Duality In 19th And 20th Century Mathematical Thinking
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Duality In 19th And 20th Century Mathematical Thinking
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Author : Ralf Krömer
language : en
Publisher: Springer Nature
Release Date : 2024-07-01
Duality In 19th And 20th Century Mathematical Thinking written by Ralf Krömer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-01 with Mathematics categories.
This volume brings together scholars across various domains of the history and philosophy of mathematics, investigating duality as a multi-faceted phenomenon. Encompassing both systematic analysis and historical examination, the book endeavors to elucidate the status, roles, and dynamics of duality within the realms of 19th and 20th-century mathematics. Eschewing a priori notions, the contributors embrace the diverse interpretations and manifestations of duality, thus presenting a nuanced and comprehensive perspective on this intricate subject. Spanning a broad spectrum of mathematical topics and historical periods, the book uses detailed case studies to investigate the different forms in which duality appeared and still appears in mathematics, to study their respective histories, and to analyze interactions between the different forms of duality. The chapters inquire into questions such as the contextual occurrences of duality in mathematics, the influence of chosen forms of representation, the impact of investigations of duality on mathematical practices, and the historical interconnections among various instances of duality. Together, they aim to answer a core question: Is there such a thing as duality in mathematics, or are there just several things called by the same name and similar in some respect? What emerges is that duality can be considered as a basic structure of mathematical thinking, thereby opening new horizons for the research on the history and the philosophy of mathematics and the reflection on mathematics in general. The volume will appeal not only to experts in the discipline but also to advanced students of mathematics, history, and philosophy intrigued by the complexities of this captivating subject matter.
Research In History And Philosophy Of Mathematics
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Author : Maria Zack
language : en
Publisher: Springer Nature
Release Date : 2024-01-18
Research In History And Philosophy Of Mathematics written by Maria Zack and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-18 with Mathematics categories.
This volume contains 8 papers that have been collected by the Canadian Society for History and Philosophy of Mathematics. It showcases rigorously reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics.Some of the topics explored include: A way to rethink how logic is taught to philosophy students by using a rejuvenated version of the Aristotelian idea of an argument schema A quantitative approach using data from Wikipedia to study collaboration between nineteenth-century British mathematicians The depiction and perception of Émilie Du Châtelet’s scientific contributions as viewed through the frontispieces designed for books written by or connected to her A study of the Cambridge Women’s Research Club, a place where British women were able to participate in scholarly scientific discourse in the middle of the twentieth century An examination of the research and writing process of mathematicians by looking at their drafts and other preparatory notes A global history of al-Khwārāzmī’s Kitāb al-jabr wa-l-muqābala as obtained by tracing its reception through numerous translations and commentaries Written by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.
Handbook Of The History And Philosophy Of Mathematical Practice
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Author : Bharath Sriraman
language : en
Publisher: Springer Nature
Release Date : 2024-04-26
Handbook Of The History And Philosophy Of Mathematical Practice written by Bharath Sriraman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-26 with Mathematics categories.
The purpose of this unique handbook is to examine the transformation of the philosophy of mathematics from its origins in the history of mathematical practice to the present. It aims to synthesize what is known and what has unfolded so far, as well as to explore directions in which the study of the philosophy of mathematics, as evident in increasingly diverse mathematical practices, is headed. Each section offers insights into the origins, debates, methodologies, and newer perspectives that characterize the discipline today. Contributions are written by scholars from mathematics, history, and philosophy – as well as other disciplines that have contributed to the richness of perspectives abundant in the study of philosophy today – who describe various mathematical practices throughout different time periods and contrast them with the development of philosophy. Editorial Advisory Board Andrew Aberdein, Florida Institute ofTechnology, USA Jody Azzouni, Tufts University, USA Otávio Bueno, University of Miami, USA William Byers, Concordia University, Canada Carlo Cellucci, Sapienza University of Rome, Italy Chandler Davis, University of Toronto, Canada (1926-2022) Paul Ernest, University of Exeter, UK Michele Friend, George Washington University, USA Reuben Hersh, University of New Mexico, USA (1927-2020) Kyeong-Hwa Lee, Seoul National University, South Korea Yuri Manin, Max Planck Institute for Mathematics, Germany (1937-2023) Athanase Papadopoulos, University of Strasbourg, France Ulf Persson, Chalmers University of Technology, Sweden John Stillwell, University of San Francisco, USA David Tall, University of Warwick, UK (1941-2024) This book with its exciting depth and breadth, illuminates us about the history, practice, and the very language of our subject; about the role of abstraction, ofproof and manners of proof; about the interplay of fundamental intuitions; about algebraic thought in contrast to geometric thought. The richness of mathematics and the philosophy encompassing it is splendidly exhibited over the wide range of time these volumes cover---from deep platonic and neoplatonic influences to the most current experimental approaches. Enriched, as well, with vivid biographies and brilliant personal essays written by (and about) people who play an important role in our tradition, this extraordinary collection of essays is fittingly dedicated to the memory of Chandler Davis, Reuben Hersh, and Yuri Manin. ---Barry Mazur, Gerhard Gade University Professor, Harvard University This encyclopedic Handbook will be a treat for all those interested in the history and philosophy of mathematics. Whether one is interested in individuals (from Pythagoras through Newton and Leibniz to Grothendieck), fields (geometry, algebra, number theory, logic, probability, analysis), viewpoints (from Platonism to Intuitionism), or methods (proof, experiment, computer assistance), the reader will find a multitude of chapters that inform and fascinate. ---John Stillwell, Emeritus Professor of Mathematics, University of San Francisco; Recipient of the 2005 Chauvenet Prize Dedicating a volume to the memory of three mathematicians – Chandler Davis, Reuben Hersh, and Yuri Manin –, who went out of their way to show to a broader audience that mathematics is more than what they might think, is an excellent initiative. Gathering authors coming from many different backgrounds but who are very strict about the essays they write was successfully achieved by the editor-in-chief. The result: a great source of potential inspiration! ---Jean-Pierre Bourguignon; Nicolaas Kuiper Honorary Professor at the Institut des Hautes Études Scientifiques
Framing Global Mathematics
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Author : Norbert Schappacher
language : en
Publisher: Springer Nature
Release Date : 2022-06-15
Framing Global Mathematics written by Norbert Schappacher and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-15 with Mathematics categories.
This open access book is about the shaping of international relations in mathematics over the last two hundred years. It focusses on institutions and organizations that were created to frame the international dimension of mathematical research. Today, striking evidence of globalized mathematics is provided by countless international meetings and the worldwide repository ArXiv. The text follows the sinuous path that was taken to reach this state, from the long nineteenth century, through the two wars, to the present day. International cooperation in mathematics was well established by 1900, centered in Europe. The first International Mathematical Union, IMU, founded in 1920 and disbanded in 1932, reflected above all the trauma of WW I. Since 1950 the current IMU has played an increasing role in defining mathematical excellence, as is shown both in the historical narrative and by analyzing data about the International Congresses of Mathematicians. For each of the three periods discussed, interactions are explored between world politics, the advancement of scientific infrastructures, and the inner evolution of mathematics. Readers will thus take a new look at the place of mathematics in world culture, and how international organizations can make a difference. Aimed at mathematicians, historians of science, scientists, and the scientifically inclined general public, the book will be valuable to anyone interested in the history of science on an international level.
Monoidal Category Theory
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Author : Noson S. Yanofsky
language : en
Publisher: MIT Press
Release Date : 2024-11-05
Monoidal Category Theory written by Noson S. Yanofsky and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-05 with Computers categories.
A comprehensive, cutting-edge, and highly readable textbook that makes category theory and monoidal category theory accessible to students across the sciences. Category theory is a powerful framework that began in mathematics but has since expanded to encompass several areas of computing and science, with broad applications in many fields. In this comprehensive text, Noson Yanofsky makes category theory accessible to those without a background in advanced mathematics. Monoidal Category Theorydemonstrates the expansive uses of categories, and in particular monoidal categories, throughout the sciences. The textbook starts from the basics of category theory and progresses to cutting edge research. Each idea is defined in simple terms and then brought alive by many real-world examples before progressing to theorems and uncomplicated proofs. Richly guided exercises ground readers in concrete computation and application. The result is a highly readable and engaging textbook that will open the world of category theory to many. Makes category theory accessible to non-math majors Uses easy-to-understand language and emphasizes diagrams over equations Incremental, iterative approach eases students into advanced concepts A series of embedded mini-courses cover such popular topics as quantum computing, categorical logic, self-referential paradoxes, databases and scheduling, and knot theory Extensive exercises and examples demonstrate the broad range of applications of categorical structures Modular structure allows instructors to fit text to the needs of different courses Instructor resources include slides
Arithmetic Duality Theorems
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Author : J. S. Milne
language : en
Publisher:
Release Date : 1986
Arithmetic Duality Theorems written by J. S. Milne and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry. The text covers these theorems in Galois cohomology, ,tale cohomology, and flat cohomology and addresses applications in the above areas. The writing is expository and the book will serve as an invaluable reference text as well as an excellent introduction to the subject.
Reader S Guide To The History Of Science
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Author : Arne Hessenbruch
language : en
Publisher: Routledge
Release Date : 2013-12-16
Reader S Guide To The History Of Science written by Arne Hessenbruch and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-16 with History categories.
The Reader's Guide to the History of Science looks at the literature of science in some 550 entries on individuals (Einstein), institutions and disciplines (Mathematics), general themes (Romantic Science) and central concepts (Paradigm and Fact). The history of science is construed widely to include the history of medicine and technology as is reflected in the range of disciplines from which the international team of 200 contributors are drawn.
Love And Math
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Author : Edward Frenkel
language : en
Publisher: Basic Books
Release Date : 2013-10-01
Love And Math written by Edward Frenkel and has been published by Basic Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-01 with Mathematics categories.
An awesome, globe-spanning, and New York Times bestselling journey through the beauty and power of mathematics What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren't even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we've never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space. Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man's journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century's leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat's last theorem, that had seemed intractable before. At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.
Visualization Explanation And Reasoning Styles In Mathematics
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Author : P. Mancosu
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Visualization Explanation And Reasoning Styles In Mathematics written by P. Mancosu 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 2006-03-30 with Mathematics categories.
In the 20th century philosophy of mathematics has to a great extent been dominated by views developed during the so-called foundational crisis in the beginning of that century. These views have primarily focused on questions pertaining to the logical structure of mathematics and questions regarding the justi?cation and consistency of mathematics. Paradigmatic in this - spect is Hilbert’s program which inherits from Frege and Russell the project to formalize all areas of ordinary mathematics and then adds the requi- ment of a proof, by epistemically privileged means (?nitistic reasoning), of the consistency of such formalized theories. While interest in modi?ed v- sions of the original foundational programs is still thriving, in the second part of the twentieth century several philosophers and historians of mat- matics have questioned whether such foundational programs could exhaust the realm of important philosophical problems to be raised about the nature of mathematics. Some have done so in open confrontation (and hostility) to the logically based analysis of mathematics which characterized the cl- sical foundational programs, while others (and many of the contributors to this book belong to this tradition) have only called for an extension of the range of questions and problems that should be raised in connection with an understanding of mathematics. The focus has turned thus to a consideration of what mathematicians are actually doing when they produce mathematics. Questions concerning concept-formation, understanding, heuristics, changes instyle of reasoning, the role of analogies and diagrams etc.
Journal For Research In Mathematics Education
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Author :
language : en
Publisher:
Release Date : 2000
Journal For Research In Mathematics Education written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.