Wikipedia

Pengguna:Kekavigi/bak pasir 2

< Pengguna:Kekavigi


Bentuk asli dari nama pribadi ini adalah Halmos Pál. Artikel ini memakai urutan nama Barat saat menyebut seseorang.
Mohon jangan gunakan templat "{{Infobox Person}}" di ruang nama pengguna Anda. Gunakan {{Infobox pengguna}}.

Paul Richard Halmos (bahasa Hongaria: Halmos Pál; 3 Maret 1916 – 2 Oktober 2006) adalah seorang matematikawan dan statistikawan Amerika keturunan Hungaria yang membuat kemajuan besar di bidang logika matematika, teori peluang, statistika, teori operator, dan analisis fungsional (khususnya ruang Hilbert). Ia juga dikenal sebagai seorang pemapar matematika yang hebat.

recheck CV kerja di infobox!

Masa kecil dan pendidikan

sunting

Lahir di Hungaria dari keluarga Yahudi, Halmos tiba di AS pada usia 13 tahun.

Paul Halmos merupakan anak ketiga dari Sándor Halmos dan Paula Rosenberg. Sándor dan Paula menikah pada tahun 1903, dan dikaruniai tiga anak, yaitu George (lahir sekitar tahun 1909), John (lahir sekitar tahun 1911), dan Paul. Paul lahir di Budapest, Hongaria, pada tahun 1916. Malangnya, ibu Paul meninggal saat Paul berusia hanya enam bulan. Ayah Paul adalah seorang dokter yang sukses di Budapest. Menyadari masalah-masalah yang akan menimpa Eropa, ayah Paul beremigrasi ke Amerika Serikat pada tahun 1924, dan meninggalkan Paul dan kedua kakak laki-lakinya di Budapest. Di sana mereka dirawat oleh seorang dokter yang mengambil alih praktik ayahnya.

Di Amerika Serikat, Sándor Halmos bekerja selama satu tahun sebagai dokter magang di sebuah rumah sakit di Omaha sebelum pindah ke Chicago dan membuka praktiknya sendiri. Setelah lima tahun di Amerika Serikat, ayah Paul menjadi warga negara Amerika naturalisasi dan membawa Paul dari Hongaria untuk bergabung dengannya di Chicago. Ayah Paul menyatakan bahwa Paul datang ke Amerika Serikat pada tahun 1929, namun mungkin karena kesalahan pengisian, Sensus 1930 menyatakan bahwa Paul Halmos beremigrasi ke Amerika Serikat pada tahun 1924. Fakta yang lebih membingungkan adalah Sensus 1930 memberikan N/A (tidak tersedia) untuk tahun ketika dua kakak laki-laki Paul memasuki Amerika Serikat. Tapi menurut Paul, mereka datang untuk bergabung dengan ayah mereka, sebelum dia.


Paul Halmos attended school in Budapest up to the age of thirteen

As the result of confusion about the Hungarian school system, Halmos entered the American school system at a level somewhere between a junior and a senior in high school.

After reaching the United States, he attended high school in Chicago but rather remarkably he missed out four years schooling in the process. Halmos says that there was some confusion since in Hungary four years of primary schooling were followed by eight years of secondary schooling. He had completed seven of these twelve years but Halmos said ...?

While still fifteen years old he entered the University of Illinois to study chemical engineering. He had considered other options such as studying law at a law school but opted for chemistry

In 1931, at the age of fifteen, he left Chicago to attend the University of Illinois, intending to study chemical engineering.

After one year he became disappointed with chemistry, saying he got his hands dirty, so he changed to mathematics and philosophy but did not particularly shine at mathematics

Despite being so young when he entered his undergraduate course and despite changing from chemical engineering to mathematics and philosophy he still completed the four year degree in three years graduating in 1934.

He graduated three years later (1934) with a bachelors degree in mathematics and philosophy.

Ia memperoleh gelar B.A. dari Universitas Illinois, jurusan matematika, tetapi memenuhi persyaratan untuk gelar matematika dan filsafat. ?????

He took only three years to obtain the degree, and was only 19 when he graduated.

Halmos then entered graduate school at the University of Illinois to pursue a Ph.D. in philosophy.

He began graduate studies at the University of Illinois at Urbana-Champaign, still with philosophy as his main subject, and mathematics as his minor subject.

It was not until the end of the academic year 1935-36 that Halmos made the move from philosophy to mathematics. This came about mainly because he had preformed poorly in the oral comprehensive examination for the Masters' Degree in philosophy. It was in September 1935 that he taught his first course, namely freshman algebra

After failing the oral comprehensive exam for the masters degree, he changed the focus of his graduate studies and registered as a student in the department of mathematics.

He then began a Ph.D. in philosophy, still at the Champaign–Urbana campus; but, after failing his masters' oral exams,[1] he shifted to mathematics, graduating in 1938.

Joseph L. Doob supervised his dissertation, titled Invariants of Certain Stochastic Transformations: The Mathematical Theory of Gambling Systems.[2]

Halmos earned his doctorate in mathematics under Joseph L. Doob in 1938.

maaspotlight https://maa.org/archives-spotlight-the-paul-halmos-papershttps://mathshistory.st-andrews.ac.uk/Biographies/Halmos/ [3]

Karir

sunting

Shortly after his graduation, Halmos left for the Institute for Advanced Study, lacking both job and grant money. Six months later, he was working under John von Neumann, which proved a decisive experience. While at the Institute, Halmos wrote his first book, Finite Dimensional Vector Spaces, which immediately established his reputation as a fine expositor of mathematics.[4]


Following the completion of his doctorate, Halmos served as John von Neumann's assistant at the Institute of Advanced Study (1939'1942), a post that led to the publication of his first book, Finite Dimensional Vector Spaces, in 1942.


After leaving the IAS, Halmos taught soldiers in the Army's Specialized Training Program at Syracuse University before

moving to the University of Chicago, where he stayed from 1946 to 1960, and the University of Michigan (1961 to 1967). After one year as the mathematics department chair at the University of Hawaii, he began a professorship at Indiana University, where he would stay until 1985, with the exception of two years spent at the University of California, Santa Barbara (1975'77).

In 1985, he moved to Santa Clara University where he taught until his retirement in 1996. In addition to these posts, Halmos held visiting appointments at the University of Montevideo, Uruguay (1951'52), the University of Miami (1965'66), and the University of Washington (1959), among others

https://maa.org/archives-spotlight-the-paul-halmos-papers


After leaving the Institute for Advanced Study, Halmos was appointed to Syracuse University, New York. While in Syracuse he took part in teaching soldiers in the Army's Specialized Training Program. In 1945 he married Virginia Templeton Pritchett. Virginia had been born on 21 December 1915 in Omaha, Nebraska and had studied at Vassar College followed by graduate study in logic and the foundations of mathematics at Brown University. mshistory


From 1967 to 1968 he was the Donegall Lecturer in Mathematics at Trinity College Dublin.

Halmos taught at Syracuse University, the University of Chicago (1946–60), the University of Michigan (1961–67), the University of Hawaii (1967–68), Indiana University (1969–85), and the University of California at Santa Barbara (1976–78) (75-77??). From his 1985 retirement from Indiana until his death, he was affiliated with the Mathematics department at Santa Clara University (1985–2006) (-96?).

Prestasi

sunting

In a series of papers reprinted in his 1962 Algebraic Logic, Halmos devised polyadic algebras, an algebraic version of first-order logic differing from the better known cylindric algebras of Alfred Tarski and his students. An elementary version of polyadic algebra is described in monadic Boolean algebra.

In addition to his original contributions to mathematics, Halmos was an unusually clear and engaging expositor of university mathematics. He won the Lester R. Ford Award in 1971[5] and again in 1977 (shared with W. P. Ziemer, W. H. Wheeler, S. H. Moolgavkar, J. H. Ewing and W. H. Gustafson).[6] Halmos chaired the American Mathematical Society committee that wrote the AMS style guide for academic mathematics, published in 1973. In 1983, he received the AMS's Leroy P. Steele Prize for exposition.

In the American Scientist 56(4): 375–389, Halmos argued that mathematics is a creative art, and that mathematicians should be seen as artists, not number crunchers. He discussed the division of the field into mathology and mathophysics, further arguing that mathematicians and painters think and work in related ways.

Halmos's 1985 "automathography" I Want to Be a Mathematician is an account of what it was like to be an academic mathematician in 20th century America. He called the book "automathography" rather than "autobiography", because its focus is almost entirely on his life as a mathematician, not his personal life. The book contains the following quote on Halmos' view of what doing mathematics means:

Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?

What does it take to be [a mathematician]? I think I know the answer: you have to be born right, you must continually strive to become perfect, you must love mathematics more than anything else, you must work at it hard and without stop, and you must never give up.

— Paul Halmos, 1985

In these memoirs, Halmos claims to have invented the "iff" notation for the words "if and only if" and to have been the first to use the "tombstone" notation to signify the end of a proof,[7] and this is generally agreed to be the case. The tombstone symbol ∎ (Unicode U+220E) is sometimes called a halmos.[8]

In 2005, Halmos and his wife Virginia funded the Euler Book Prize, an annual award given by the Mathematical Association of America for a book that is likely to improve the view of mathematics among the public. The first prize was given in 2007, the 300th anniversary of Leonhard Euler's birth, to John Derbyshire for his book about Bernhard Riemann and the Riemann hypothesis: Prime Obsession.[9]

In 2009 George Csicsery featured Halmos in a documentary film also called I Want to Be a Mathematician.[10]

Books by Halmos

sunting

Books by Halmos have led to so many reviews that lists have been assembled.[11][12]

Referensi

sunting
  1. ^ The Legend of John Von Neumann. P. R. Halmos. The American Mathematical Monthly, Vol. 80, No. 4. (Apr., 1973), pp. 382–394.
  2. ^ Halmos, Paul R. "Invariants of certain stochastic transformations: The mathematical theory of gambling systems." Duke Mathematical Journal 5, no. 2 (1939): 461–478.
  3. ^ Halmos, Paul Richard; Ewing, John; Gehring, F. W. (1991-05-20). PAUL HALMOS Celebrating 50 Years of Mathematics: Celebrating 50 Years of Mathematics (dalam bahasa Inggris). Springer Science & Business Media. ISBN 978-0-387-97509-2. 
  4. ^ Albers, Donald J. (1982). "Paul Halmos: Maverick Mathologist". Two-Year College Mathematics Journal. Mathematical Association of America. 13 (4): 226–242. doi:10.2307/3027125. JSTOR 3027125. 
  5. ^ Halmos, Paul R. (1970). "Finite-dimensional Hilbert spaces". Amer. Math. Monthly. 77 (5): 457–464. doi:10.2307/2317378. JSTOR 2317378. 
  6. ^ Ziemer, William P.; Wheeler, William H.; Moolgavkar; Halmos, Paul R.; Ewing, John H.; Gustafson, William H. (1976). "American mathematics from 1940 to the day before yesterday". Amer. Math. Monthly. 83 (7): 503–516. doi:10.2307/2319347. JSTOR 2319347. 
  7. ^ Halmos, Paul (1950). Measure Theory. New York: Van Nostrand. hlm. vi. The symbol ∎ is used throughout the entire book in place of such phrases as "Q.E.D." or "This completes the proof of the theorem" to signal the end of a proof. 
  8. ^ "The symbol is definitely not my invention — it appeared in popular magazines (not mathematical ones) before I adopted it, but, once again, I seem to have introduced it into mathematics. It is the symbol that sometimes looks like ▯, and is used to indicate an end, usually the end of a proof. It is most frequently called the 'tombstone', but at least one generous author referred to it as the 'halmos'.", Halmos (1985) p. 403.
  9. ^ The Mathematical Association of America's Euler Book Prize Diarsipkan 27 January 2013 di Wayback Machine., retrieved 2011-02-01.
  10. ^ I Want to Be a Mathematician on IMdB
  11. ^ "Reviews of Paul Halmos' books Part 1 (books from 1942 to 1966)". MacTutor. 
  12. ^ "Reviews of Paul Halmos's books Part 2 (books from 1967 and later)". MacTutor. 
  13. ^ Kac, Mark (1943). "Review: Finite-dimensional vector spaces, by P. R. Halmos" (PDF). Bull. Amer. Math. Soc. 49 (5): 349–350. doi:10.1090/s0002-9904-1943-07899-8  . 
  14. ^ Oxtoby, J. C. (1953). "Review: Measure theory, by P. R. Halmos" (PDF). Bull. Amer. Math. Soc. 59 (1): 89–91. doi:10.1090/s0002-9904-1953-09662-8  . 
  15. ^ Lorch, E. R. (1952). "Review: Introduction to Hilbert space and the theory of spectral multiplicity, by P. R. Halmos" (PDF). Bull. Amer. Math. Soc. 58 (3): 412–415. doi:10.1090/s0002-9904-1952-09595-1  . 
  16. ^ Dowker, Yael N. (1959). "Review: Lectures on ergodic theory, by P. R. Halmos" (PDF). Bull. Amer. Math. Soc. 65 (4): 253–254. doi:10.1090/s0002-9904-1959-10331-1  . 
  17. ^ Zaanen, Adriaan (1979). "Review: Bounded integral operators on L² spaces, by P. R. Halmos and V. S. Sunder" (PDF). Bull. Amer. Math. Soc. (N.S.). 1 (6): 953–960. doi:10.1090/s0273-0979-1979-14699-8  . 
  18. ^ Johnson, Mark (February 11, 1999). "Review of Logic as Algebra by Paul Halmos and Steven Givant". MAA Reviews, Mathematical Association of America. 
  19. ^ Givant, Steven; Halmos, Paul (2 December 2008). Introduction to Boolean Algebras. Springer. ISBN 978-0387402932. 

Bacaan lebih lanjut

sunting

Pranala luar

sunting
 
Wikiquote memiliki koleksi kutipan yang berkaitan dengan: Kekavigi/bak pasir 2.


Diperoleh dari "https://wiki-indonesia.club/w/index.php?title=Pengguna:Kekavigi/bak_pasir_2&oldid=24525531"