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Modern Algebra and the Rise of Mathematical Structures Paperback – November 27, 2003

ISBN-13: 978-3764370022 ISBN-10: 3764370025 Edition: 2nd Revised

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Product Details

  • Paperback: 452 pages
  • Publisher: Birkhäuser; 2nd Revised edition (November 27, 2003)
  • Language: English
  • ISBN-10: 3764370025
  • ISBN-13: 978-3764370022
  • Product Dimensions: 9.1 x 6.1 x 1 inches
  • Shipping Weight: 2.8 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #1,009,674 in Books (See Top 100 in Books)

Editorial Reviews

Review

    "[The author], through the use of a few clear metamathematical tools, offers the reader a convincing and well-documented historical reconstruction of the rise of the structural image of algebra... [The] book, by reason of its historical approach, could be associated with the so-called 'new historiography of mathematics'. But, unlike some of these works, it is a very good example of the fine balance between historical data and philosophical interpretaion.   
  -- M. Mazzotti, British Journal of the History of Science    --This text refers to an alternate Paperback edition.

From the Back Cover

The notion of a mathematical structure is among the most pervasive ones in twentieth-century mathematics. Modern Algebra and the Rise of Mathematical Structures describes two stages in the historical development of this notion: first, it traces its rise in the context of algebra from the mid-nineteenth century to its consolidation by 1930, and then it considers several attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea.

Part one dicusses the process whereby the aims and scope of the discipline of algebra were deeply transformed, turning it into that branch of mathematics dealing with a new kind of mathematical entities: the "algebraic structures". The transition from the classical, nineteenth-century, image of the discipline to the thear of ideals, from Richard Dedekind to Emmy Noether, and culminating with the publication in 1930 of Bartel L. van der Waerden's Moderne Algebra. Following its enormous success in algebra, the structural approach has been widely adopted in other mathematical domains since 1930s. But what is a mathematical structure and what is the place of this notion within the whole fabric of mathematics? Part Two describes the historical roots, the early stages and the interconnections between three attempts to address these questions from a purely formal, mathematical perspective: Oystein Ore's lattice-theoretical theory of structures, Nicolas Bourbaki's theory of structures, and the theory of categories and functors.


More About the Author

I am a historian of mathematics working at Tel-Aviv University. You can see more about my work, here: http://www.tau.ac.il/~corry/

My research has focused on an attempt to understand the historical development of some of the main threads of twentieth-century mathematics. Among other things my research has dealt with the rise of modern algebra, the development of the idea of a mathematical structure, the rise of the modern axiomatic method, the introduction of digital computers into research in pure mathematics, and the works of some leading figures such as David Hilbert, Emmy Noether, Nicolas Bourbaki, and others.

As part of a more general academic interest in history and philosophy of science, in 1999-2009 I was editor of the journal Science in Context (Cambridge University Press), and in 2003-2009 I was director of the Cohn Institute for History and Philosophy of Science at Tel-Aviv University.

I also have a keen interest in Latin American literature. I wrote an introductory overview (in Hebrew) to the prose of Jorge Luis Borges, and also translated several books into Hebrew, including Mario Vargas Llosa's "La Casa Verde".

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Most Helpful Customer Reviews

5 of 6 people found the following review helpful By Gary L. Herstein on November 20, 2011
Format: Kindle Edition Verified Purchase
Corry's work is a truly amazing piece of scholarship. As appreciative as I normally am for histories of mathematics, I was utterly clueless about the techtonic shift in attitudes toward algegraic and structural/relational thinking which has become the hallmark or contemporary mathematics that occurred in the late 19th, early 20th Centuries.

This is an exceptionally careful bit of scholarship that should be of substantial interest to anyone with even a casual interest in mathematics, algebra, and logic. It does not bog the reader down with excessive mathematical detail -- it is, after all, a work in history rather than mathematics 'simpliciter.' Corry develops his argument with a meticulous attention to detail coupled with a well-crafted prose style that makes this book a "MUST HAVE" for anyone with even a tangential concern for the history &/or philosophy of mathematics, or any of the fields related to those.
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