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  1. Zermelo's axiom of choice: Its origins, development, and influence (Studies in the history of mathematics and physical sciences 8) by Gregory H. Moore, 1982-11-17
  2. Ernst Zermelo: An Approach to His Life and Work by Heinz-Dieter Ebbinghaus, 2010-11-30
  3. Einführung in die Mengenlehre: Die Mengenlehre Georg Cantors und ihre Axiomatisierung durch Ernst Zermelo (Springer-Lehrbuch) (German Edition) by Oliver Deiser, 2009-10-29
  4. Ernst Zermelo - Collected Works/Gesammelte Werke: Volume I/Band I - Set Theory, Miscellanea/Mengenlehre, Varia (Schriften der Mathematisch-naturwissenschaftlichen ... Wissenschaften) (English and German Edition) by Ernst Zermelo, 2010-03-05
  5. Ernst Zermelo - Collected Works/Gesammelte Werke: Volume II/Band II - Calculus of Variations, Applied Mathematics, and Physics/Variationsrechnung, Angewandte ... und Physik (English and German Edition) by Ernst Zermelo, 2011-06-29
  6. Untersuchungen zur Variations-rechnung (German Edition) by Ernst Zermelo, 1894-01-01
  7. Gesammelte Abhandlungen mathematischen und philosophischen Inhalts: Mit erläuternden Anmerkungen sowie mit Ergänzungen aus dem Briefwechsel Cantor-Dedekind (German Edition) by Georg Cantor, 1980-09-01
  8. Untersuchungen zur Variations-Rechnung, Inaugural-Dissertation... von Ernst Zermelo,... by Ernst Friedrich Ferdinand (1871-1953). ZERMELO, 1894-01-01
  9. Gesammelte Abhandlungen Mathematischen Und Philosophischen Inhalts by Georg, Herausgegeben Von Ernst Zermelo Cantor, 1966

1. Zermelo
Ernst Friedrich Ferdinand Zermelo. Born 27 Ernst Zermelo s parents wereFerdinand Zermelo and Maria Augusta Elisabeth Ziegler. His father
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Zermelo.html
Ernst Friedrich Ferdinand Zermelo
Born: 27 July 1871 in Berlin, Germany
Died: 21 May 1953 in Freiburg im Breisgau, Germany
Click the picture above
to see a larger version Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index
Ernst Zermelo Gymnasium in Berlin and he graduated from the gymnasium in 1889. At this time it was the custom for students in Germany to study at a number of different universities and indeed that is precisely what Zermelo did. His studies were undertaken at three universities, namely Berlin, Halle and Freiburg, and the subjects he studied were quite wide ranging and included mathematics, physics and philosophy. At these universities he attended courses by Frobenius , Lazarus, Fuchs Planck Schmidt Schwarz and Edmund Husserl. This was an impressive collection of inspiring lecturers and Zermelo began to undertake research in mathematics after completing his first degree. His doctorate was completed in 1894 when the University of Berlin awarded him the degree for a dissertation Untersuchungen zur Variationsrechnung which followed the Weierstrass approach to the calculus of variations . In this thesis he [1]:- ... extended Weierstrass 's method for the extrema of integrals over a class of curves to the case of integrands depending on derivatives of arbitrarily high order, at the same time giving a careful definition of the notion of neighbourhood in the space of curves.

2. Education World Search
zermelo ernst Friedrich Ferdin and Zermelo (18711953) Zermelo in 1908 was the first to attempt an and.ac.uk/~history/Mathematicians/ Zermelo.html. Meissel. Ernst. http//www-groups
http://www.educationworld.com/search/search.jhtml;$sessionid$CYMF1MIAADJGFQFIABV

3. Ernst Zermelo - Wikipedia, The Free Encyclopedia
Printable version Disclaimers. Not logged in. Log in Help. Other languages Deutsch. Ernst Zermelo. ( Ernst Friedrich Ferdinand Zermelo ( July 27, 1871 May 21, 1953) was a Germanmathematician .
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Ernst Zermelo
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From Wikipedia , the free encyclopedia.
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Ernst Friedrich Ferdinand Zermelo July 27 May 21 ) was a German mathematician Zermelo was born in Berlin Germany . His secondary school education was at the Luisenstädtisches Gymnasium in Berlin where he graduated in . He then studied mathematics physics and philosophy at the universities of Berlin Halle and Freiburg . He finished his doctorate in and was awarded by the University of Berlin for his dissertation on the calculus of variations . Zermelo remained at the University of Berlin where he was appointed assistant to Planck and under his guidance began to study hydrodynamics . In , Zermelo went to Göttingen , at that time the leading centre for mathematical research in the world, where he completed his thesis in In , in the Paris conference of the International Congress of Mathematicians David Hilbert challenged the mathematical community with his famous Hilbert's problems , a list of 23 unsolved fundamental questions which mathematicians should attack during the coming century. The first of these, a problem of set theory , was the continuum hypothesis introduced by Cantor in Zermelo began to work on the problems of set theory and in published his first work concerning the addition of transfinite cardinals . In 1904, he succeeded in taking the first step suggested by Hilbert towards the

4. Ernst Zermelo - Wikipedia, The Free Encyclopedia
Ernst Zermelo. From Wikipedia, the free encyclopedia. Ernst Friedrich FerdinandZermelo (July 27, 1871 May 21, 1953) was a German mathematician.
http://en.wikipedia.org/wiki/Ernst_Zermelo
Ernst Zermelo
Categories Mathematicians
From Wikipedia , the free encyclopedia.
Ernst Friedrich Ferdinand Zermelo July 27 May 21 ) was a German mathematician Zermelo was born in Berlin Germany . His secondary school education was at the Luisenstädtisches Gymnasium in Berlin where he graduated in . He then studied mathematics physics and philosophy at the universities of Berlin Halle and Freiburg . He finished his doctorate in and was awarded by the University of Berlin for his dissertation on the calculus of variations . Zermelo remained at the University of Berlin where he was appointed assistant to Planck and under his guidance began to study hydrodynamics . In , Zermelo went to Göttingen , at that time the leading centre for mathematical research in the world, where he completed his thesis in In , in the Paris conference of the International Congress of Mathematicians David Hilbert challenged the mathematical community with his famous Hilbert's problems , a list of 23 unsolved fundamental questions which mathematicians should attack during the coming century. The first of these, a problem of set theory , was the continuum hypothesis introduced by Cantor in Zermelo began to work on the problems of set theory and in published his first work concerning the addition of transfinite cardinals . In 1904, he succeeded in taking the first step suggested by Hilbert towards the

5. Ernst Zermelo
Ernst Zermelo. Ernst Friedrich Ferdinand Zermelo (July 27, 1871 May 21,1953) was a German mathematician. Zermelo was born in Berlin, Germany.
http://www.fact-index.com/e/er/ernst_zermelo.html
Main Page See live article Alphabetical index
Ernst Zermelo
Ernst Friedrich Ferdinand Zermelo July 27 May 21 ) was a German mathematician Zermelo was born in Berlin Germany . His secondary school education was at the Luisenstädtisches Gymnasium in Berlin where he graduated in . He then studied mathematics physics and philosophy at the universities of Berlin Halle and Freiburg . He finished his doctorate in and was awarded by the University of Berlin for his dissertation on the calculus of variations . Zermelo remained at the University of Berlin where he was appointed assistant to Planck and under his guidance began to study hydrodynamics . In , Zermelo went to Göttingen , at that time the leading centre for mathematical research in the world, where he completed his thesis in In , in the Paris conference of the International Congress of Mathematicians David Hilbert challenged the mathematical community with his famous Hilbert's problems , a list of 23 unsolved fundamental questions which mathematicians should attack during the coming century. The first of these, a problem of set theory , was the continuum hypothesis introduced by Cantor in Zermelo began to work on the problems of set theory and in published his first work concerning the addition of transfinite cardinalss . In 1904, he succeeded in taking the first step suggested by Hilbert towards the

6. Ernst Zermelo | Mathe Board Lexikon
Translate this page Ernst Zermelo. Definition, Erklärung, Bedeutung. Ernst Zermelo. ErnstFriedrich Ferdinand Zermelo (* 27. Juli 1871 in Berlin, † 21.
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Ernst Zermelo
Ernst Friedrich Ferdinand Zermelo 27. Juli in Berlin 21. Mai in Freiburg im Breisgau ) war ein deutscher Mathematiker Zermelo besuchte das Luisenstädtisches Gymnasium in Berlin bis zum Abitur . Er studierte Mathematik Physik und Philosophie an den Universität en von Berlin, Halle (Saale) und Freiburg . Er graduierte und wurde für seine Doktorarbeit von der Universität Berlin ausgezeichnet. Dort studierte er unter Max Planck Hydrodynamik ging Zermelo nach Göttingen , damals das Weltzentrum der Mathematik. bekam Zermelo den Lehrstuhl für Mathematik an der Universität Zürich , den er wieder aufgab. Er arbeitete ab ehrenhalber in Freiburg im Breisgau, gab diese Arbeit als Protest gegen Hitler wieder auf. Nach dem Zweiten Weltkrieg bezog er seine Position wieder bis
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7. Zermelo
Translate this page zermelo ernst, allemand, 1871-1953. Etudiant à Berlin, Zermelo enseignaà Göttingen, Zürich et Freiburg. Auteur du célèbre
http://www.sciences-en-ligne.com/momo/chronomath/chrono2/Zermelo.html
ZERMELO Ernst, allemand, 1871-1953 axiome du choix Fraenkel Skolem Cantor Fraenkel ) dits parfois ZF ou ZFC, pour signifier respectivement axiomes de Z ermelo- F raenkel et axiomes de Z ermelo- F raenkel axiome du C hoix L'axiome du choix :
d'existence crise des fondements
Russell
Le produit cartésien de toute classe d'ensembles non vides est non vide ou encore : Pour toute classe d'ensembles non vides et disjoints, en nombre fini ou non, il existe un algorithme (dit fonction de choix d'ensembles : choisir, c'est discerner un élément parmi d'autres. Dans le cas fini ou dénombrable, les éléments peuvent être rangés, comptés; on peut alors choisir. Mais dans le cas infini non dénombrable, comment choisir dans un ensemble continu Peano Hadamard Lebesgue ... Baire et Borel En 1938, sans l'axiome du choix et sans l' , alors elle le demeure avec leurs adjonctions.
En 1963, Paul J. Cohen
L
'axiome du choix bon ordre sur un ensemble : Cantor se posa la question de savoir (1883) s'il existait, sur un ensemble, une N est trivial : l'ordre total usuel est manifestement un bon ordre. Mais concernant R Zorn : Les 23 problèmes de Hilbert : Pour en savoir plus :

8. Ernst Zermelo
Ernst Zermelo.
http://wikipedia.infostar.cz/e/er/ernst_zermelo.html
švodn­ str¡nka Tato str¡nka v origin¡le
Ernst Zermelo
Ernst Friedrich Ferdinand Zermelo 27. července 21. května ) byl Němec matematik Zermelo byl narozen v Berl­n Německo . Jeho středoÅ¡kolsk© vzděl¡n­ bylo u Luisenst � dtisches tělocvična v Berl­ně kde on promoval v . On pak studoval matematika fyzika a filozofie u univerzit Berl­n Halle a Freiburg . On dokončil jeho doktor¡t v a byl udělen Univerzita Berl­na pro jeho disertaci na počet variac­ . Zermelo zůstal u univerzity Berl­na kde on byl jmenov¡n asistentem k Planck a dolů jeho veden­ začalo studovat hydrodynamics . V , Zermelo Å¡el do G � ttingen , v t© době vedouc­ centrum pro matematick½ v½zkum na světě, kde on dokončil jeho tezi v V , v Pař­Å¾i konference Mezin¡rodn­ kongres matematiků David Hilbert napadal matematickou komunitu s jeho slavn½ Hilbertovy probl©my , seznam 23 nevyřeÅ¡en½ch z¡kladn­ch ot¡zek kteř­ matematici měl by ºtok během nadch¡zej­c­ho stolet­. Prvn­ tito, probl©m teorie množin , byl hypot©za kontinua představen½ Cantor v Zermelo začal pracovat na probl©mech teorie množin a v publikoval jeho prvn­ knihu ohledně sč­t¡n­ transfinite cardinalss . V 1904, on uspěl v br¡t navrhovan½ prvn­ krok Hilbert k

9. Ernst Zermelo - Information
An online Encyclopedia with information and facts Ernst Zermelo Information, anda wide range of other subjects. Ernst Zermelo - Information. deErnst Zermelo.
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Ernst Friedrich Ferdinand Zermelo July 27 May 21 ) was a German mathematician Zermelo was born in Berlin Germany . His secondary school education was at the Luisenstädtisches Gymnasium in Berlin where he graduated in . He then studied mathematics physics and philosophy at the universities of Berlin Halle and Freiburg . He finished his doctorate in and was awarded by the University of Berlin for his dissertation on the calculus of variations . Zermelo remained at the University of Berlin where he was appointed assistant to Planck and under his guidance began to study hydrodynamics . In , Zermelo went to Göttingen , at that time the leading centre for mathematical research in the world, where he completed his thesis in In , in the Paris conference of the International Congress of Mathematicians David Hilbert challenged the mathematical community with his famous Hilbert's problems , a list of 23 unsolved fundamental questions which mathematicians should attack during the coming century. The first of these, a problem of set theory , was the continuum hypothesis introduced by Cantor in Zermelo began to work on the problems of set theory and in published his first work concerning the addition of transfinite cardinals . In 1904, he succeeded in taking the first step suggested by Hilbert towards the

10. CELEBRITES 2
Translate this page logiciens de ce siècle. Par exemple, la flèche vole et est immobile.zermelo ernst. Mathématicien et logicien allemand. Il est né à
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Wagner Richard
Tristan et Isolde
Wasiti (al-)
Watson James Dewey
Watson-Watt sir Robert Alexander
Watt James
Wedgwood Josiah
Erturia
Whitehead Robert
Xenakis Iannis
Young Thomas
Yourcenar Marguerite de Crayencour
et Souvenirs pieux
Yun Isang
Zarqali (al-)
Zeeman Pieter
Zermelo Ernst
Zernike Frederik
Zwicky Fritz
Zworykin Vladimir

11. Ernst Zermelo - Wikipedia
Translate this page Ernst Zermelo. aus Wikipedia, der freien Enzyklopädie. Ernst FriedrichFerdinand Zermelo (* 27. Juli 1871 in Berlin, † 21.
http://de.wikipedia.org/wiki/Ernst_Zermelo
Ernst Zermelo
aus Wikipedia, der freien Enzyklopädie
Ernst Friedrich Ferdinand Zermelo 27. Juli in Berlin 21. Mai in Freiburg im Breisgau ) war ein deutscher Mathematiker Zermelo besuchte das Luisenstädtisches Gymnasium in Berlin bis zum Abitur . Er studierte Mathematik Physik und Philosophie an den Universitäten von Berlin, Halle (Saale) und Freiburg . Er graduierte und wurde für seine Doktorarbeit von der Universität Berlin ausgezeichnet. Dort studierte er unter Max Planck Hydrodynamik ging Zermelo nach Göttingen , damals das Weltzentrum der Mathematik. bekam Zermelo den Lehrstuhl für Mathematik an der Universität Zürich , den er wieder aufgab. Er arbeitete ab ehrenhalber in Freiburg im Breisgau, gab diese Arbeit als Protest gegen Hitler wieder auf. Nach dem Zweiten Weltkrieg bezog er seine Position wieder bis bearbeiten
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12. Einige Der Bedeutenden Mathematiker
Translate this page Wiener Norbert, 1894-1964. Wittgenstein Ludwig Josef, 1889-1951. WaringEdward, 1734-1798. Zenon von Elea, 490-430 v.Chr. zermelo ernst, 1871-1953.
http://www.zahlenjagd.at/mathematiker.html
Einige der bedeutenden Mathematiker
Abel Niels Hendrik Appolonius von Perga ~230 v.Chr. Archimedes von Syrakus 287-212 v.Chr. Babbage Charles Banach Stefan Bayes Thomas Bernoulli Daniel Bernoulli Jakob Bernoulli Johann Bernoulli Nicolaus Bessel Friedrich Wilhelm Bieberbach Ludwig Birkhoff Georg David Bolyai János Bolzano Bernhard Boole George Borel Emile Briggs Henry Brouwer L.E.J. Cantor Georg Ferdinand Carroll Lewis Cassini Giovanni Domenico Cardano Girolamo Cauchy Augustin Louis Cayley Arthur Ceulen, Ludolph van Chomsky Noel Chwarismi Muhammed Ibn Musa Al Church Alonzo Cohen Paul Joseph Conway John Horton Courant Richard D'Alembert Jean Le Rond De Morgan Augustus Dedekind Julius Wilhelm Richard Descartes René Dieudonné Jean Diophantos von Alexandria ~250 v. Chr. Dirac Paul Adrien Maurice Dirichlet Peter Gustav Lejeune Eratosthenes von Kyrene 276-194 v.Chr. Euklid von Alexandria ~300 v.Chr. Euler Leonhard Fatou Pierre Fermat Pierre de Fischer Ronald A Sir Fourier Jean-Baptiste-Joseph Fraenkel Adolf Frege Gottlob Frobenius Ferdinand Georg Galois Evariste Galton Francis Sir Gauß Carl Friedrich Germain Marie-Sophie Gödel Kurt Goldbach Christian Hadamard Jacques Hamilton William Rowan Hausdorff Felix Hermite Charles Heawood Percy Heron von Alexandrien ~60 n.Chr.

13. Zermelo
Ernst Friedrich Ferdinand Zermelo. Born 27 Ernst Zermelo attended coursesby Frobenius, Fuchs, Planck, Schmidt and Schwarz. He was
http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/Zrml.htm
Ernst Friedrich Ferdinand Zermelo
Born: 27 July 1871 in Berlin, Germany
Died: 21 May 1953 in Freiburg im Breisgau, Germany
Show birthplace location Previous (Chronologically) Next Biographies Index
Previous
(Alphabetically) Next Welcome page Ernst Zermelo attended courses by Frobenius Fuchs Planck Schmidt and Schwarz . He was appointed to a chair at Freiburg but he renounced his chair in 1935 because of disapproval of Hitler's regime. He was reinstated in 1946. Zermelo is best known for his work on the axiom of choice and axiomatic set theory. After studying the set paradoxes, he made the first attempt to axiomatise set theory in 1908. He gave seven axioms : Axiom of extensionality, Axiom of elementary sets, Axiom of separation, Power set axiom, Union axiom, Axiom of choice and Axiom of infinity. Zermelo usually stated his axioms and theorems in words rather than symbols. Zermelo, in fact, did not often use the formal language for quantifiers such as or and binding variables that were then being used, instead, he used ordinary expressions such as "there exists" or "for all". Zermelo also contributed to the calculus of variations and to statistical mechanics.

14. Ernst Zermelo - Wikipédia
Translate this page Autres langues Deutsch English. Ernst Zermelo. Ernst Friedrich Ferdinand Zermelo(27 juillet 1871 - 21 mai 1953) était un mathématicien allemand.
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15. Zermelo
Ernst Zermelo. Ernst Zermelo (18711953). Zermelo is the premiere Windows applicationfor running table tennis tournaments. Zermelo Imports a rating list.
http://www.davidmarcus.com/zermelo/
Ernst Zermelo (1871-1953) Zermelo is the premiere Windows application for running table tennis tournaments. Zermelo: Imports a rating list Makes the draw Calls matches and prints match cards Keeps track of which players have checked in or are playing Prints updated draw sheets that show all results Handles the most popular event formats: Single elimination Round robin (up to twelve players per group) Multiple round robin groups with one or two players advancing from each group to a single-elimination or round-robin second stage Submits results to Ratings Central or USATT Has a complete user's manual in PDF Is especially designed to handle USATT-sanctioned tournaments Is free for running Ratings Central tournaments in North America and reasonably priced for other tournaments System requirements are any computer running Windows 98, 98SE, ME, 2000, or XP (95 may also worktry it and see) and a printer. Your screen resolution must be at least 800 by 600 pixels.

16. Zermelo
Biography of ernst zermelo (18711953) ernst Friedrich Ferdinand zermelo. Born 27 July 1871 in Berlin, Germany ernst zermelo's parents were Ferdinand zermelo and Maria Augusta Elisabeth Ziegler
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Zermelo.html
Ernst Friedrich Ferdinand Zermelo
Born: 27 July 1871 in Berlin, Germany
Died: 21 May 1953 in Freiburg im Breisgau, Germany
Click the picture above
to see a larger version Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index
Ernst Zermelo Gymnasium in Berlin and he graduated from the gymnasium in 1889. At this time it was the custom for students in Germany to study at a number of different universities and indeed that is precisely what Zermelo did. His studies were undertaken at three universities, namely Berlin, Halle and Freiburg, and the subjects he studied were quite wide ranging and included mathematics, physics and philosophy. At these universities he attended courses by Frobenius , Lazarus, Fuchs Planck Schmidt Schwarz and Edmund Husserl. This was an impressive collection of inspiring lecturers and Zermelo began to undertake research in mathematics after completing his first degree. His doctorate was completed in 1894 when the University of Berlin awarded him the degree for a dissertation Untersuchungen zur Variationsrechnung which followed the Weierstrass approach to the calculus of variations . In this thesis he [1]:- ... extended Weierstrass 's method for the extrema of integrals over a class of curves to the case of integrands depending on derivatives of arbitrarily high order, at the same time giving a careful definition of the notion of neighbourhood in the space of curves.

17. Zermelo, Ernst (1871-1956) -- From Eric Weisstein's World Of Scientific Biograph
Mathematicians. Nationality. German. zermelo, ernst (18711956) German mathematician who formulated zermelo's Axiom of Choice ( the "axiom of choice."
http://scienceworld.wolfram.com/biography/Zermelo.html
Branch of Science Mathematicians Nationality German
Zermelo, Ernst (1871-1956)

German mathematician who formulated Zermelo's Axiom of Choice (the "axiom of choice.", which states that given any set of mutually exclusive nonempty sets, the exists at least one set that contains exactly one element in common with each of the nonempty sets.
Additional biographies: MacTutor (St. Andrews)

18. References For Zermelo
References for ernst zermelo. Articles GH Moore, ernst zermelo, AE Harward, andthe axiomatization of set theory, Historia Mathematica 3 (2) (1976), 206209.
http://www-gap.dcs.st-and.ac.uk/~history/References/Zermelo.html
References for Ernst Zermelo
  • Biography in Dictionary of Scientific Biography (New York 1970-1990). Books:
  • G Heinzmann (ed.), (Paris, 1986).
  • G H Moore, Zermelo's axiom of choice : its origins, development, and influence (New York, 1982).
  • J van Heijenoort, (Cambridge, Mass., 1966). Articles:
  • G H Moore, Ernst Zermelo, A E Harward, and the axiomatization of set theory, Historia Mathematica
  • Hist. Philos. Logic Main index Birthplace Maps Biographies Index
    History Topics
    ... Anniversaries for the year
    JOC/EFR February 1999 School of Mathematics and Statistics
    University of St Andrews, Scotland
    The URL of this page is:
    http://www-history.mcs.st-andrews.ac.uk/References/Zermelo.html
  • 19. Zermelo - Ernst Friedrich Ferdinand From FOLDOC
    zermelo ernst Friedrich Ferdinand. biography, history of philosophy German mathematician (1871-1953) who developed the first
    http://www.swif.uniba.it/lei/foldop/foldoc.cgi?Zermelo - Ernst Friedrich Ferdina

    20. Zermelo
    Biography (18711953).
    http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Zermelo.html
    Ernst Friedrich Ferdinand Zermelo
    Born: 27 July 1871 in Berlin, Germany
    Died: 21 May 1953 in Freiburg im Breisgau, Germany
    Click the picture above
    to see a larger version Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index
    Ernst Zermelo Gymnasium in Berlin and he graduated from the gymnasium in 1889. At this time it was the custom for students in Germany to study at a number of different universities and indeed that is precisely what Zermelo did. His studies were undertaken at three universities, namely Berlin, Halle and Freiburg, and the subjects he studied were quite wide ranging and included mathematics, physics and philosophy. At these universities he attended courses by Frobenius , Lazarus, Fuchs Planck Schmidt Schwarz and Edmund Husserl. This was an impressive collection of inspiring lecturers and Zermelo began to undertake research in mathematics after completing his first degree. His doctorate was completed in 1894 when the University of Berlin awarded him the degree for a dissertation Untersuchungen zur Variationsrechnung which followed the Weierstrass approach to the calculus of variations . In this thesis he [1]:- ... extended Weierstrass 's method for the extrema of integrals over a class of curves to the case of integrands depending on derivatives of arbitrarily high order, at the same time giving a careful definition of the notion of neighbourhood in the space of curves.

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