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E-raamat: Pearls from a Lost City

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  • Formaat: 231 pages
  • Sari: History of Mathematics
  • Ilmumisaeg: 30-Aug-2014
  • Kirjastus: American Mathematical Society
  • ISBN-13: 9781470415273
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  • Formaat: 231 pages
  • Sari: History of Mathematics
  • Ilmumisaeg: 30-Aug-2014
  • Kirjastus: American Mathematical Society
  • ISBN-13: 9781470415273
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Lvov is a beautiful city in the Western Ukraine, one of the great tourist destinations of the region with a rich and magnificent history, but there is more to it than medieval walls and museums: it also has a history of mathematical thought and innovation. The Lvov school flourished between the wars, emerging suddenly and surprisingly, seemingly from nowhere: there was no significant mathematical tradition there. But it produced many of the most important mathematical thinkers of all time, in a short period: Banach, Ulam, Sierpinski, Mazur, Steinhaus and many others worked and made some of their fundamental discoveries here. This short history of the Lvov School of Mathematics combines biographical sketches with descriptions and solutions of many mathematical problems that had occupied these thinkers. The first part provides the background for the growth of mathematical school in Lvov before the First World War, and an overview of actively developing mathematical fields in Poland at the time; the second part contains the problems, research details and biographies. The achievements of the schools are the subject of a series of following chapters, and final concluding remarks discuss the effect of Soviet and German policies on the school and its loss of international significance, and a chronological review of its work and significance in international context. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

Arvustused

Many journal articles have been devoted to various aspects of mathematics in Lvov or to biographies of Lvov mathematicians, but Duda's book is the first comprehensive exposition...In summary, I conclude that Duda's book is a must for everyone interested in the history of functional analysis or in the history of mathematics in Poland." - Lech Maligranda, Mathematical Intelligencer

"This eagerly awaited translation of the book Pearls describes a world-class Polish school of mathematics at Lvov (now the Ukrainian Lviv) that thrived during the interwar period and has left an enduring legacy that remains part of the folklore today. Published in English translation after a somewhat protracted period of negotiation, this important work fills a niche in the history of science and should become a standard source of mathematics in Poland, especially the genesis of functional analysis during its Golden Age, 1918-1939. Moreover, the translator, Oxford's Daniel Davies, explains material that is unlikely to be familiar to readers outside Poland." - Isis, A Journal of the History of Science Society

"Many journal articles have been devoted to various aspects of mathematics in Lwów or to biographies of Lwów mathematicians, but Duda's book is the first comprehensive exposition. It is a must-read for everyone interested in the history of functional analysis or of mathematics in Poland, where the original Polish edition from 2007 ... has been highly successful. There is good reason to assume that the English version will be likewise successful." - Dirk Werner, ZMATH

"This book gives the history of Lvov as a mathematical center, from pre-WWI to Soviet and Ukrainian times, looking especially at the interwar golden age and the special favorable environment for mathematical scholarship. The author also describes the ways in which the Soviets and Germans destroyed this rich environment. The book includes a list, with biographical sketches, of mathematicians associated with Lvov, and a Lvov biography. It was a special time and place for mathematics, disrupted by war and politics and oppression and murder, and one wonders what more could have been achieved in a peaceful environment." - CHOICE Reviews

"The book under review is well and carefully written. The translation from Polish into English is polished and lively... I highly recommend the book for all university libraries, and I recommend it to those interested in the history of mathematics. The general mathematical reader will find it an entertaining and informative story about mathematicians and a truly extraordinary mathematical community." - Henry Heatherly, MAA Reviews

Preface ix
Part I BACKGROUND
1(24)
Chapter 1 The University and the Polytechnic in Lvov
3(4)
Chapter 2 Polish Mathematics at the Turn of the Twentieth Century
7(4)
Chapter 3 Sierpinski's Stay at the University of Lvov (1908--1914)
11(6)
Chapter 4 The University in Warsaw and Janiszewski's Program (1915--1920)
17(4)
Chapter 5 World Mathematics (Active Fields in Poland) Around 1920
21(4)
Part II THE GOLDEN AGE: Individuals and Community
25(58)
Chapter 6 The Mathematical Community in Lvov after World War I
27(10)
Chapter 7 Mathematical Studies and Students
37(6)
Chapter 8 Journals, Monographs, and Congresses
43(6)
Chapter 9 The Popularization of Mathematics
49(6)
Chapter 10 Social Life (the Scottish Cafe, the Scottish Book)
55(8)
Chapter 11 The Polish Mathematical Society
63(4)
Chapter 12 Collaboration with Other Centers
67(2)
Chapter 13 In the Eyes of Others
69(14)
13.1 Stefan Banach
69(4)
13.2 Hugo Steinhaus
73(3)
13.3 Stanislaw Mazur
76(1)
13.4 Kazimierz Kuratowski
77(1)
13.5 Stanislaw Ulam
78(1)
13.6 Juliusz Schauder and Zbigniew Lomnicki
79(1)
13.7 Wlodzimierz Stozek
80(1)
13.8 Herman Auerbach
81(1)
13.9 Others
81(2)
Part III THE GOLDEN AGE: Achievements
83(50)
Chapter 14 Stefan Banach's Doctoral Thesis and Priority Claims
85(6)
Chapter 15 Probability Theory
91(6)
Chapter 16 Measure Theory
97(6)
Chapter 17 Game Theory: A Revelation Without Follow-up
103(2)
Chapter 18 Operator Theory in the 1920s
105(4)
Chapter 19 Methodological Audacity
109(4)
Chapter 20 Banach's Monograph: Polishing the Pearls
113(6)
Chapter 21 Operator Theory in the 1930s: The Dazzle of Pearls
119(4)
Chapter 22 New Perspectives for Which Time Did Not Allow
123(8)
22.1 Nonlinear functional analysis
123(2)
22.2 The theory of partial differential equations
125(1)
22.3 The theory of linear topological spaces
126(1)
22.4 The theory of recursive functions
127(1)
22.5 Algebra, specifically Banach algebras
127(1)
22.6 Noncommutative probability theory
128(1)
22.7 Graph theory
128(1)
22.8 Applications of mathematics
129(1)
22.9 Numerical analysis
130(1)
Chapter 23 On the Periphery
131(2)
Part IV OBLIVION
133(20)
Chapter 24 Ukrainization the Soviet Way (1939--1941)
135(6)
Chapter 25 The German Occupation (1941--1944)
141(8)
Chapter 26 The Expulsion of Poles (1945--1946)
149(4)
Part V HISTORICAL SIGNIFICANCE
153(24)
Chapter 27 Chronological Overview
155(10)
Chapter 28 Chronology of Events as Perceived Elsewhere
165(4)
Chapter 29 Influence on Mathematics of the Lvov School
169(4)
Chapter 30 A Tentative Summary
173(2)
Chapter 31 Mathematics in Lvov after 1945
175(2)
Part VI LIST OF LVOV MATHEMATICIANS
177(16)
Mathematicians Associated with Lvov
179(14)
Part VII BIBLIOGRAPHIES
193(32)
A Mathematical Works by Lvov Mathematicians
195(10)
B Personal Recollections, Surveys, and Historical Source Material
205(14)
C Other Mathematical Works Cited
219(6)
List of Illustrations and Acknowledgments 225(2)
Index of Names 227
Roman Duda, University of Wroclaw, Poland.