هرمان شڤارتس Hermann Schwarz
هرمان شڤارتس | |
|---|---|
Hermann Schwarz | |
_by_Louis_Zipfel.jpg&filetimestamp=20250328121251&) شڤارتس ح. 1890 | |
| وُلِدَ | 25 يناير 1843 |
| توفي | 30 نوفمبر 1921 (aged 78) |
| الجنسية | پروسي |
| المدرسة الأم | Gewerbeinstitut |
| عـُرِف بـ | Cauchy–Schwarz inequality |
| السيرة العلمية | |
| المجالات | رياضيات |
| الهيئات | جامعة هاله Swiss Federal Polytechnic Göttingen University |
| المشرف على الدكتوراه | Karl Weierstrass Ernst Kummer |
| طلاب الدكتوراه | Lipót Fejér Harris Hancock Gerhard Hessenberg Paul Koebe Leon Lichtenstein Heinrich Maschke Robert Remak Rudolf Rothe Theodor Vahlen Ernst Zermelo |
Karl Hermann Amandus Schwarz (de; 25 January 1843 – 30 November 1921) was a German mathematician, known for his work in complex analysis.
الحياة
Schwarz was born in Hermsdorf, Silesia (now Sobieszów, Poland). In 1868 he married Marie Kummer,[1] who was the daughter to the mathematician Ernst Eduard Kummer[2] and Ottilie née Mendelssohn (a daughter of Nathan Mendelssohn's and granddaughter of Moses Mendelssohn). Schwarz and Kummer had six children, including his daughter Emily Schwarz.[2]
Schwarz originally studied chemistry in Berlin but Ernst Eduard Kummer and Karl Theodor Wilhelm Weierstrass persuaded him to change to mathematics.[3] He received his Ph.D. from the Universität Berlin in 1864 and was advised by Kummer and Weierstrass.[4] Between 1867 and 1869 he worked at the University of Halle, then at the Swiss Federal Polytechnic.[5] From 1875 he worked at Göttingen University,[5] dealing with the subjects of complex analysis, differential geometry and the calculus of variations. He died in Berlin.
العمل
Schwarz's works include Bestimmung einer speziellen Minimalfläche, which was crowned by the Berlin Academy in 1867 and printed in 1871, and Gesammelte mathematische Abhandlungen (1890).
Among other things, Schwarz improved the proof of the Riemann mapping theorem,[6] developed a special case of the Cauchy–Schwarz inequality, and gave a proof that the ball has less surface area than any other body of equal volume.[7] His work on the latter allowed Émile Picard to show solutions of differential equations exist (the Picard–Lindelöf theorem).[3]
In 1892 he became a member of the Berlin Academy of Science and a professor at the University of Berlin, where his students included Lipót Fejér, Paul Koebe and Ernst Zermelo. In total, he advised at least 22 Ph. D students.[4] In 1914 Schwarz's friends and former students published a volume with 34 articles in celebration of the 50th anniversary of his doctoral dissertation.[8]
His name is attached to many ideas in mathematics,[2] including the following:
- Abstract additive Schwarz method
- Additive Schwarz method
- Schwarz alternating method
- Schwarzian derivative
- Schwarz function
- Schwarz lantern
- Schwarz lemma
- Schwarz's list
- Schwarz minimal surface
- Schwarz theorem (also known as Clairaut's theorem)
- Schwarz integral formula
- Schwarz–Christoffel mapping
- Schwarz–Ahlfors–Pick theorem
- Schwarz reflection principle
- Schwarz triangle
- Schwarz triangle function
- Cauchy–Schwarz inequality
- Theorem of Pohlke and Schwarz
المنشورات
- Schwarz, H. A. (1871), Bestimmung einer speziellen Minimalfläche, Dümmler, https://books.google.com/books?id=7HEXcgAACAAJ
- Schwarz, H. A. (1972), Gesammelte mathematische Abhandlungen. Band I, II, Bronx, N.Y.: AMS Chelsea Publishing, ISBN 978-0-8284-0260-6, https://archive.org/details/gesammeltemathem01schwuoft
الهامش
- ^ Carathéodory, C (1921). "Hermann Amandus Schwarz". Deutsches biographisches Jahrbuch. III (6): 236–238. Bibcode:1921ZaMM....1..494M. doi:10.1002/zamm.19210010615. Retrieved 7 July 2021.
- ^ أ ب ت Agarwal, Ravi; Sen, Syamal (2014-11-11). Creators of Mathematical and Computational Sciences (in الإنجليزية). Springer. pp. 297–298. ISBN 9783319108704.
- ^ أ ب O'Connor, J. J.; Robertson, E. F. "Schwarz biography". www-gap.dcs.st-and.ac.uk. The MacTutor History of Mathematics. Archived from the original on 2016-06-05. Retrieved 2016-05-22.
- ^ أ ب "The Mathematics Genealogy Project – Hermann Schwarz". www.genealogy.math.ndsu.nodak.edu. Retrieved 2016-05-22.
- ^ أ ب Chang, Sooyoung (2011-01-01). Academic Genealogy of Mathematicians (in الإنجليزية). World Scientific. pp. 77–78. ISBN 9789814282291.
- ^ Bottazzini, Umberto (2003-04-30). "Algebraic truths vs geometric fantasies: Weierstrass' Response to Riemann". arXiv:math/0305022.
- ^ Schwarz, Hermann Amandus (1884). "Proof of the theorem that the ball has less surface area than any other body of the same volume". News of the Royal Society of Sciences and the Georg-August-Universität Göttingen. 1884: 1–13.
- ^ Gronwall, T. H. (1916). "Book Review: Mathematische Abhandlungen, Hermann Amandus Schwarz zu seinem fünfzigjährigen Doktorjubiläum am 6. August 1914 gewidmet von Freunden und Schülern". Bulletin of the American Mathematical Society. 22 (8): 406–408. doi:10.1090/S0002-9904-1916-02811-4.
وصلات خارجية
- O'Connor, John J.; Robertson, Edmund F., "هرمان شفارتس", MacTutor History of Mathematics archive
- هرمان شفارتس at the Mathematics Genealogy Project
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- مواليد 1843
- وفيات 1921
- 20th-century German mathematicians
- 19th-century German mathematicians
- Academic staff of ETH Zurich
- Academic staff of the University of Göttingen
- Academic staff of the Martin Luther University of Halle-Wittenberg
- Academic staff of the Humboldt University of Berlin
- Corresponding members of the Saint Petersburg Academy of Sciences
- People from the Province of Silesia
- People from Głogów County
- Members of the Royal Society of Sciences in Uppsala