Pages : 260

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Book Description
In 2010, French mathematician Cédric Villani received the Fields Medal, the most coveted prize in mathematics, in recognition of a proof which he devised with his close collaborator Clément Mouhot to explain one of the most surprising theories in classical physics. Birth of aTheorem is Villani's own account of the years leading up to the award. It invites readers inside the mind of a great mathematician as he wrestles with the most important work of his career. But you don't have to understand nonlinear Landau damping to love Birth of aTheorem. It doesn't simplify or overexplain; rather, it invites readers into collaboration. Villani's diaries, emails, and musings enmesh you in the process of discovery. You join him in unproductive lulls and late-night breakthroughs. You're privy to the dining-hall conversations at the world's greatest research institutions. Villani shares his favorite songs, his love of manga, and the imaginative stories he tells his children. In mathematics, as in any creative work, it is the thinker's whole life that propels discovery—and with Birth of aTheorem, Cédric Villani welcomes you into his.

Author: Jordan Ellenberg
Publisher: Penguin Press
ISBN: 1594205221
Category : Mathematics
Languages : en
Pages : 480

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Book Description
A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.

Author: Ptolemy
Publisher: Princeton University Press
ISBN: 0691002606
Category : Science
Languages : en
Pages : 712

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Book Description
Ptolemy's Almagest is one of the most influential scientific works in history. A masterpiece of technical exposition, it was the basic textbook of astronomy for more than a thousand years, and still is the main source for our knowledge of ancient astronomy. This translation, based on the standard Greek text of Heiberg, makes the work accessible to English readers in an intelligible and reliable form. It contains numerous corrections derived from medieval Arabic translations and extensive footnotes that take account of the great progress in understanding the work made in this century, due to the discovery of Babylonian records and other researches. It is designed to stand by itself as an interpretation of the original, but it will also be useful as an aid to reading the Greek text.

Author: Leigh N Wood
Publisher: Springer Science & Business Media
ISBN: 9400729847
Category : Education
Languages : en
Pages : 193

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Book Description
This book considers the views of participants in the process of becoming a mathematician, that is, the students and the graduates. This book investigates the people who carry out mathematics rather than the topics of mathematics. Learning is about change in a person, the development of an identity and ways of interacting with the world. It investigates more generally the development of mathematical scientists for a variety of workplaces, and includes the experiences of those who were not successful in the transition to the workplace as mathematicians. The research presented is based on interviews, observations and surveys of students and graduates as they are finding their identity as a mathematician. The book contains material from the research carried out in South Africa, Northern Ireland, Canada and Brunei as well as Australia.