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L. Maligranda REVIEW of the BOOK by MARIUSZ URBANEK
Математичнi Студiї. Т.50, №1 Matematychni Studii. V.50, No.1 УДК 51 L. Maligranda REVIEW OF THE BOOK BY MARIUSZ URBANEK, “GENIALNI – LWOWSKA SZKOL A MATEMATYCZNA” (POLISH) [GENIUSES – THE LVOV SCHOOL OF MATHEMATICS] L. Maligranda. Review of the book by Mariusz Urbanek, “Genialni – Lwowska Szko la Matema- tyczna” (Polish) [Geniuses – the Lvov school of mathematics], Wydawnictwo Iskry, Warsaw 2014, 283 pp. ISBN: 978-83-244-0381-3 , Mat. Stud. 50 (2018), 105–112. This review is an extended version of my short review of Urbanek's book that was published in MathSciNet. Here it is written about his book in greater detail, which was not possible in the short review. I will present facts described in the book as well as some false information there. My short review of Urbanek’s book was published in MathSciNet [24]. Here I write about his book in greater detail. Mariusz Urbanek, writer and journalist, author of many books devoted to poets, politicians and other figures of public life, decided to delve also in the world of mathematicians. He has written a book on the phenomenon in the history of Polish science called the Lvov School of Mathematics. Let us add that at the same time there were also the Warsaw School of Mathematics and the Krakow School of Mathematics, and the three formed together the Polish School of Mathematics. The Lvov School of Mathematics was a group of mathematicians in the Polish city of Lvov (Lw´ow,in Polish; now the city is in Ukraine) in the period 1920–1945 under the leadership of Stefan Banach and Hugo Steinhaus, who worked together and often came to the Scottish Caf´e (Kawiarnia Szkocka) to discuss mathematical problems. -
COMPLEXITY of CURVES 1. Introduction in This Note We Study
COMPLEXITY OF CURVES UDAYAN B. DARJI AND ALBERTO MARCONE Abstract. We show that each of the classes of hereditarily locally connected, 1 ¯nitely Suslinian, and Suslinian continua is ¦1-complete, while the class of 0 regular continua is ¦4-complete. 1. Introduction In this note we study some natural classes of continua from the viewpoint of descriptive set theory: motivations, style and spirit are the same of papers such as [Dar00], [CDM02], and [Kru03]. Pol and Pol use similar techniques to study problems in continuum theory in [PP00]. By a continuum we always mean a compact and connected metric space. A subcontinuum of a continuum X is a subset of X which is also a continuum. A continuum is nondegenerate if it contains more than one point. A curve is a one- dimensional continuum. Let us start with the de¯nitions of some classes of continua: all these can be found in [Nad92], which is our main reference for continuum theory. De¯nition 1.1. A continuum X is hereditarily locally connected if every subcon- tinuum of X is locally connected, i.e. a Peano continuum. A continuum X is hereditarily decomposable if every nondegenerate subcontin- uum of X is decomposable, i.e. is the union of two proper subcontinua. A continuum X is regular if every point of X has a neighborhood basis consisting of sets with ¯nite boundary. A continuum X is rational if every point of X has a neighborhood basis consisting of sets with countable boundary. The following classes of continua were de¯ned by Lelek in [Lel71]. -
L. Maligranda REVIEW of the BOOK by ROMAN
Математичнi Студiї. Т.46, №2 Matematychni Studii. V.46, No.2 УДК 51 L. Maligranda REVIEW OF THE BOOK BY ROMAN DUDA, “PEARLS FROM A LOST CITY. THE LVOV SCHOOL OF MATHEMATICS” L. Maligranda. Review of the book by Roman Duda, “Pearls from a lost city. The Lvov school of mathematics”, Mat. Stud. 46 (2016), 203–216. This review is an extended version of my two short reviews of Duda's book that were published in MathSciNet and Mathematical Intelligencer. Here it is written about the Lvov School of Mathematics in greater detail, which I could not do in the short reviews. There are facts described in the book as well as some information the books lacks as, for instance, the information about the planned print in Mathematical Monographs of the second volume of Banach's book and also books by Mazur, Schauder and Tarski. My two short reviews of Duda’s book were published in MathSciNet [16] and Mathematical Intelligencer [17]. Here I write about the Lvov School of Mathematics in greater detail, which was not possible in the short reviews. I will present the facts described in the book as well as some information the books lacks as, for instance, the information about the planned print in Mathematical Monographs of the second volume of Banach’s book and also books by Mazur, Schauder and Tarski. So let us start with a discussion about Duda’s book. In 1795 Poland was partioned among Austria, Russia and Prussia (Germany was not yet unified) and at the end of 1918 Poland became an independent country. -
L. Maligranda REVIEW of the BOOK BY
Математичнi Студiї. Т.50, №1 Matematychni Studii. V.50, No.1 УДК 51 L. Maligranda REVIEW OF THE BOOK BY MARIUSZ URBANEK, “GENIALNI – LWOWSKA SZKOL A MATEMATYCZNA” (POLISH) [GENIUSES – THE LVOV SCHOOL OF MATHEMATICS] L. Maligranda. Review of the book by Mariusz Urbanek, “Genialni – Lwowska Szko la Matema- tyczna” (Polish) [Geniuses – the Lvov school of mathematics], Wydawnictwo Iskry, Warsaw 2014, 283 pp. ISBN: 978-83-244-0381-3 , Mat. Stud. 50 (2018), 105–112. This review is an extended version of my short review of Urbanek's book that was published in MathSciNet. Here it is written about his book in greater detail, which was not possible in the short review. I will present facts described in the book as well as some false information there. My short review of Urbanek’s book was published in MathSciNet [24]. Here I write about his book in greater detail. Mariusz Urbanek, writer and journalist, author of many books devoted to poets, politicians and other figures of public life, decided to delve also in the world of mathematicians. He has written a book on the phenomenon in the history of Polish science called the Lvov School of Mathematics. Let us add that at the same time there were also the Warsaw School of Mathematics and the Krakow School of Mathematics, and the three formed together the Polish School of Mathematics. The Lvov School of Mathematics was a group of mathematicians in the Polish city of Lvov (Lw´ow,in Polish; now the city is in Ukraine) in the period 1920–1945 under the leadership of Stefan Banach and Hugo Steinhaus, who worked together and often came to the Scottish Caf´e (Kawiarnia Szkocka) to discuss mathematical problems. -
Leaders of Polish Mathematics Between the Two World Wars
COMMENTATIONES MATHEMATICAE Vol. 53, No. 2 (2013), 5-12 Roman Duda Leaders of Polish mathematics between the two world wars To Julian Musielak, one of the leaders of post-war Poznań mathematics Abstract. In the period 1918-1939 mathematics in Poland was led by a few people aiming at clearly defined but somewhat different goals. They were: S. Zaremba in Cracow, W. Sierpiński and S. Mazurkiewicz in Warsaw, and H. Steinhaus and S. Banach in Lvov. All were chairmen and editors of mathematical journals, and each promoted several students to continue their efforts. They were highly successful both locally and internationally. When Poland regained its independence in 1918, Polish mathematics exploded like a supernova: against a dark background there flared up, in the next two deca- des, the Polish Mathematical School. Although the School has not embraced all mathematics in the country, it soon attracted common attention for the whole. Ho- wever, after two decades of a vivid development the School ended suddenly also like a supernova and together with it there silenced, for the time being, the rest of Polish mathematics. The end came in 1939 when the state collapsed under German and Soviet blows from the West and from the East, and the two occupants cooperated to cut short Polish independent life. After 1945 the state and mathematics came to life again but it was a different state and a different mathematics. The aim of this paper is to recall great leaders of the short-lived interwar Polish mathematics. By a leader we mean here a man enjoying an international reputation (author of influential papers or monographs) and possessing a high position in the country (chairman of a department of mathematics in one of the universities), a man who had a number of students and promoted several of them to Ph.D. -
The Emergence of “Two Warsaws”: Transformation of the University In
The emergence of “two Warsaws”: Transformation of the University in Warsaw and the analysis of the role of young, talented and spirited mathematicians in this process Stanisław Domoradzki (University of Rzeszów, Poland), Margaret Stawiska (USA) In 1915, when the front of the First World War was moving eastwards, Warsaw, which had been governed by Russians for over a century, found itself under a German rule. In the summer of 1915 the Russians evacuated the Imperial University to Rostov-on-Don and in the fall of 1915 general Hans von Beseler opened a Polish-language University of Warsaw and gave it a statute. Many Poles from other occupied territories as well as those studying abroad arrived then to Warsaw, among others Kazimierz Kuratowski (1896–1980), from Glasgow. At the beginning Stefan Mazurkiewicz (1888–1945) played the leading role in the university mathematics, joined in 1918 by Zygmunt Janiszewski (1888–1920) after complet- ing service in the Legions. The career of both scholars was related to scholarly activities of Wacław Sierpi ński (1882–1969) in Lwów. Janiszewski worked there since 1912, nostrified a doctorate from Sorbonne and got veniam legendi (1913), Mazurkiewicz obtained a doctorate (1913). During the war Sierpi ński was interned in Russia as an Austro-Hungarian subject. In 1918 he was nominated for a chair in mathematics at the University of Warsaw. The commu- nity congregating around these mathematicians managed to create somewhat later a solid mathematical school focused on set theory and its applications. It corresponded to a vision of a mathematical school presented by Janiszewski. Warsaw had an efficiently functioning mathematical community for several decades. -
Kazimierz Kuratowski (Warsaw)
Kazimierz Kuratowski (Warsaw) THE PAST AND THE PRESENT OF THE POLISH SCHOOL OF MATHEMATICS I am concentrating in this article on two main subjects. Firstly: I am trying to answer the question what brought about such an “explosion” of mathematics in a country in whose scientific tradition there was hardly any mathematics and which happened at the time when after an over-one-century-long foreign rule the nation was trying hard to reconstruct its now independent country, ravaged by the First World War. Secondly: was this explosion a short-lived enthusiasm or, on the contrary, the Polish school of .mathematics struck roots so deeply that it was sub sequently able to survive the cataclysm of the Second World War and rebuild in the new circumastances — in People’s Poland — the internationally re cognized edifice of Polish mathematics? There will be in this article no mathematical theorems, no definitions or geometrical constructions. I shall be trying to use the language which can be understood without mathematical qualifications. It is therefore my hope that this text will be intelligible not only to mathematicians.1 1. PRECURSORS OF THE POLISH SCHOOL OF MATHEMATICS It was the years 1918—1920 when the Polish School of Mathematics was emerging. Before describing this period and the subsequent years one should, I think, review, be it only summarily, the contemporary state of Polish mathematics. I am going to mention those of its representatives the majority of whom had in fact been active in the 19th century but who also worked in the 20th century and so could influence the formation of the School of Mathematics being thus its precursors as it were. -
Contribution of Warsaw Logicians to Computational Logic
axioms Article Contribution of Warsaw Logicians to Computational Logic Damian Niwi ´nski Institute of Informatics, University of Warsaw, 02-097 Warsaw, Poland; [email protected]; Tel.: +48-22-554-4460 Academic Editor: Urszula Wybraniec-Skardowska Received: 22 April 2016; Accepted: 31 May 2016; Published: 3 June 2016 Abstract: The newly emerging branch of research of Computer Science received encouragement from the successors of the Warsaw mathematical school: Kuratowski, Mazur, Mostowski, Grzegorczyk, and Rasiowa. Rasiowa realized very early that the spectrum of computer programs should be incorporated into the realm of mathematical logic in order to make a rigorous treatment of program correctness. This gave rise to the concept of algorithmic logic developed since the 1970s by Rasiowa, Salwicki, Mirkowska, and their followers. Together with Pratt’s dynamic logic, algorithmic logic evolved into a mainstream branch of research: logic of programs. In the late 1980s, Warsaw logicians Tiuryn and Urzyczyn categorized various logics of programs, depending on the class of programs involved. Quite unexpectedly, they discovered that some persistent open questions about the expressive power of logics are equivalent to famous open problems in complexity theory. This, along with parallel discoveries by Harel, Immerman and Vardi, contributed to the creation of an important area of theoretical computer science: descriptive complexity. By that time, the modal m-calculus was recognized as a sort of a universal logic of programs. The mid 1990s saw a landmark result by Walukiewicz, who showed completeness of a natural axiomatization for the m-calculus proposed by Kozen. The difficult proof of this result, based on automata theory, opened a path to further investigations. -
Notices of the American Mathematical Society
OF THE AMERICAN MATHEMATICAL SOCIETY VOLUME 16, NUMBER 3 ISSUE NO. 113 APRIL, 1969 OF THE AMERICAN MATHEMATICAL SOCIETY Edited by Everett Pitcher and Gordon L. Walker CONTENTS MEETINGS Calendar of Meetings ..................................... 454 Program for the April Meeting in New York ..................... 455 Abstracts for the Meeting - Pages 500-531 Program for the April Meeting in Cincinnati, Ohio ................. 466 Abstracts for the Meeting -Pages 532-550 Program for the April Meeting in Santa Cruz . ......... 4 73 Abstracts for the Meeting- Pages 551-559 PRELIMINARY ANNOUNCEMENT OF MEETING ....................•.. 477 NATIONAL REGISTER REPORT .............. .. 478 SPECIAL REPORT ON THE BUSINESS MEETING AT THE ANNUAL MEETING IN NEW ORLEANS ............•................... 480 INTERNATIONAL CONGRESS OF MATHEMATICIANS ................... 482 LETTERS TO THE EDITOR ..................................... 483 APRIL MEETING IN THE WEST: Some Reactions of the Membership to the Change in Location ....................................... 485 PERSONAL ITEMS ........................................... 488 MEMORANDA TO MEMBERS Memoirs ............................................. 489 Seminar of Mathematical Problems in the Geographical Sciences ....... 489 ACTIVITIES OF OTHER ASSOCIATIONS . 490 SUMMER INSTITUTES AND GRADUATE COURSES ..................... 491 NEWS ITEMS AND ANNOUNCEMENTS ..... 496 ABSTRACTS OF CONTRIBUTED PAPERS .................•... 472, 481, 500 ERRATA . • . 589 INDEX TO ADVERTISERS . 608 MEETINGS Calendar of Meetings NOn:: This Calendar lists all of the meetings which have been approved by the Council up to the date at which this issue of the c;Noticei) was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the American Mathematical Society. The meeting dates which fall rather far in the future are subject to change. This is particularly true of the meetings to which no numbers have yet been assigned. -
Document Mune
DOCUMENT MUNE ID 175 699 SE 028 687 AUTHOR Schaaf, William L., Ed. TITLE Reprint Series: Memorable Personalities in Mathematics - Twentieth Century. RS-12. INSTITUTION Stanford Gniv.e Calif. School Mathematics Study Group. 2 SPONS AGENCT National Science Foundation, Washington, D.C. 1 PUB DATE 69 NOTE 54p.: For related documents, see SE 028 676-690 EDRS PRICE 81101/PC03 Plus Postage. DESCRIPTORS Curriculum: *Enrichsent: *History: *Instruction: *Mathematicians: Mathematics Education: *Modern Mathematics: Secondary Education: *Secondary School Sathematics: Supplementary Reading Materials IDENTIFIERS *School Mathematics study Group ABSTRACT This is one in a series of SHSG supplementary and enrichment pamphlets for high school students. This series makes available espcsitory articles which appeared in a variety of mathematical periodials. Topics covered include:(1) Srinivasa Ramanuian:12) Minkomski: (3) Stefan Banach:(4) Alfred North Whitehead: (5) Waclaw Sierptnski: and (6)J. von Neumann. (MP) *********************************************************************** Reproductions supplied by EDRS are the best that can be made from the original document. *********************************************************************** OF NEM TN U S DEPARTMENT "PERMISSION EDUCATION II %WELFARE TO REPROnUCE OF MATERIAL THIS NATIONAL INSTITUTE HAS SEEN EDUCATION GRANTEDBY wc 0Oi ,,V11. NTHt.',Iii t iFf I ROF' all( F 0 f IA. T v A WI (I 1 Ttit P1I4S0 1.41114')WGAN,ZTIf)N01414014 AIHF0,tfvf1,14 Ts 01 ,11-A OF: Ofolv4ION.y STAll 0 04.3 NOT NI-I E55A1,0)V REPRE ,Ak NAFaINA, INSIF011 Of SF Fe 1)1. F P01,I Ot,t AT ION P00,0T,0IN OkI TO THE EDUCATIONAL INFORMATION RESOURCES CENTER(ERIC)." Financial support for the School Mathematics Study Group bas been provided by the National Science Foundation. -
The Reception of Logic in Poland: 1870‒1920 Recepcja
TECHNICAL TRANSACTIONS CZASOPISMO TECHNICZNE FUNDAMENTAL SCIENCES NAUKI PODSTAWOWE 1-NP/2014 JAN WOLEŃSKI* THE RECEPTION OF LOGIC IN POLAND: 1870‒1920 RECEPCJA LOGIKI W POLSCE: 1870‒1920 Abstract This paper presents the reception of mathematical logic (semantics and methodology of science are entirely omitted, but the foundations of mathematics are included) in Poland in the years 1870–1920. Roughly speaking, Polish logicians, philosophers and mathematicians mainly followed Boole’s algebraic ideas in this period. Logic as shaped by works of Gottlob Frege and Bertrand Russell became known in Poland not earlier than about 1905. The foundations for the subsequent rapid development of logic in Poland in the interwar period were laid in the years 1915–1920. The rise of Polish Mathematical School and its program (the Janiszewski program) played the crucial role in this context. Further details can be found in [8]. This paper uses the material published in [20‒24]. Keywords: traditional logic, algebraic logic, mathematical logic, mathematics, philosophy, the Lvov-Warsaw School, Polish Mathematical School, logic in Cracow Streszczenie W artykule przedstawiono recepcję logiki matematycznej w Polsce w latach 1870–1920. Polscy logicy, zarówno filozofowie jak i matematycy, kontynuowali algebraiczne idee Boole’a w tym okresie. Logika w stylu Gottloba Fregego i Bertranda Russella stała się znana w Polsce około 1905 r. Podwaliny pod dalszy szybki rozwój logiki w okresie międzywojennym zostały położone w latach 1915–1920. Powstanie Polskiej Szkoły Matematycznej i jej program (pro- gram Janiszewskiego) odegrały kluczową rolę w tym kontekście. Dalsze szczegóły można zna- leźć w [8, 12]. Niniejszy artykuł korzysta z materiału zawartego w [20‒24]. -
Topics in Continuum Theory John Samples a Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master O
Topics in Continuum Theory John Samples a thesis submitted in partial fulfillment of the requirements for the degree of Master of Science University of Washington 2017 Committee: Ken Bube John Palmieri Program Authorized to Offer Degree: Mathematics © Copyright 2017 John Samples 2 University of Washington Abstract Topics in Continuum Theory John Samples Chair of the Supervisory Committee: Professor Ken Bube Mathematics Continuum Theory is the study of compact, connected, metric spaces. These spaces arise naturally in the study of topological groups, compact manifolds, and in particular the topol- ogy and dynamics of one-dimensional and planar systems, and the area sits at the crossroads of topology and geometry. Major contributors to its development include, but are not lim- ited to, Urysohn, Borsuk, Moore, Sierpi´nski,Menger, Mazurkiewicz, Ulam, Hahn, Whyburn, Kuratowski, Knaster, Moise, Cechˇ and Bing. After the 1950's the area fell out of style, pri- marily due to the increased interest in the then-developing field of algebraic topology. Current efforts in complex and topological dynamics, including many open problems, often fall within the purview of continuum theory. This paper covers a selection of the standard topics in continuum theory, as well as a number of topics not yet available in book form, e.g. Kelley continua and some classical results concerning the pseudo-arc. As well, many known results are given their first explicit proofs, and two new results are obtained, one concerning slc continua and the other a broad generalization of a result of Menger. 3 Basic Definitions The following definitions are assumed throughout the text.