Pengguna:Kekavigi/bak pasir 2

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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

Paul Halmos's parents were Sándor Halmos and Paula Rosenberg. Sándor and Paula were married in 1903 and they had three children, George (born about 1909), John (born about 1911) and Paul (the subject of this biography). Paul's mother, Paula, died when Paul was six months old. Paul's father was a successful physician in Budapest who had the rather remarkable foresight to realise the problems that were going to befall Europe. So in 1924 Paul's father emigrated to the United States, leaving Paul and his two elder brothers in Budapest. There they were looked after by the physician who took over his father's practice. In the United States, Sándor Halmos worked for a year as an intern in a hospital in Omaha before moving to Chicago where he set up his own practice.


After five years in the United States, Paul's father, known in America as Alexander Charles Halmos, became a naturalised American citizen and, at that time, brought Paul from Hungary to join him in Chicago.


The information that Paul came to the United States in 1929 after his father became an American citizen comes from his own account of his life but the 1930 Census states that Paul Halmos emigrated to the United States in 1924. This must be an error in filling in the Census form. Somewhat more puzzling is the fact that the 1930 Census form gives N/A (not available) for the year in which Paul's two older brothers entered the United States. According to Paul they came to join their father before he did.


Halmos was born in Budapest, Hungary, in 1916. In 1929 he immigrated to the United States and lived with his family in Chicago. 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. In 1931, at the age of fifteen, he left Chicago to attend the University of Illinois, intending to study chemical engineering. He graduated three years later (1934) with a bachelorâ??s degree in mathematics and philosophy. Halmos then entered graduate school at the University of Illinois to pursue a Ph.D. in philosophy. After failing the oral comprehensive exam for the masterâ??s degree, he changed the focus of his graduate studies and registered as a student in the department of mathematics. Halmos earned his doctorate in mathematics under Joseph L. Doob in 1938. maaspotlight https://maa.org/archives-spotlight-the-paul-halmos-papers


Once Alexander Halmos had established himself in Chicago he had remarried. His second wife, Irene, was a widow with two daughters Alice Reich (born in Illinois around 1917) and Jean Reich (born in Illinois around 1920).


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

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

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 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

https://mathshistory.st-andrews.ac.uk/Biographies/Halmos/

000

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

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


[1]


Born in Hungary into a Jewish family, Halmos arrived in the U.S. at 13 years of age. He obtained his B.A. from the University of Illinois, majoring in mathematics, but fulfilling the requirements for both a math and philosophy degree. He took only three years to obtain the degree, and was only 19 when he graduated. He then began a Ph.D. in philosophy, still at the Champaign–Urbana campus; but, after failing his masters' oral exams,[2] 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.[3]

Karir

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 Neumannâ??s assistant at the Institute of Advanced Study (1939â??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 Armyâ??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 (1975â??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 (1951â??52), the University of Miami (1965â??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

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

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

Referensi

  1. ^ 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. 
  2. ^ The Legend of John Von Neumann. P. R. Halmos. The American Mathematical Monthly, Vol. 80, No. 4. (Apr., 1973), pp. 382–394.
  3. ^ Halmos, Paul R. "Invariants of certain stochastic transformations: The mathematical theory of gambling systems." Duke Mathematical Journal 5, no. 2 (1939): 461–478.
  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 alt=Dapat diakses gratis. 
  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 alt=Dapat diakses gratis. 
  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 alt=Dapat diakses gratis. 
  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 alt=Dapat diakses gratis. 
  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 alt=Dapat diakses gratis. 
  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. 

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