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El. knyga: Mathematics across the Iron Curtain

  • Formatas: 441 pages
  • Serija: History of Mathematics
  • Išleidimo metai: 30-Jul-2014
  • Leidėjas: American Mathematical Society
  • ISBN-13: 9781470417178
Kitos knygos pagal šią temą:
  • Formatas: 441 pages
  • Serija: History of Mathematics
  • Išleidimo metai: 30-Jul-2014
  • Leidėjas: American Mathematical Society
  • ISBN-13: 9781470417178
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This is a unique study, tracing the development of a branch of mathematics and its divergence due to political reasons. The theory of semigroups is a recent development--the term "semigroup" was not even coined until 1904, only a few years before the Revolution of 1917 and the beginning of the isolation of the academic world of the Soviet Union after Lenin's death. Most of the developments in ti took place after World War 2, when Soviet and Western scientists and mathematicians had almost no contact at all. As such, the traditions and methods of the theory evolved differently in East and West. This branch of mathematics can truly be called "Cold War Science". The author, after providing an historical overview of algebra in the early 20th century, looks at the mathematical developments in political context, giving us a spectacular description of the process of divergence of specific methods, areas of interest, and theoretical underpinnings of something that we would, a priori, consider to be politically neutral. The influence of isolation on the development of science is clearly demonstrated (in fact, one is reminded of biological evolutionary theory and clearly, parallels with speciation are in order here). An appendix includes an overview of the theory under investigation. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

Recenzijos

The book is very readable, and both non-experts and experts may find it interesting. The former can see the book as a case study of how a new area of mathematics can grow from a handful of more or less independently working mathematicians to a truly international, collaborative community, despite the difficulties of communication across the Iron Curtain... For experts, a comprehensive study of the early years of semigroup theory might shed light on some previously unnoticed connections between different branches of semigroup theory or between semigroup theory and other parts of mathematics." - Miklós Hartmann, ACTA Sci. Math.

"This detailed study of the history of semigroup theory is an important contribution both to the history of algebra in the 20th century and to the history of the relations between mathematicians working on both sides of the Iron Curtain." - S.C. Coutinho, Mathematical Gazette

"The book itself is a mixture of history and of mathematics throughout. Although the emphasis is squarely on the mathematics, there are biographies of key figures, explaining who these people were along with the occasional anecdote about their mathematical lives, reflecting their characters. For example, Lyapin was not one of the original editors of Semigroup Forum because the Soviet authorities refused him permission... Overall, this is valuable reference work, detailing much of the history of algebraic semigroups that might otherwise be lost. For connoisseurs of the subject, it represents a really good read." - Mathematical Reviews

"Hollings has done a masterful job. The book is well written, both in telling the story and in explaining the mathematics involved. It is an important and valuable contribution to the history of mathematics in the 20th century. This book should be in the libraries of all research institutions, and on the shelves of those interested in the history of abstract algebra, as well as those of semigroup researchers." - MAA Reviews

Algebra at the beginning of the twentieth century
Communication between East and West
Anton Kazimirovich Sushkevich
Unique factorisation in semigroups
Embedding semigroups in groups
The Rees Theorem
The French school of 'demi-groupes'
The expansion of the theory in the 1940s and 1950s
The post-Sushkevich Soviet school
The development of inverse semigroups
Matrix representations of semigroups
Books, seminars, conferences, and journals
Basic theory
Notes
Bibliography
List of abbreviations of journal titles
Name index
Subject index
Christopher Hollings, MMath, PhD, FIMA is Departmental Lecturer in Mathematics and History and Clifford Norton Senior Research Fellow in the History of Mathematics at The Queen's College, Oxford, UK.