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Modern Algebra and the Rise of Mathematical Structures 2nd Revised Edition

5.0 out of 5 stars 1 customer review
ISBN-13: 978-3764370022
ISBN-10: 3764370025
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    "[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.

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Product Details

  • Paperback: 452 pages
  • Publisher: Birkhäuser; 2nd Revised edition (October 4, 2013)
  • Language: English
  • ISBN-10: 3764370025
  • ISBN-13: 978-3764370022
  • Product Dimensions: 7 x 1.1 x 10 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: #2,088,252 in Books (See Top 100 in Books)

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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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