Jovan Karamata at work

Jovan Karamata (Serbian] Cyrillic: Јован Карамата) (1902-1967) was one of the greatest Serbian mathematicians of the 20th century. Image File history File links Karamata. ... Image File history File links Karamata. ... The Serbian language is one of the standard versions of the Å tokavian dialect (former standard was known as Serbo-Croatian language). ... The Cyrillic alphabet (or azbuka, from the old name of the first letters) is an alphabet used to write six natural Slavic languages (Belarusian, Bulgarian, Macedonian, Russian, Serbian, and Ukrainian) and many other languages of the former Soviet Union, Asia and Eastern Europe. ... 1902 (MCMII) was a common year starting on Wednesday (see link for calendar). ... 1967 (MCMLXVII) was a common year starting on Sunday of the Gregorian calendar. ... ... A mathematician is a person whose area of study and research is mathematics. ... (19th century - 20th century - 21st century - more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s As a means of recording the passage of time, the 20th century was that century which lasted from 1901–2000 in the sense of the Gregorian calendar (1900–1999 in the...

Life

Jovan Karamata was born in Zagreb on February 1, 1902 to a Serbian-Aromanian father and a Serbian mother. His family descends from a merchant family from the city of Zemun in Serbia. His family's business affairs on the borders of the Austro-Hungarian and Ottoman empires were very well known. In 1914, he finished most of his primary school in Zemun but because of constant warfare on the borderlands, Karamata's father sent him, together with his brothers and his sister, to Switzerland for their own safety. In Lausanne, 1920, he finished primary school oriented towards mathematics and sciences. In the same year he enrolled at the Engineering faculty of Belgrade University and, after several years moved to the Philosophy and Mathematicians sector, where he graduated in 1925. February 1 is the 32nd day of the year in the Gregorian Calendar. ... 1902 (MCMII) was a common year starting on Wednesday (see link for calendar). ... ... Aromanians (also called: Macedo-Romanians or Vlachs, in Aromanian they call themselves arumâni, armâni or aromâni) are a population living as a minority in Northern Greece, Serbia, the Former Yugoslav Republic of Macedonia, Bulgaria; their number is estimated to about one or two million. ... Coat of Zemun Zemun (Земун, Hungarian: Zimony, German: Semlin) is a major suburb of Belgrade situated on the left bank of the Sava river. ... The Republic of Serbia (Serbian: Република Србија) is a republic in southeastern and central Europe, which is united with Montenegro in a loose commonwealth known as the State Union of Serbia and Montenegro. ... Austria-Hungary, also known as the Dual monarchy (or: the k. ... Ottoman (in Turkish Osmanlı) may refer to: Look up Ottoman and ottoman in Wiktionary, the free dictionary. ... 1914 (MCMXIV) is a common year starting on Thursday. ... Coat of Zemun Zemun (Земун, Hungarian: Zimony, German: Semlin) is a major suburb of Belgrade situated on the left bank of the Sava river. ... Lausanne (, ) is a city in the French-speaking part of Switzerland, situated on the shores of Lake Geneva (French: Lac Léman), and facing Évian-les-Bains (France). ... 1920 (MCMXX) was a leap year starting on Thursday (link will take you to calendar) // Events January January 7 - Forces of Russian White admiral Kolchak surrender in Krasnoyarsk. ... University of Belgrade is the highest educational institution in Belgrade and Serbia. ... 1925 (MCMXXV) was a common year starting on Thursday (link will take you to calendar). ...

He spent the years 1927-1928 in Paris, as a fellow of the Rockefeller Foundation, and in 1928 he became Assistant for Mathematics at the Faculty of Philosophy of Belgrade University. In 1930 he became Assistant Professor, in 1937 Associate Professor and, after the end of World War II, in 1950 he became Full Professor. In 1951 he was elected Full Professor at the University of Geneva. In 1933 he became a member of Yugoslav Academy of Science, Czech Royal Society in 1936, and Serbian Royal Academy in 1939 as well as a fellow of Serbian Academy of Sciences in 1948. He was one of the founders of the Mathematical Institute of the Serbian Academy of Sciences and Arts in 1946. 1927 (MCMXXVII) was a common year starting on Saturday (link will take you to calendar). ... 1928 (MCMXXVIII) was a leap year starting on Sunday (link will take you to calendar). ... The Eiffel Tower has become a symbol of Paris throughout the world. ... The Rockefeller Foundation is a charitable organization that operates out of New York City. ... 1928 (MCMXXVIII) was a leap year starting on Sunday (link will take you to calendar). ... 1930 (MCMXXX) is a common year starting on Wednesday. ... Combatants Allies: • Soviet Union, • UK & Commonwealth, • USA, • France/Free France, • China, • Poland, • ...and others Axis: • Germany, • Japan, • Italy, • ...and others Commanders Strength Casualties Full list Full list World War II, also known as the Second World War, was a large scale military conflict that took place between 1939 and 1945. ... 1950 (MCML) was a common year starting on Sunday (link will take you to calendar). ... The University of Geneva (Université de Genève) is one of the oldest universities in the world. ... 1933 (MCMXXXIII) was a common year starting on Sunday (link will take you to calendar). ... 1936 (MCMXXXVI) was a leap year starting on Wednesday (link will take you to calendar). ... 1939 (MCMXXXIX) was a common year starting on Sunday (link will take you to calendar). ... 1948 (MCMXLVIII) was a leap year starting on Thursday (the link is to a full 1948 calendar). ... 1946 (MCMXLVI) was a common year starting on Tuesday. ...

Karamata was member of the Swiss, French and German mathematical societies, the French Association for the Development of Science, and the primary editor of the journal L’Enseignement Mathématique in Geneva. He also taught at the University of Novi Sad. Geneva (French: Genève, German: Genf, Italian: Ginevra) is the second most populous city in Switzerland, situated where Lake Geneva (French Lac Léman) flows into the Rhône River. ... The University of Novi Sad (Univerzitet u Novom Sadu/Универзитет у Новом Саду) is a university located in Novi Sad, the second largest city in Serbia and Montenegro. ...

In 1931 he married Emilija Nikolajevic, who gave birth to their two sons and a daughter. His wife died in 1959. After a long illness, Jovan Karamata died on August 14, 1967 in Geneva. His ashes rest in his native town of Zemun. 1931 (MCMXXXI) is a common year starting on Thursday. ... 1959 (MCMLIX) was a common year starting on Thursday of the Gregorian calendar. ... August 14 is the 226th day of the year in the Gregorian Calendar (227th in leap years), with 139 days remaining. ... 1967 (MCMLXVII) was a common year starting on Sunday of the Gregorian calendar. ...

Legacy

Jovan Karamata was one of the most prolific mathematicians of his time. He published 122 scientific papers, 15 monographs and text-books as well as 7 professional-pedagogical papers. Karamata is best known for his work on mathematical analysis. He created the theory of regularly-varying sequences and theorems of Tauberian type: today described as Karamata's Tauberian theorems. Karamata also added to numerous other theorems, including the Weierstrass theorem, Schmidt theorem, and Littlewood's theorem. These works, as well as those related to slowly varying functions, Mercer’s theorems, inequalities, trigonometrical integrals, Froullani’s integrals, and others have frequently been quoted in various papers. In Serbia, Karamata is immortalized in the "Karamata s (Yugoslav) school of mathematics”. Today, Karamata is the most frequently cited Serbian mathematican. He is the developer and co-developer of dozens of mathematicial theorems and has a lasting influence in 20th century mathematics. Analysis is the generic name given to any branch of mathematics which depends upon the concepts of limits and convergence, and studies closely related topics such as continuity, integration, differentiability and transcendental functions. ... In mathematics, a large number of methods have been proposed for the summation of divergent series. ... Karl Theodor Wilhelm Weierstraß (October 31, 1815 – February 19, 1897) was a German mathematician who is often cited as the father of modern analysis. (The letter ß may be transliterated as ss; one often writes Weierstrass. ... John Edensor Littlewood (June 9, 1885 - September 6, 1977) was a British mathematician. ... James Mercer (January 15, 1883 - February 21, 1932) was a mathematician, born in Bootle, Liverpool, England. ...

See also

• Mathematical Analysis
• Tauberian theorem
• Lah number
• Stirling number
• John Edensor Littlewood
• Mihailo Petrovic

Analysis is the generic name given to any branch of mathematics which depends upon the concepts of limits and convergence, and studies closely related topics such as continuity, integration, differentiability and transcendental functions. ... In mathematics, a large number of methods have been proposed for the summation of divergent series. ... In mathematics, Lah numbers, discovered by Ivo Lah in 1955 are coefficients expressing rising factorials in terms of falling factorials. ... In mathematics, Stirling numbers arise in a variety of combinatorics problems. ... John Edensor Littlewood (June 9, 1885 - September 6, 1977) was a British mathematician. ... Mihailo Petrovic-Alas - the famous Serbian mathematician and inventor Mihailo Petrović Alas (Serbian Cyrillic: Михаило Петровић Алас) (1868 - 1943), was a greatly influential Serbian mathematician and inventor. ...

Resources

External links

• Jovan Karamata Biography and Analysis of Work
• Jovan Karamata Biography and Achievements

Further reading

1. N.H. Bingham, C.M. Goldie, J.L. Teugels, Regular Variation, Encyclopedia of Mathematics and its Applications, vol. 27, Cambridge Univ. Press, 1987.
2. J.L. Geluk, L. de Haan, Regular Variation Extensions and Tauberian Theorems, CWI Tract 40, Amsterdam, 1987.
3. Maric V, Radasin Z, Regularly Varying Functions in Asymptotic Analysis
4. Nikolic A, About two famous results of Jovan Karamata, Archives Internationales d’Histoire des Sciences
5. Nikolic A, Jovan Karamata (1902-1967), Lives and work of the Serbian scietists, SANU, Biographies and bibliographies, Book 5
6. Tomic M, Academician Jovan Karamata, on occasion of his death, SANU, Vol CDXXIII, t. 37, Belgrade, 1968 (in Serbian)
7. Tomic M, Jovan Karamata (1902-1967), L’Enseignement Mathématique
8. Tomic M, Aljancic S, Remembering Karamata, Publications de l’Institut Mathématique