41. Encyclopaedia Britannica Entry banach, stefan. Born March 30, 1892, Kraków, AustriaHungary now in PolandDied Aug. 31, 1945, Lvov, Ukrainian SSR. Polish mathematician who founded http://www.aam314.vzz.net/EB/Banach.html

Banach, Stefan Born: Died: Aug. 31, 1945, Lvov, Ukrainian S.S.R. Polish mathematician who founded modern functional analysis and helped develop the theory of topological vector spaces. A lecturer in mathematics at the Institute of Technology, Lvov, from 1919, Banach became a lecturer at the University of Lvov in 1922 and a full professor in 1927. He contributed to the theory of orthogonal series and made innovations in the theory of measure and integration, but his most important contribution was in functional analysis. Of his published works, his (1932; "Theory of Linear Operations") is the most important. Banach and his coworkers summarized the previously developed concepts and theorems of functional analysis and integrated them into a comprehensive system. Banach himself introduced the concept of normed linear spaces, which are now known as Banach spaces. He also proved several fundamental theorems in the field, and his applications of theory inspired much of the work in functional analysis for the next few decades. : Encyclopaedia Britannica 2000

42. Stefan Banach, Mathematician stefan banach. banach was one of the founders of functional analysis. Spaces nowcalled banach spaces are more general than Hilbert spaces, in that the norm http://www.mth.kcl.ac.uk/~streater/Banach.html

Stefan Banach Banach was one of the founders of functional analysis. Spaces now called Banach spaces are more general than Hilbert spaces, in that the norm might not be derivable from a scalar product. In fact, a norm is so derivable if and only if it satisfies Appollonius's equality. Whereas Hilbert spaces have a simple classification (up to isomorphism) in terms of their dimension, the search for a classifying space for Banach spaces has been perhaps a waste of time. Go to my HOME PAGE for more links.

43. The Mathematics Genealogy Project - Stefan Banach According to our current online database, stefan banach has 2 students and 83descendants. We welcome any additional information. http://www.genealogy.math.ndsu.nodak.edu/html/id.phtml?id=12681

44. The Mathematics Genealogy Project - Update Data For Stefan Banach If you have Mathematics Subject Classifications to submit for an entire group ofindividuals (for instance all those that worked under a particular advisor) http://www.genealogy.math.ndsu.nodak.edu/html/php/submit-update.php?id=12681

45. Stefan Banach Born in Krakow, stefan banach studied mathematics at the Jagiellonian Universitythere. Lecturing in the Institute of Technology and then the University of http://www.geocities.com/arekgondek/banach.html

Main Where is Poland Basics Environment ... Other resources Stefan Banach Born in Krakow, Stefan Banach studied mathematics at the Jagiellonian University there. Lecturing in the Institute of Technology and then the University of Lvov, he became professor of Mathematics at the University of Lvov in 1927. Banach founded modern functional analysis and made major contributions to the theory of topological vector spaces. His dissertation of 1920 defined axiomatically what is today called a Banach space. Banach algebra's are also his work. A Banach space is a real or complex normed vector space that is complete as a metric space under the metric d(x, y) = llx-yll induced by the norm. The completeness is important as this means that Cauchy sequences in Banach spaces converge. Many important theorems are named after Banach. There is the Hahan-Banach theorem, Banach-Steinhaus theorem, the Banach-Alaoglu theorem, the Banach fixed-point theorem and the Banach-Tarski paradoxical decomposition of a ball. His most important work is the Theorie des operations lineaires of 1932. Attributed to Banach by S.M Lam in his book Adventure of a Mathematician is the comment that good mathematicians see analogies between theories, the very best ones see analogies between analogies.

46. The Life Of Stefan Banach This review of Roman Kaluza s 1996 book The Life of stefan banach was published in In 1928 stefan banach and his colleague Hugo Steinhaus founded Studia http://www.axler.net/Banach.html

The Life of Stefan Banach Sheldon Axler This review of Roman Kaluza's 1996 book The Life of Stefan Banach was published in American Mathematical Monthly In at least one printing of the current (fifteenth) edition of the Encyclopedia Britannica , the entry on Stefan Banach did not contain the words "Poland" or "Polish". The Britannica called Banach a "Soviet mathematician". The encyclopedia fixed its error in later printings, but the mathematics community has not yet adequately documented Banach's life and ideas. A computer search of Mathematical Reviews reveals more than eleven thousand publications with the word "Banach" in the title; "Hilbert" occurs in only seven thousand titles. Yet no mathematician or historian of mathematics has produced a book-length biography of Stefan Banach. The book under review was written neither by a mathematician nor by a historian. The author, a Polish reporter and journalist, writes well about mathematics without using any mathematical symbols. Professional mathematicians will spot a few technical errors of the type that inevitably creep into exposition at this level. For example, we read that "the only linear transformations" on a finite-dimensional Euclidean space are "translations, rotations, and reflections". Such small mistakes in mathematical details can easily be forgiven because the author does a good job of capturing the flavor of early functional analysis and its creators. As another example of a tantalizing tidbit from the book that needs more explanation, consider the following account (page 51) of Banach's support for the mathematical logician Leon Chwistek:

47. Stefan Banach -- Facts, Info, And Encyclopedia Article stefan banach. Categories Polish mathematicians, 1945 deaths, 1892 birthsstefan banach (March 30, 1892 in (An industrial city in southern Poland on the http://www.absoluteastronomy.com/encyclopedia/s/st/stefan_banach.htm

Stefan Banach [Categories: Polish mathematicians, 1945 deaths, 1892 births] Stefan Banach (March 30, 1892 in (An industrial city in southern Poland on the Vistula) Kraków (A republic in central Europe; the invasion of Poland by Germany in 1939 started World War II) Poland (Click link for more info and facts about L'viv) L'viv (A republic in southeastern Europe; formerly a European soviet; the center of the original Russian state which came into existence in the ninth century) Ukraine ), was a (The property of being smooth and shiny) Polish (A person skilled in mathematics) mathematician , one of the moving spirits of the (Click link for more info and facts about Lwów School of Mathematics) Lwów School of Mathematics in pre-war (A republic in central Europe; the invasion of Poland by Germany in 1939 started World War II) Poland . He was largely self-taught in mathematics; his genius was accidentally discovered by (Click link for more info and facts about Hugo Steinhaus) Hugo Steinhaus When (A war between the Allies (Australia, Belgium, Bolivia, Brazil, Canada, China, Colombia, Costa Rica, Cuba, Czechoslovakia, Dominican Republic, El Salvador, Ethiopia, France, Greece, Guatemala, Haiti, Honduras, India, Iran, Iraq, Luxembourg, Mexico, Netherl) World War II began, Banach was President of the Polish Mathematical Society and a full professor of University of Lwów. Being a corresponding member of Academy of Sciences of the

48. List Of Poland-related Topics -- Facts, Info, And Encyclopedia Article Russian navy) Baltic Sea (Click link for more info and facts about banach,stefan) banach, stefan - (Click link for more info and facts about Bathory, http://www.absoluteastronomy.com/encyclopedia/l/li/list_of_poland-related_topics

List of Poland-related topics [Categories: Lists of country-related topics] This page aims to list articles on Wikipedia that are related to (A republic in central Europe; the invasion of Poland by Germany in 1939 started World War II) Poland . This is so that those interested in the subject can monitor changes to the pages by clicking on Related changes in the sidebar. The list is under construction - if you see an article that should be here but is not (or one that should not be here but is), please do update the page accordingly. (Click link for more info and facts about 966) A (Click link for more info and facts about Adalbert of Prague) Adalbert of Prague (Click link for more info and facts about Adam Mickiewicz) Adam Mickiewicz (Click link for more info and facts about Akira Fujimoto) Akira Fujimoto (Click link for more info and facts about Albert of Prussia) Albert of Prussia (Click link for more info and facts about Armia Krajowa) Armia Krajowa - August II - August III B (Click link for more info and facts about Balice International Airport) Balice International Airport (A sea in northern Europe; stronghold of the Russian navy)

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50. NewPoland - Famous Poles: Scientists banach, stefan (18921945), born in Krakow, Poland. He was a mathematician,developed the major concepts and theorems of functional analysis; http://www.newpoland.com/famous_poles_scientists_main.htm

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51. AllRefer.com - Stefan Banach (Mathematics, Biography) - Encyclopedia AllRefer.com reference and encyclopedia resource provides complete informationon stefan banach, Mathematics, Biographies. Includes related research links. http://reference.allrefer.com/encyclopedia/B/Banach-S.html

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52. Stefan Banach - Zycie I Twórczosc stefan banach was born in Kraków in 1892.He was an illegitmate child of However,when banach s grandmother took ill,stefan banach was arranged to be http://republika.pl/lozagan/uk/banach_uk.htm

Stefan Banach: Live Live "Scottisch Book" Scientific Creer More important dates His outstanding maths abilities were discovered accidentally in the summer 1916 by Hugo Steinhaus.He overheard his talk to Otto Nikodym about 'Lebesgue integral'.Stefan Banach enrolled in the Faculty of Engineering at Lvov Technical University.The outbreake of the World War I saw Banach leave Lvov and break his study at half way.After the war he didn't come back to Lvov to end his studies.He didn't finish any other studies.Once being asked by his son why he replied'I wasn't interested in a university course,as I have it at my finger's end,I was already completely further...' Banach was not trite.He postponed writing his dissertation.He submitted a dissertation for his doctorate under Lomnicki's supervision.This was,of course,not the standrd route to a doctorate.He was asked to the Dean's office to talk about maths.Actually it was defense of his doctorate dissertation. In 1939-1941 Stefan Banach was the Dean of the Faculty of Science at the University.In 1944 as soon as the Soviet troops retook Lvov Banach started organising scientific and pedagogical work at the Lvov University.He became the chairman of the Lvov Mathematical Society.He was a co-editor of a scientific paper.In 1945 he stayed in a rest-house of Russian Academy of Sciences outside Moscow.

53. Stefan Banach - Zycie I Twórczosc stefan banach studiowal na Politechnice we Lwowie. W latach 193941 stefanbanach pelnil funkcje dziekana Wydzialu Matematyczno Przyrodniczego. http://republika.pl/lozagan/pl/banach.html

Stefan Banach: ¯ycie i twórczo¶æ ¯ycie i twórczo¶æ "Szkocka ksiêga" Kariera naukowa Wa¿niejsze daty Urodzi³ sie w Krakowie w 1892. By³ nie¶lubnym dzieckiem Katarzyny Banach i Stefana Greczka. Pochodzili z rodzin góralskich. Zaraz po urodzeniu Stefan zosta³ oddany na wychowanie Marii P³owej, krakowskiej praczce. W roku 1902 gdy ukonczy³ 10 lat zosta³ przyjety do pierwszej klasy IV Gimnazjum w Krakowie. Kolega z klasy, mówi³ o Banachu: "(...) Stefan by³ ch³opcem spokojnym, nie pozbawionym ³agodnego humoru, dobrym koleg±. By³ zawsze w czystym porz±dnym mundurku." Bêd±c jeszcze w gimnazjum studiowa³ samodzielnie teorie funkcji rzeczywistych z francuskiego podrêcznika Tannery'ego. Jezyk francuski zna³ od dziecinstwa - uczy³ go Luis Mien. Stefan zna³ te¿ niemiecki, ³acinê i grekê. W gimnazjum uchodzi³ za s³abego ucznia, dobre wyniki uzyskiwa³ jedynie w matematyce i gramatyce ³acinskiej. Jego genialne zdolno¶ci matematyczne odkry³ przypadkowo latem 1916 roku Hugo Steinhaus. Przys³uchuj±c sie jego rozmowie z Otto Nikodymem na temat ca³ki Lebesuque'a. Stefan Banach studiowa³ na Politechnice we Lwowie. Mimo fascynacji matematyk± by³y to studia in¿ynierskie. Zaliczy³ po³owe tych studiów a dalsz± nauke przerwa³a wojna. Po wojnie Banach nie wróci³ do Lwowa by ukonczyæ studia nigdy te¿ nie ukonczy³ ¿adnych innych. Pytany kiedy¶ przez syna dlaczego, odpowiedzia³: "Nie interesowa³ mnie kurs uniwersytecki, mia³em go w jednym palcu, by³em ju¿ zupe³nie daleko..."

54. Polish School Of Mathematics Any Examination Of Twentieth Century As noted above, Janiszewski, along with stefan banach, Waclaw Sierpinski, andStanislaw Hugo Steinhaus often bragged that stefan banach was his greatest http://www.math.wfu.edu/~kuz/Stamps/PolishSchool/PolishSchool.htm

Polish School of Mathematics Any examination of twentieth century mathematics shows the surprising depth, originality and quantity of Polish contributions to the discipline. Similarly, any list of important twentieth century mathematicians contains Polish names in a frequency out of proportion to the size of the country. How did such creativity and mathematical influence develop in a country that had little tradition in research, that was partitioned under foreign domination from 1795 until the end of World War I, and whose educational institutions were suppressed by foreign powers. Surprisingly, it was planned! What was to become known as the Polish School of Mathematics was established following a plan proposed by Zygmunt Janiszewski. Poradnik dla Samoukow (Guidebooks for Self-Instruction) . These were designed to get around the Russian and German e ducational restrictions and were written by prominent mathematicians including Janiszewski, Sierpinski, and Zaremba; they covered topics such as series, differential and integral equations, and topology. Another series it supported was ; the first issue (1917) contained two articles which were to be very important to the establishment of the Polish School of Mathematics.

55. Encyclopedia: Stefan Banach In mathematics, banach spaces, named after stefan banach who studied them, In functional analysis, a banach algebra, named after stefan banach, http://www.nationmaster.com/encyclopedia/Stefan-Banach

Supporter Benefits Signup Login Sources ... Pies Related Articles People who viewed "Stefan Banach" also viewed: Banach algebra Stanislaw Mazur Banach_Steinhaus theorem Banach space ... Samuel Eilenberg What's new? Our next offering Latest newsletter Student area Lesson plans Recent Updates Aerocoach Aeneid Adyghe language Acapulco ... More Recent Articles Top Graphs Richest Most Murderous Most Taxed Most Populous ... More Stats Encyclopedia: Stefan Banach Updated 38 days 16 hours 44 minutes ago. Other descriptions of Stefan Banach Stefan Banach Stefan Banach March 30 in Krak³w Poland August 31 in L'viv Ukraine ), was a Polish mathematician , one of the moving spirits of the Lw³w School of Mathematics in pre-war Poland . He was largely self-taught in mathematics; his genius was accidentally discovered by Hugo Steinhaus Stefan Banach User:Stako 08:59, 10 Feb 2005 (UTC)~ File links The following pages link to this file: Stefan Banach Categories: GFDL images ... Stefan Banach User:Stako 08:59, 10 Feb 2005 (UTC)~ File links The following pages link to this file: Stefan Banach Categories: GFDL images ... March 30 is the 89th day of the year in the Gregorian Calendar (90th in Leap years). ...

56. American Mathematical Monthly: June-July, 1997 The Life of stefan banach. By Roman Kaluza by Sheldon Axler. 101 Careers inMathematics. Edited by Andrew Sterrett by J. Kevin Colligan. TELEGRAPHIC REVIEWS http://www.maa.org/pubs/monthly_june97_toc.html

Search MAA Online MAA Home January February ... December Click on the months above to see summaries of articles in the M ONTHLY An archive for all the 1997 issues is now available American Mathematical Monthly June-July, 1997 Approximate Isometries on Euclidean Spaces by Rajendra Bhatia and Peter Semrl rbh@isid.ernet.in, peter.semrl@uni-mb.si These two theorems are explained in this paper. It is also shown that if X is a Euclidean space, and Y=X, then the conclusion of the Hyers-Ulam Theorem is unaffected if surjectivity is dropped from the hypotheses. The method of proof uses the Hyers-Ulam ideas, but includes modifications that lead to sharp bounds. How To Do Monthly Problems With Your Computer wilf@math.upenn.edu, Istvan.Nemes@risc.uni-linz.ac.at, Marko.Petkovsek@mat.uni-lj.si, zeilberg@euclid.math.temple.edu The problem of finding simple evaluations of major classes of sums that involve factorials, binomial coefficients, and their q-analogues, has been completely solved. Sums that have the rather general form specified in Section 3 can all be done algorithmically, that is to say, you can do them on your own PC. Your computer evaluates the sum as a simple formula, if that's possible, and gives you a proof that you can check, or gives you a proof that your sum cannot be "done" in simple closed form, if that is the case. We first briefly describe the algorithms and the theory that have achieved this goal. Second, to illustrate both the scope of the method and the fact that in some interesting cases human intervention still helps, we show how these computer methods would have fared in attacking 27 problems that have appeared over the years in the Problems section of this MONTHLY.

57. Biografia De Banach, Stefan Translate this page banach, stefan. (1892-1945) Matemático polaco, n. en Cracovia y m. en Lvov, quedesarrolló el modelo matemático de análisis funcional y la teoría de los http://www.biografiasyvidas.com/biografia/b/banach.htm

Inicio Buscador Las figuras clave de la historia Reportajes Los protagonistas de la actualidad Banach, Stefan (1892-1945) Matemático polaco, n. en Cracovia y m. en Lvov, que desarrolló el modelo matemático de análisis funcional y la teoría de los vectores espaciales y de los espacios lineales normados. Desde 1927 fue profesor de la Universidad de Lvov y en 1932 publicó su más importante libro, Théorie des opérations linéaires, en el que desarrolla su teoría del análisis funcional y un sistema de conceptos y teoremas que inspiró los trabajos de matemáticas puras de las siguientes décadas. Inicio Buscador Recomendar sitio

58. Legendsscience stefan banach Waclaw Sierpinski Florian Witold Znaniecki The soul, on theother hand, was personified by stefan banach at the University of Lwow http://www.polamjournal.com/Library/Biographies/legendsscience/legendsscience.ht

Contributions of Polish Men and Women of Science and Mathematics by Jan P. Muczyk Polish American Journal, September 1994 M ikolaj Kopernik Jan Heweliusz Tadeusz Banachewicz ... Alfred Korzybski M ikolaj Kopernik Latin Nicolaus Copernicus, was the son of a Torun burgher. Copernicus completed mathematical and astronomical studies at Krakow University (also known as the Jagiellonian University) and then studied the liberal arts at Bologna, medicine at Padua, and law at the University of Ferrara, from which he emerged with a doctorate in canon law. Using the instruments he constructed (the originals are in the Uppsala museum in Sweden, taken by the Swedes during the Deluge), Copernicus discovered and proved the heliocentric system, upsetting the medieval notion that the earth was the center of the universe. His theory, "De Revolutionibus Orbium Coelestium," was published in Nuremberg, May 24, 1543, while Copernicus was on his deathbed. He was reluctant to have it published earlier because it was in conflict with the official teachings of the Catholic Church, which had adopted the Ptolemaic system because it was compatible with the literal interpretations of the Bible. The Copernican view was later corroborated and improved by the great German astronomer, Johannes Kepler (1771-1630) who, relying on the empirical measurements of the Danish astronomer, Tycho Brahe (1546-1601) made the orbits of the planets elliptical rather than circular.

59. Stefan Banach-genialny Lwowski Matematyk stefan banach urodzil sie 30 marca 1892 roku w Krakowie. stefan banach Wiadomojedynie, ze pochodzil z rodziny góralskiej i ze dziecinstwo mial bardzo http://www.lwow.com.pl/m.htm

Zajêcia z matematyki na 3 i 4 semestrze podczas moich studiow na Politechnice Gdañskiej prowadzi³ "œwie¿o upieczony" doktor matematyki. Wtedy nazywaliœmy go "szalonym Heniem", bo i styl prowadzenia zajêæ by³ trochê niezwyczajny i tematy, ktore porusza³ wydawa³y nam siê dziwne, a na egzaminie pojawia³y siê tematy tak niebezpieczne, jak np. przeksztalcenie... sto³u w przestrzeni Banacha (teraz, kiedy nastêpne pokolenie zdobywa in¿ynierskie szlify na PG, wyk³adowca ten zdoby³ ju¿ miano "krwawego Henia") Ale nie o nim zasadniczo ma byæ mowa, lecz o bohaterze pewnej dziedziny matematyki, ca³kiem jak na tê naukê nowej, mianowicie - analizie funkcjonalnej . Wtedy jedn¹ z nielicznych pewnych dla nas wiadomoœci by³a ta, ¿e jednym z jej twórców by³ genialny polski matematyk - Stefan Banach Jakie¿ wiêc by³o moje zdumienie, gdy wêdruj¹c po Cmentarzu £yczakowskim, tu¿ obok znanego grobu Marii Konopnickiej, na solidnym - z czarnego granitu wykonanym grobowcu rodziny Riedlow zobaczy³em nazwisko Stefana Banacha, zmar³ego we Lwowie 31.VIII.1945 roku i pochowanego tam w³aœnie, obok poetki, na grobie której niezale¿nie od pory roku s¹ zawsze œwie¿e kwiaty. Bêd¹c tam spójrzmy na s¹siedni - z lewej strony stoj¹cy - grobowiec Riedlów i z³ó¿my i tam symboliczny kwiat temu wybitnemu Polakowi, znanemu wœród matematycznej braci ca³ego œwiata, twórcy znanej w œwiecie

60. B Index banach limit,; banach space,; banach, stefan,; banachAlaoglu theorem,;banach-Steinhaus theorem,; banach-Tarski theorem,; bang-bang principle,; bar, http://www.mathresources.com/products/mathresource/demo/indices/index_b.htm

B Vocabulary Index B, B*-algebra, Babbage's engine, backward difference, backward error analysis, backward induction, Baire category, Baire category theorem, Baire set, Baire space, baker's transformation, balanced, balanced block design, ball, Banach algebra, Banach contraction mapping theorem, Banach limit, Banach space, Banach, Stefan, Banach-Alaoglu theorem, Banach-Steinhaus theorem, Banach-Tarski theorem, bang-bang principle, bar, bar chart, bar induction, Barcan formula, barrel, barrelled, barrier function, barycenter, barycentric coordinates, base, base clause, base field, base period, basic feasible solution, basic variables, basis, basis theorem, Bayes's theorem, Bayesian, bcd, Begriffsschrift behavioural variable, bell-shaped curve, Bellman's principle of optimality, below, bending moment, Bernoulli equation, Bernoulli number, Bernoulli trial, Bernoulli's theorem, Bernoulli, Jakob, Bernstein polynomials, Bernstein's theorem, Berry's paradox, Bertrand's postulate, Bessel function, Bessel's equation

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

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