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词条 Howard Levi
释义

  1. Biography

  2. Selected publications

      Books    Articles    Expository writing  

  3. References

{{Distinguish|Howard Levy}}{{Infobox scientist
| name = Howard Levi
| image =
| image_size =
| caption =
| birth_date = November 9, 1916
| birth_place = New York City
| death_date = {{death date and age|2002|9|11|1916|11|9}}
| death_place = New York City
| nationality = American
| fields = Mathematics
| alma_mater = Columbia University
| work_institutions = Columbia University
City University of New York
| doctoral_advisor = Joseph Fels Ritt
| doctoral_students =
| known_for = Levi's reduction process
}}

Howard Levi (November 9, 1916 in New York City – September 11, 2002 in New York City) was an American mathematician who worked mainly in algebra and mathematical education.[1] Levi was very active during the educational reforms in the United States, having proposed several new courses to replace the traditional ones.

Biography

Levi earned a Ph.D. in mathematics from Columbia University in 1942 as a student of Joseph Fels Ritt.[2] Soon after obtaining his degree, he became a researcher on the Manhattan Project.[3][4]

At Wesleyan University he led a group that developed a course of geometry for high school students that treated Euclidean geometry as a special case of affine geometry.[5][6] Much of the Wesleyan material was based on his book Foundations of Geometry and Trigonometry.[7]

His book Polynomials, Power Series, and Calculus, written to be a textbook for a first course in calculus,[8] presented an innovative approach, and received favorable reviews by Leonard Gillman, who wrote "[...] this book, with its wealth of imaginative ideas, deserves to be better known."[9][10]

Levi's reduction process is named after him.[11]

In his last years, he tried to find a proof of the four color theorem that did not rely on computers.[3]

Selected publications

Books

  • Elements of Algebra (Chelsea Publishing Company, 1953, 1956, 1960, 1961)[12][13][14][15]
  • Elements of Geometry (Columbia University Press, 1956)
  • Foundations of Geometry and Trigonometry (Prentice-Hall, 1956 and 1960)[16][17]
  • Fundamental Concepts of Mathematics (1957)
  • Modern Coordinate Geometry: A Wesleyan Experimental Curricular Study (co-authored with C. Robert Clements, Harry Sitomer, et al., for the School Mathematics Study Group, 1961)
  • Polynomials, Power Series, and Calculus (Van Nostrand, 1967, 1968)
  • Topics in Geometry (1968, 1975)[18]

Articles

  • "On the values assumed by polynomials". Bull. Amer. Math. Soc. 45 (1939), no. 8, pp. 570–575. (LINK)
  • "Composite polynomials with coefficients in an arbitrary field of characteristic zero". Amer. J. Math. 64 (1942), no. 1, pp. 389–400. [https://www.jstor.org/stable/2371692 (LINK)]
  • "On the structure of differential polynomials and on their theory of ideals". T. Am. Math. Soc. 51 (1942), pp. 532–568. (LINK)
  • "A characterization of polynomial rings by means of order relations". Amer. J. Math. 65 (1943), no. 2, pp. 221–234. [https://www.jstor.org/discover/10.2307/2371811?uid=3737664&uid=2129&uid=2&uid=70&uid=4&sid=21104000458931 (LINK)]
  • "Exact nth derivatives". Bull. Amer. Math. Soc. 49 (1943), no. 8, pp. 631–636. (LINK)
  • "The low power theorem for partial differential polynomials". Annals of Mathematics, Second Series, Vol. 46, no. 1 (1945), pp. 113–119. [https://www.jstor.org/discover/10.2307/1969151?uid=3737664&uid=2129&uid=2&uid=70&uid=4&sid=21104000458931 (LINK)]
  • "A geometric construction of the Dirichlet kernel". Trans. N. Y. Acad. Sci., Volume 36, Issue 7 (1974), Series II, pp. 640–643. {{cite journal|doi=10.1111/j.2164-0947.1974.tb03023.x | volume=36 | issue=7 Series II | title=A GEOMETRIC CONSTRUCTION OF THE DIRICHLET KERNEL | year=1974 | journal=Transactions of the New York Academy of Sciences | pages=640–643 | author=Levi Howard}}
  • "An algebraic reformulation of the four color theorem." (published posthumously by Don Coppersmith, Melvin Fitting, and Paul Meyer) (LINK)

Expository writing

  • "Why Arithmetic Works.", The Mathematics Teacher, Vol. 56, No. 1 (January 1963), pp. 2–7. [https://www.jstor.org/discover/10.2307/27956728?uid=3737664&uid=2129&uid=2&uid=70&uid=4&sid=21104000458931 (LINK)]
  • "Plane Geometries in Terms of Projections.", Proc. Am. Math. Soc, 1965, Vol. 16, No. 3, pp. 503–511. [https://www.jstor.org/discover/10.2307/2034683?uid=3737664&uid=2129&uid=2&uid=70&uid=4&sid=21104000458931 (LINK)]
  • "An Algebraic Approach to Calculus.", Trans. N. Y. Acad. Sci., Volume 28, Issue 3 Series II, pp. 375–377, January 1966 {{cite journal|doi=10.1111/j.2164-0947.1966.tb02349.x | volume=28 | issue=3 Series II | title=AN ALGEBRAIC APPROACH TO CALCULUS | year=1966 | journal=Transactions of the New York Academy of Sciences | pages=375–377 | author=Levi Howard}}
  • "Classroom Notes: Integration, Anti-Differentiation and a Converse to the Mean Value Theorem", Amer. Math. Monthly 74 (1967), no. 5, 585–586. [https://www.jstor.org/stable/2314907 (LINK)]
  • "Foundations of Geometric Algebra", Rendiconti di Matematica, 1969, Vol. 2, Serie VI, pp. 1–32.
  • "Geometric Algebra for the High School Program.", Educational Studies in Mathematics, June 1971, Volume 3, Issue 3–4, pp 490–500. [https://link.springer.com/article/10.1007%2FBF00302310 (LINK)]
  • "Geometric Versions of Some Algebraic Identities.", Ann. N. Y. Acad. Sci., Vol. 607, pp. 54–60, November 1990. {{cite journal|doi=10.1111/j.1749-6632.1990.tb22746.x | volume=607 | issue=1 Mathematical | title=Geometric Versions of Some Algebraic Identities | year=1990 | journal=Annals of the New York Academy of Sciences | pages=54–60 | author=Levi Howard}}

References

1. ^Notices of the AMS, June/July 2003, Volume 50, Number 6, p. 705.
2. ^{{MathGenealogy|id=37383}}
3. ^1 Melvin Fitting – The Four Color Theorem
4. ^For some details, consult: Mildred Goldberg – Personal recollections of Mildred Goldberg, secretary to the theoretical group, SAM Laboratories, The Manhattan Project; 1943-1946 (Gilder Lehrman Institute of American History).
5. ^{{cite book|author-first=Nathalie|author-last=Sinclair|authorlink=Nathalie Sinclair|title=The History of the Geometry Curriculum in the United States|url=https://books.google.com/books?id=K7U6I3fxRSoC&pg=PA64|year=2008|publisher=IAP|isbn=978-1-59311-697-2|pages=64}}
6. ^Sitomer, H. – Coordinate geometry with an affine approach, Mathematics Teacher 57 (1964), 404–405.
7. ^C. Ray Wylie, An Affine Approach to Euclidean Geometry (p. 237 from the PDF document, p. 231 from the document itself)
8. ^[https://www.jstor.org/stable/2312681 Levi, Howard — An Experimental Course in Analysis for College Freshmen]
9. ^{{cite journal|author= Gillman, Leonard|authorlink=Leonard Gillman|title=An Axiomatic Approach to the Integral|journal=The American Mathematical Monthly|year=1993|volume=100|issue=1|pages=16–25|url=https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/Gillman16-25.pdf|doi=10.2307/2324809|jstor=2324809}}
10. ^{{cite journal|author= Gillman, Leonard|authorlink=Leonard Gillman|title=Review: Polynomials, Power Series, and Calculus by Howard Levi|journal=The American Mathematical Monthly|year=1974|volume=81|issue=5|pages=532–533|jstor=2318616|doi=10.2307/2318616}}
11. ^{{cite journal|author=Mead, D. G.|title=The Equation of Ramanujan-Nagell and [y2]|journal=Proceedings of the American Mathematical Society|date=December 1973|volume=41|issue=2|pages=333–341|url=http://www.ams.org/journals/proc/1973-041-02/S0002-9939-1973-0327725-4/S0002-9939-1973-0327725-4.pdf|doi=10.2307/2039090|jstor=2039090}}
12. ^{{cite journal|author= Halmos, Paul R.|authorlink=Paul Halmos|title=Review: Elements of algebra by Howard Levi|journal=Bull. Amer. Math. Soc.|year=1955|volume=61|issue=3|pages=245–247|url=http://projecteuclid.org/download/pdf_1/euclid.bams/1183519732|doi=10.1090/S0002-9904-1955-09905-1}}
13. ^{{cite journal|author= Lott, Fred W.|title=Review: Elements of algebra by Howard Levi|journal=The Mathematics Teacher|year=1955|volume=48|issue=5|pages=353–354|jstor=27954922}}
14. ^{{cite journal|author= Lee, Herbert L.|title=Review: Elements of algebra by Howard Levi|journal=The Scientific Monthly|year=1955|volume=80|issue=6|pages=387|jstor=21575}}
15. ^{{cite journal|author= Rajaratnam, Nageswari|title=Review: Elements of algebra by Howard Levi|journal=The Mathematics Teacher|year=1960|volume=53|issue=7|pages= 585–586|jstor=27956256}}
16. ^{{cite journal|author= Dickson, Douglas G.|title=Review: Foundations of Geometry and Trigonometry by Howard Levi|journal=Science Magazine|year=1962|volume=137|issue=3533|pages=846–847|url=http://www.sciencemag.org/content/137/3533/846.5.citation|doi=10.1126/science.137.3533.846-d}}
17. ^{{cite journal|author= Bezuszka, S. J.|title=Review: Foundations of Geometry and Trigonometry by Howard Levi|journal=The American Mathematical Monthly|year=1965|volume=72|issue=5|pages=565|jstor= 2314158|doi=10.2307/2314158}}
18. ^{{cite journal|author=Chakerian, G. D.|title=Review: Topics in Geometry by Howard Levi|journal=The American Mathematical Monthly|year=1969|volume=76|issue=8|pages=962|jstor=2317992|doi=10.2307/2317992}}
{{Authority control}}{{DEFAULTSORT:Levi, Howard}}

12 : 1916 births|2002 deaths|20th-century American mathematicians|21st-century American mathematicians|Columbia University alumni|Textbook writers|Algebraists|Columbia University faculty|Hunter College faculty|Lehman College faculty|Manhattan Project people|Mathematics educators
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