Items related to Modern Algebra and the Rise of Mathematical Structures
Synopsis
A historical presentation of the two stages of development in the idea of mathematical structure. Corry traces the structural approach from the mid 19th century to its consolidation in the 1930s into "algebraic structures." On the other hand, the more elusive attempt to address the meaning of structure from a mathematical perspective begins in 1930 and is defined by Oystein Ore's lattice-theoretical theory of structures, Nicolas Bourbaki's theory of structures, and the theory of categories and functors. Annotation c. by Book News, Inc., Portland, Or.
"synopsis" may belong to another edition of this title.
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.
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
"About this title" may belong to another edition of this title.
- PublisherBirkhäuser Basel
- Publication date1996
- ISBN 10 3764353112
- ISBN 13 9783764353117
- BindingHardcover
- LanguageEnglish
- Edition number1
- Number of pages467
- Rating
(No Available Copies)
Search Books: Create a WantCan't find the book you're looking for? We'll keep searching for you. If one of our booksellers adds it to AbeBooks, we'll let you know!
Create a Want
