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Lajos Pósa (mathematician)

January 07, 2023

The native form of this personal name is Pósa Lajos. This article uses Western name order when mentioning individuals.

Lajos Pósa (born December 9, 1947 in Budapest) is a Hungarian mathematician working in the topic of combinatorics, and one of the most prominent mathematics educators of Hungary, best known for his mathematics camps for gifted students. He is a winner of the Széchenyi Prize. Paul Erdős's favorite "child", he discovered theorems at the age of 16. Since 2002, he has worked at the Rényi Institute of the Hungarian Academy of Sciences; earlier he was at the Eötvös Loránd University, at the Departments of Mathematical Analysis, Computer Science.

Biography

He was born in Budapest, Hungary on December 9, 1947. His father was a chemist, his mother a mathematics teacher. He was a child prodigy. While still in elementary school, the educator Rózsa Péter, friend of his mother introduced him to Paul Erdős, who invited him for lunch in a restaurant, and bombarded him with mathematical questions. Pósa finished the problems sooner than his soup, which impressed Erdős, who himself had been a child prodigy, and who supported young talents with much care and competence. That is how Pósa’s first paper was born, co-authored with Erdős (hence his Erdős number is 1).

He went to the first special mathematics class of the country at Fazekas Mihály Secondary School from 1962 to 1966, where his classmates included Miklós Laczkovich, László Lovász, József Pelikán [hu], Zsolt Baranyai, István Berkes, Katalin Vesztergombi, Péter Major. He won the first prize on the International Mathematical Olympiad in 1966 (Bulgaria) and second prize in 1965 (Germany).[1]

He started his Mathematics studies at ELTE University in 1966, and graduated in 1971. From 1971 to 1982 he worked at the Department of Mathematical Analysis at ELTE University, and he obtained a doctorate in 1983 with his dissertation about Hamiltonian circuits of random graphs. From 1984 to 2002 he worked at the Department of Computer Science at ELTE University, and since 2002 he has been a member of the Rényi Mathematical Institute.

Despite his significant results in mathematical research, he stopped research and devoted himself fully to Mathematics Education. Erdős, who preferred him among all his protégés, expressed his regret that Pósa had stopped research with the typical Erdős style phrase "Pósa is dead."

Mathematics education

He started teaching mathematics very early. He tutored his secondary school classmates, and during his first year at university he started teaching extracurricular courses at his former secondary school. His students at that time included: László Babai, György Elekes, Péter Komjáth, Imre Z. Ruzsa.

At the beginning of the 1970s he got involved with the school reform movement called complex teaching of mathematics led by Tamás Varga. Pósa worked on the reform of secondary mathematics teaching, while he taught at Radnóti Miklós Secondary School from 1976 to 1980. From 1982 to 1989 he was a member of the Research Group on Mathematics Education led by János Surányi. From 1982 to 1991 he had two experimental classes at Eötvös József Secondary School. His teaching materials written at that time were tested in several classes, and based on these he and colleagues have written a textbook series for the four years of secondary school.

Nevertheless, Pósa is best known for finding and teaching gifted students. Since 1988 he has been organizing his own week-end maths camps. There are several groups of 20-35 students, and each group has two or three camps a year. In a camp, students mostly work in groups of 2-4, but there are also plenary sessions where they discuss solutions, and sum up important thoughts. Students work on problems carefully built on each other. There are several topics running parallelly, and one topic spans several camps. The emphasis is on thinking, proving, and the connection between seemingly distant ideas. The camps are also an important scene of teacher training, as prospective teachers observe and help in the camps.

Mathematical research

Prizes, awards

  • Prize for Children Support („Gyermekekért” díj), 1989
  • Beke Manó Prize I. degree by Bolyai János Mathematical Society, 1994
  • Officer’s Cross Order of Merit of the Republic of Hungary, 1998
  • Charles Simonyi Scholarship, 2000
  • MOL prize for Gifted Education (“Tehetséggondozásért” díj), 2008
  • Széchenyi Prize, 2011

Publications

  • Pósa Lajos: A prímszámok egy tulajdonságáról, Matematikai Lapok, 11 (1960), 124-128.
  • P. Erdős, L. Pósa: On the maximal number of disjoint circuits of a graph, Publ. Math. Debrecen, 9 (1962), 3-13.
  • L. Pósa: A theorem concerning Hamilton lines, MTA Mat. Kut. Int. Közl. 7 (1962), 225-226.
  • L. Pósa: On the circuits of finite graphs, MTA Mat. Kut. Int. Közl. 8 (1964), 355-361.
  • P. Erdős, L. Pósa: On independent circuits contained in a graph, Can. J. Math. 17 (1965), 347-352.
  • P. Erdős, A. W. Goodman, L. Pósa: The representation of a graph by set intersection, Can. J. Math. 18 (1966), 106-112.
  • P. Erdős, A. Hajnal, L. Pósa: Strong embeddings of graphs into colored graphs, Infinite and finite sets (Colloq. Keszthely 1973; dedicated to P. Erdős on his 60th birthday), Vol. I. Colloq. Math. Soc. J. Bolyai, Vol. 10, North Holland, Amsterdam, 1975, 585-595.
  • L. Pósa: Hamiltonian circuits in random graphs, Discrete Mathematics, 14 (1976), 359-364.
  • Pósa Lajos: Véletlen gráfok Hamilton körei, egyetemi doktori értekezés, Budapest, 1982.
  • Pósa Lajos: Beszélgetés az új felvételi rendszer tervéről, Köznevelés, XXXV (1979) (20), 7-8.
  • Pósa Lajos: Variációk egy témára, Matematika-tanárképzés – matematikatanár-továbbképzés, 3 (1995), 41-59.

Textbooks

  • Pósa Lajos: Analízis I. Differenciálszámítás, 11. o., Műszaki Könyvkiadó Kft., 2000
  • Pósa Lajos: Analízis I. Differenciálszámítás. Tanári útmutató, 11. o., Műszaki Könyvkiadó Kft., 2000
  • Pósa Lajos: Analízis II. - Integrálszámítás, Műszaki Könyvkiadó Kft.
  • Pósa Lajos: Analízis II. Integrálszámítás (tanári útmutató), Műszaki Könyvkiadó Kft.
  • Pósa Lajos: Összefoglalás. Algebra. Megoldások, Műszaki Könyvkiadó Kft., 1999
  • Pósa Lajos: Összefoglalás. Algebra, függvények, Műszaki Könyvkiadó Kft., 1999
  • Pósa Lajos: Sorozatok 11.-12. o. Műszaki Könyvkiadó Kft., 1998
  • Pósa Lajos: Sorozatok. Tanári útmutató 11.-12. o., Műszaki Könyvkiadó Kft., 1998
  • Pósa Lajos: Vegyes feladatok 1. 7.-9. o., Műszaki Könyvkiadó Kft., 1998
  • Pósa Lajos: Vegyes feladatok 1. Tanári útmutató 9. o., Műszaki Könyvkiadó Kft., 1998
  • Pósa Lajos: Hatványozás kiterjesztése és logaritmus-feladatsorok, Műszaki Könyvkiadó Kft.
  • Pósa Lajos: Hatványozás kiterjesztése és logaritmus-megoldások, végeredmények, Műszaki Könyvkiadó Kft.
  • Pósa Lajos: Vegyes feladatok tanári útmutató 1. osztály (2. kiadás, Műszaki Könyvkiadó, Budapest, 1999.)
  • Pósa Lajos: Vegyes feladatok 2. - Tanári útmutató (Műszaki Könyvkiadó, Budapest, 2000.)
  • Pósa Lajos: Vektorok és koordinátageometria - Feladatsorok (Műszaki Könyvkiadó, Budapest)
  • Pósa Lajos: Vektorok és koordinátageometria - Megoldások, végeredmények (Műszaki Könyvkiadó, Budapest)
  • Pósa Lajos: Vektorok és koordináta geometria - Tanári útmutató (Műszaki Könyvkiadó, Budapest, 2000.)
  • Pósa Lajos: Összefoglalás - Matematika, elmélet, feladatok (Műszaki Könyvkiadó, Budapest)
  • Pósa Lajos: Összefoglalás - Matematika, megoldások (Műszaki Könyvkiadó, Budapest)
  • Pósa Lajos - Halmos Mária - Gábos Adél: Kombinatorika (Műszaki Könyvkiadó, Budapest, 1998.)
  • Gábos Adél - Halmos Mária - Pósa Lajos: Kombinatorika - Tanári útmutató (Műszaki Könyvkiadó, Budapest, 2000.)

References

  1. ^ "International Mathematical Olympiad".
  2. ^ Pósa, Lajos (1976). "Hamiltonian circuits in random graphs". Discrete Mathematics. 14 (4): 359–364. doi:10.1016/0012-365X(76)90068-6.
  3. ^ Komlós, János; Szemerédi, Endre (1983). "Limit distribution for the existence of hamiltonian cycles in a random graph". Discrete Mathematics. 43 (1): 55–63. doi:10.1016/0012-365X(83)90021-3.

See also

January 07, 2023
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The native form of this personal name is Posa Lajos This article uses Western name order when mentioning individuals Lajos Posa born December 9 1947 in Budapest is a Hungarian mathematician working in the topic of combinatorics and one of the most prominent mathematics educators of Hungary best known for his mathematics camps for gifted students He is a winner of the Szechenyi Prize Paul Erdos s favorite child he discovered theorems at the age of 16 Since 2002 he has worked at the Renyi Institute of the Hungarian Academy of Sciences earlier he was at the Eotvos Lorand University at the Departments of Mathematical Analysis Computer Science Contents 1 Biography 2 Mathematics education 3 Mathematical research 4 Prizes awards 5 Publications 6 Textbooks 7 References 8 See alsoBiography EditHe was born in Budapest Hungary on December 9 1947 His father was a chemist his mother a mathematics teacher He was a child prodigy While still in elementary school the educator Rozsa Peter friend of his mother introduced him to Paul Erdos who invited him for lunch in a restaurant and bombarded him with mathematical questions Posa finished the problems sooner than his soup which impressed Erdos who himself had been a child prodigy and who supported young talents with much care and competence That is how Posa s first paper was born co authored with Erdos hence his Erdos number is 1 He went to the first special mathematics class of the country at Fazekas Mihaly Secondary School from 1962 to 1966 where his classmates included Miklos Laczkovich Laszlo Lovasz Jozsef Pelikan hu Zsolt Baranyai Istvan Berkes Katalin Vesztergombi Peter Major He won the first prize on the International Mathematical Olympiad in 1966 Bulgaria and second prize in 1965 Germany 1 He started his Mathematics studies at ELTE University in 1966 and graduated in 1971 From 1971 to 1982 he worked at the Department of Mathematical Analysis at ELTE University and he obtained a doctorate in 1983 with his dissertation about Hamiltonian circuits of random graphs From 1984 to 2002 he worked at the Department of Computer Science at ELTE University and since 2002 he has been a member of the Renyi Mathematical Institute Despite his significant results in mathematical research he stopped research and devoted himself fully to Mathematics Education Erdos who preferred him among all his proteges expressed his regret that Posa had stopped research with the typical Erdos style phrase Posa is dead Mathematics education EditHe started teaching mathematics very early He tutored his secondary school classmates and during his first year at university he started teaching extracurricular courses at his former secondary school His students at that time included Laszlo Babai Gyorgy Elekes Peter Komjath Imre Z Ruzsa At the beginning of the 1970s he got involved with the school reform movement called complex teaching of mathematics led by Tamas Varga Posa worked on the reform of secondary mathematics teaching while he taught at Radnoti Miklos Secondary School from 1976 to 1980 From 1982 to 1989 he was a member of the Research Group on Mathematics Education led by Janos Suranyi From 1982 to 1991 he had two experimental classes at Eotvos Jozsef Secondary School His teaching materials written at that time were tested in several classes and based on these he and colleagues have written a textbook series for the four years of secondary school Nevertheless Posa is best known for finding and teaching gifted students Since 1988 he has been organizing his own week end maths camps There are several groups of 20 35 students and each group has two or three camps a year In a camp students mostly work in groups of 2 4 but there are also plenary sessions where they discuss solutions and sum up important thoughts Students work on problems carefully built on each other There are several topics running parallelly and one topic spans several camps The emphasis is on thinking proving and the connection between seemingly distant ideas The camps are also an important scene of teacher training as prospective teachers observe and help in the camps Mathematical research EditHe gave sufficient conditions for the existence of Hamiltonian circuit He proved that a random graph on n vertices with cn log n edges almost surely contains a Hamiltonian circuit 2 thus affirming a conjecture of Erdos and Renyi also proved by A D Korshunov The result was later improved by Komlos and Szemeredi 3 With Erdos he proved the Erdos Posa theorem Prizes awards EditPrize for Children Support Gyermekekert dij 1989 Beke Mano Prize I degree by Bolyai Janos Mathematical Society 1994 Officer s Cross Order of Merit of the Republic of Hungary 1998 Charles Simonyi Scholarship 2000 MOL prize for Gifted Education Tehetseggondozasert dij 2008 Szechenyi Prize 2011Publications EditPosa Lajos A primszamok egy tulajdonsagarol Matematikai Lapok 11 1960 124 128 P Erdos L Posa On the maximal number of disjoint circuits of a graph Publ Math Debrecen 9 1962 3 13 L Posa A theorem concerning Hamilton lines MTA Mat Kut Int Kozl 7 1962 225 226 L Posa On the circuits of finite graphs MTA Mat Kut Int Kozl 8 1964 355 361 P Erdos L Posa On independent circuits contained in a graph Can J Math 17 1965 347 352 P Erdos A W Goodman L Posa The representation of a graph by set intersection Can J Math 18 1966 106 112 P Erdos A Hajnal L Posa Strong embeddings of graphs into colored graphs Infinite and finite sets Colloq Keszthely 1973 dedicated to P Erdos on his 60th birthday Vol I Colloq Math Soc J Bolyai Vol 10 North Holland Amsterdam 1975 585 595 L Posa Hamiltonian circuits in random graphs Discrete Mathematics 14 1976 359 364 Posa Lajos Veletlen grafok Hamilton korei egyetemi doktori ertekezes Budapest 1982 Posa Lajos Beszelgetes az uj felveteli rendszer terverol Kozneveles XXXV 1979 20 7 8 Posa Lajos Variaciok egy temara Matematika tanarkepzes matematikatanar tovabbkepzes 3 1995 41 59 Textbooks EditPosa Lajos Analizis I Differencialszamitas 11 o Muszaki Konyvkiado Kft 2000 Posa Lajos Analizis I Differencialszamitas Tanari utmutato 11 o Muszaki Konyvkiado Kft 2000 Posa Lajos Analizis II Integralszamitas Muszaki Konyvkiado Kft Posa Lajos Analizis II Integralszamitas tanari utmutato Muszaki Konyvkiado Kft Posa Lajos Osszefoglalas Algebra Megoldasok Muszaki Konyvkiado Kft 1999 Posa Lajos Osszefoglalas Algebra fuggvenyek Muszaki Konyvkiado Kft 1999 Posa Lajos Sorozatok 11 12 o Muszaki Konyvkiado Kft 1998 Posa Lajos Sorozatok Tanari utmutato 11 12 o Muszaki Konyvkiado Kft 1998 Posa Lajos Vegyes feladatok 1 7 9 o Muszaki Konyvkiado Kft 1998 Posa Lajos Vegyes feladatok 1 Tanari utmutato 9 o Muszaki Konyvkiado Kft 1998 Posa Lajos Hatvanyozas kiterjesztese es logaritmus feladatsorok Muszaki Konyvkiado Kft Posa Lajos Hatvanyozas kiterjesztese es logaritmus megoldasok vegeredmenyek Muszaki Konyvkiado Kft Posa Lajos Vegyes feladatok tanari utmutato 1 osztaly 2 kiadas Muszaki Konyvkiado Budapest 1999 Posa Lajos Vegyes feladatok 2 Tanari utmutato Muszaki Konyvkiado Budapest 2000 Posa Lajos Vektorok es koordinatageometria Feladatsorok Muszaki Konyvkiado Budapest Posa Lajos Vektorok es koordinatageometria Megoldasok vegeredmenyek Muszaki Konyvkiado Budapest Posa Lajos Vektorok es koordinata geometria Tanari utmutato Muszaki Konyvkiado Budapest 2000 Posa Lajos Osszefoglalas Matematika elmelet feladatok Muszaki Konyvkiado Budapest Posa Lajos Osszefoglalas Matematika megoldasok Muszaki Konyvkiado Budapest Posa Lajos Halmos Maria Gabos Adel Kombinatorika Muszaki Konyvkiado Budapest 1998 Gabos Adel Halmos Maria Posa Lajos Kombinatorika Tanari utmutato Muszaki Konyvkiado Budapest 2000 References Edit International Mathematical Olympiad Posa Lajos 1976 Hamiltonian circuits in random graphs Discrete Mathematics 14 4 359 364 doi 10 1016 0012 365X 76 90068 6 Komlos Janos Szemeredi Endre 1983 Limit distribution for the existence of hamiltonian cycles in a random graph Discrete Mathematics 43 1 55 63 doi 10 1016 0012 365X 83 90021 3 Ross Honsberger The story of Louis Posa in Mathematical Gems The Mathematical Association of America 1973 An article on Posa in the Hungarian daily Nepszabadsag Lajos Posa s results at International Mathematical OlympiadSee also EditPosa theorem 1962 Erdos Posa theorem 1965 Retrieved from https en wikipedia org w index php title Lajos Posa mathematician amp oldid 1068930340, wikipedia, wiki, book, books, library,

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