Mathematische Annalen

Author : William Aspray,Philip Kitcher
Publisher : U of Minnesota Press
Page : 396 pages
File Size : 46,6 Mb
Release : 1988
Category : Mathematics
ISBN : 9780816615674

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History and Philosophy of Modern Mathematics by William Aspray,Philip Kitcher Pdf

History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective. The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge.

Author : Anonim
Publisher : Unknown
Page : 314 pages
File Size : 54,8 Mb
Release : 1978
Category : Mathematics
ISBN : UOM:39076000167523

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Mathematische Annalen by Anonim Pdf

Author : Dirk Jan Struik
Publisher : Courier Corporation
Page : 260 pages
File Size : 43,6 Mb
Release : 1967
Category : Mathematics
ISBN : 0486602559

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A Concise History of Mathematics by Dirk Jan Struik Pdf

This compact, well-written history covers major mathematical ideas and techniques from the ancient Near East to 20th-century computer theory, surveying the works of Archimedes, Pascal, Gauss, Hilbert, and many others. "The author's ability as a first-class historian as well as an able mathematician has enabled him to produce a work which is unquestionably one of the best." — Nature.

Author : Joseph Warren Dauben
Publisher : Princeton University Press
Page : 422 pages
File Size : 49,9 Mb
Release : 2020-06-16
Category : Science
ISBN : 9780691214207

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Georg Cantor by Joseph Warren Dauben Pdf

One of the greatest revolutions in mathematics occurred when Georg Cantor (1845-1918) promulgated his theory of transfinite sets. This revolution is the subject of Joseph Dauben's important studythe most thorough yet writtenof the philosopher and mathematician who was once called a "corrupter of youth" for an innovation that is now a vital component of elementary school curricula. Set theory has been widely adopted in mathematics and philosophy, but the controversy surrounding it at the turn of the century remains of great interest. Cantor's own faith in his theory was partly theological. His religious beliefs led him to expect paradoxes in any concept of the infinite, and he always retained his belief in the utter veracity of transfinite set theory. Later in his life, he was troubled by recurring attacks of severe depression. Dauben shows that these played an integral part in his understanding and defense of set theory.

Author : Stewart Shapiro,Geoffrey Hellman
Publisher : Oxford University Press, USA
Page : 593 pages
File Size : 55,8 Mb
Release : 2021
Category : Mathematics
ISBN : 9780198809647

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The History of Continua by Stewart Shapiro,Geoffrey Hellman Pdf

Mathematical and philosophical thought about continuity has changed considerably over the ages, from Aristotle's insistence that a continuum is a unified whole, to the dominant account today, that a continuum is composed of infinitely many points. This book explores the key ideas and debates concerning continuity over more than 2500 years.

Author : Alberto Cogliati
Publisher : Academic Press
Page : 304 pages
File Size : 52,9 Mb
Release : 2017-10-31
Category : Mathematics
ISBN : 9780128142745

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Writing Small Omegas by Alberto Cogliati Pdf

Writing Small Omegas: Elie Cartan's Contributions to the Theory of Continuous Groups 1894-1926 provides a general account of Lie’s theory of finite continuous groups, critically examining Cartan’s doctoral attempts to rigorously classify simple Lie algebras, including the use of many unpublished letters. It evaluates pioneering attempts to generalize Lie's classical ideas to the infinite-dimensional case in the works of Lie, Engel, Medolaghi and Vessiot. Within this context, Cartan’s groundbreaking contributions in continuous group theory, particularly in his characteristic and unique recourse to exterior differential calculus, are introduced and discussed at length. The work concludes by discussing Cartan’s contributions to the structural theory of infinite continuous groups, his method of moving frames, and the genesis of his geometrical theory of Lie groups. Discusses the origins of the theory of moving frames and the geometrical theory of Lie groups Reviews Cartan’s revolutionary contributions to Lie group theory and differential geometry Evaluates many unpublished sources that shed light on important aspects of the historical development of Lie algebras

Author : Francesca Biagioli
Publisher : Springer
Page : 239 pages
File Size : 44,7 Mb
Release : 2016-08-22
Category : Philosophy
ISBN : 9783319317793

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Space, Number, and Geometry from Helmholtz to Cassirer by Francesca Biagioli Pdf

This book offers a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century. Kant famously characterized space and time as a priori forms of intuitions, which lie at the foundation of mathematical knowledge. The success of his philosophical account of space was due not least to the fact that Euclidean geometry was widely considered to be a model of certainty at his time. However, such later scientific developments as non-Euclidean geometries and Einstein’s general theory of relativity called into question the certainty of Euclidean geometry and posed the problem of reconsidering space as an open question for empirical research. The transformation of the concept of space from a source of knowledge to an object of research can be traced back to a tradition, which includes such mathematicians as Carl Friedrich Gauss, Bernhard Riemann, Richard Dedekind, Felix Klein, and Henri Poincaré, and which finds one of its clearest expressions in Hermann von Helmholtz’s epistemological works. Although Helmholtz formulated compelling objections to Kant, the author reconsiders different strategies for a philosophical account of the same transformation from a neo-Kantian perspective, and especially Hermann Cohen’s account of the aprioricity of mathematics in terms of applicability and Ernst Cassirer’s reformulation of the a priori of space in terms of a system of hypotheses. This book is ideal for students, scholars and researchers who wish to broaden their knowledge of non-Euclidean geometry or neo-Kantianism.

Author : Jeremy Gray
Publisher : Oxford University Press, USA
Page : 340 pages
File Size : 55,8 Mb
Release : 2000
Category : Mathematics
ISBN : 0198506511

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The Hilbert Challenge by Jeremy Gray Pdf

David Hilbert was arguably the leading mathematician of his generation. He was among the few mathematicians who could reshape mathematics, and was able to because he brought together an impressive technical power and mastery of detail with a vision of where the subject was going and how it should get there. This was the unique combination which he brought to the setting of his famous 23 Problems. Few problems in mathematics have the status of those posed by David Hilbert in 1900. Mathematicians have made their reputations by solving individual ones such as Fermat's last theorem, and several remain unsolved including the Riemann hypotheses, which has eluded all the great minds of this century. A hundred years on, it is timely to take a fresh look at the problems, the man who set them, and the reasons for their lasting impact on the mathematics of the twentieth century. In this fascinating new book, Jeremy Gray and David Rowe consider what has made this the pre-eminent collection of problems in mathematics, what they tell us about what drives mathematicians, and the nature of reputation, influence and power in the world of modern mathematics. The book is written in a clear and lively manner and will appeal both to the general reader with an interest in mathematics and to mathematicians themselves.

Author : Janet L. Beery,Sarah J. Greenwald,Jacqueline A. Jensen-Vallin,Maura B. Mast
Publisher : Springer
Page : 405 pages
File Size : 47,5 Mb
Release : 2017-12-02
Category : Mathematics
ISBN : 9783319666945

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Women in Mathematics by Janet L. Beery,Sarah J. Greenwald,Jacqueline A. Jensen-Vallin,Maura B. Mast Pdf

This collection of refereed papers celebrates the contributions, achievements, and progress of female mathematicians, mostly in the 20th and 21st centuries. Emerging from the themed paper session “The Contributions of Women to Mathematics: 100 Years and Counting” at MAA's 2015 MathFest, this volume contains a diverse mix of current scholarship and exposition on women and mathematics, including biographies, histories, and cultural discussions. The multiplicity of authors also ensures a wide variety of perspectives. In inspiring and informative chapters, the authors featured in this volume reflect on the accomplishments of women in mathematics, showcasing the changes in mathematical culture that resulted as more women obtained tenure-track and tenured academic positions, received prestigious awards and honors, served in leadership roles in professional societies, and became more visibly active in the mathematical community. Readers will find discussions of mathematical excellence at Girton College, Cambridge, in the late 19th and early 20th centuries; of perseverance by Polish women in mathematics during and after World War II and by Black women in mathematics in the United States from the 1880s onward; and of the impact of outreach programs ranging from EDGE's promotion of graduate education to the Daughters of Hypatia dance performances. The volume also provides informative biographies of a variety of women from mathematics and statistics, many of them well-known and others less well-known, including Charlotte Angas Scott, Emmy Noether, Mina Rees, Gertrude Cox, Euphemia Lofton Haynes, Norma Hernandez, Deborah Tepper Haimo, and Teri Perl. These essays provide compelling reading for a wide audience, including mathematicians, historians of science, teachers of mathematics, and students at the high school, college, and graduate levels. Anyone interested in attracting more girls and women as students, faculty, and/or employees will also find this volume engaging and enlightening.

Author : Jeremy Gray
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 51,8 Mb
Release : 2011-02-01
Category : Mathematics
ISBN : 9780857290601

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Worlds Out of Nothing by Jeremy Gray Pdf

Based on the latest historical research, Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Topics covered in the first part of the book are projective geometry, especially the concept of duality, and non-Euclidean geometry. The book then moves on to the study of the singular points of algebraic curves (Plücker’s equations) and their role in resolving a paradox in the theory of duality; to Riemann’s work on differential geometry; and to Beltrami’s role in successfully establishing non-Euclidean geometry as a rigorous mathematical subject. The final part of the book considers how projective geometry rose to prominence, and looks at Poincaré’s ideas about non-Euclidean geometry and their physical and philosophical significance. Three chapters are devoted to writing and assessing work in the history of mathematics, with examples of sample questions in the subject, advice on how to write essays, and comments on what instructors should be looking for.

Author : David E. Rowe,John McCleary
Publisher : Academic Press
Page : 470 pages
File Size : 55,6 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483266213

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Ideas and Their Reception by David E. Rowe,John McCleary Pdf

The History of Modern Mathematics, Volume I: Ideas and their Reception documents the proceedings of the Symposium on the History of Modern Mathematics held at Vassar College in Poughkeepsie, New York on June 20-24, 1989. This book is concerned with the emergence and reception of major ideas in fields that range from foundations and set theory, algebra and invariant theory, and number theory to differential geometry, projective and algebraic geometry, line geometry, and transformation groups. Other topics include the theory of reception for the history of mathematics and British synthetic vs. French analytic styles of algebra in the early American Republic. The early geometrical works of Sophus Lie and Felix Klein, background to Gergonne's treatment of duality, and algebraic geometry in the late 19th century are also elaborated. This volume is intended for students and researchers interested in developments in pure mathematics.

Author : Anonim
Publisher : Elsevier
Page : 878 pages
File Size : 53,8 Mb
Release : 2012-01-24
Category : Mathematics
ISBN : 9780080930664

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Sets and Extensions in the Twentieth Century by Anonim Pdf

Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration Serves as a singular contribution to the intellectual history of the 20th century Contains the latest scholarly discoveries and interpretative insights

Author : Jeanne Peijnenburg,Sander Verhaegh
Publisher : Springer Nature
Page : 275 pages
File Size : 46,6 Mb
Release : 2023-01-01
Category : Philosophy
ISBN : 9783031085932

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Women in the History of Analytic Philosophy by Jeanne Peijnenburg,Sander Verhaegh Pdf

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

Author : Karine Chemla,José Ferreirós,Lizhen Ji,Erhard Scholz,Chang Wang
Publisher : Springer Nature
Page : 702 pages
File Size : 47,7 Mb
Release : 2023-11-27
Category : Mathematics
ISBN : 9783031408557

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The Richness of the History of Mathematics by Karine Chemla,José Ferreirós,Lizhen Ji,Erhard Scholz,Chang Wang Pdf

This book, a tribute to historian of mathematics Jeremy Gray, offers an overview of the history of mathematics and its inseparable connection to philosophy and other disciplines. Many different approaches to the study of the history of mathematics have been developed. Understanding this diversity is central to learning about these fields, but very few books deal with their richness and concrete suggestions for the “what, why and how” of these domains of inquiry. The editors and authors approach the basic question of what the history of mathematics is by means of concrete examples. For the “how” question, basic methodological issues are addressed, from the different perspectives of mathematicians and historians. Containing essays by leading scholars, this book provides a multitude of perspectives on mathematics, its role in culture and development, and connections with other sciences, making it an important resource for students and academics in the history and philosophy of mathematics.

Author : Shiing-Shen Chern,Friedrich Hirzebruch
Publisher : World Scientific
Page : 944 pages
File Size : 47,5 Mb
Release : 2000
Category : Mathematics
ISBN : 9812811761

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Wolf Prize in Mathematics by Shiing-Shen Chern,Friedrich Hirzebruch Pdf