Biography:Howard Levi

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Short description: American mathematician
Howard Levi
BornNovember 9, 1916
New York City
DiedSeptember 11, 2002(2002-09-11) (aged 85)
New York City
NationalityAmerican
Alma materColumbia University
Known forLevi's reduction process
Scientific career
FieldsMathematics: differential algebra
InstitutionsColumbia University
City University of New York
Doctoral advisorJoseph Fels Ritt

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. (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. (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. (LINK)
  • "A geometric construction of the Dirichlet kernel". Trans. N. Y. Acad. Sci., Volume 36, Issue 7 (1974), Series II, pp. 640–643. Levi Howard (1974). "A Geometric Construction of the Dirichlet Kernel". Transactions of the New York Academy of Sciences 36 (7 Series II): 640–643. doi:10.1111/j.2164-0947.1974.tb03023.x. 
  • "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. (LINK)
  • "Plane Geometries in Terms of Projections.", Proc. Am. Math. Soc, 1965, Vol. 16, No. 3, pp. 503–511. (LINK)
  • "An Algebraic Approach to Calculus.", Trans. N. Y. Acad. Sci., Volume 28, Issue 3 Series II, pp. 375–377, January 1966 Levi Howard (1966). "An Algebraic Approach to Calculus". Transactions of the New York Academy of Sciences 28 (3 Series II): 375–377. doi:10.1111/j.2164-0947.1966.tb02349.x. 
  • "Classroom Notes: Integration, Anti-Differentiation and a Converse to the Mean Value Theorem", Amer. Math. Monthly 74 (1967), no. 5, 585–586. (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. (LINK)
  • "Geometric Versions of Some Algebraic Identities.", Ann. N. Y. Acad. Sci., Vol. 607, pp. 54–60, November 1990.

References

  1. ↑ Notices of the AMS, June/July 2003, Volume 50, Number 6, p. 705.
  2. ↑ Howard Levi at the Mathematics Genealogy Project
  3. ↑ 3.0 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. ↑ The History of the Geometry Curriculum in the United States. IAP. 2008. pp. 64. ISBN 978-1-59311-697-2. https://books.google.com/books?id=K7U6I3fxRSoC&pg=PA64. 
  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. ↑ Levi, Howard — An Experimental Course in Analysis for College Freshmen
  9. ↑ Gillman, Leonard (1993). "An Axiomatic Approach to the Integral". The American Mathematical Monthly 100 (1): 16–25. doi:10.2307/2324809. https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/Gillman16-25.pdf. 
  10. ↑ Gillman, Leonard (1974). "Review: Polynomials, Power Series, and Calculus by Howard Levi". The American Mathematical Monthly 81 (5): 532–533. doi:10.2307/2318616. 
  11. ↑ Mead, D. G. (December 1973). "The Equation of Ramanujan-Nagell and [y2"]. Proceedings of the American Mathematical Society 41 (2): 333–341. doi:10.2307/2039090. https://www.ams.org/journals/proc/1973-041-02/S0002-9939-1973-0327725-4/S0002-9939-1973-0327725-4.pdf. 
  12. ↑ Halmos, Paul R. (1955). "Review: Elements of algebra by Howard Levi". Bull. Amer. Math. Soc. 61 (3): 245–247. doi:10.1090/S0002-9904-1955-09905-1. http://projecteuclid.org/download/pdf_1/euclid.bams/1183519732. 
  13. ↑ Lott, Fred W. (1955). "Review: Elements of algebra by Howard Levi". The Mathematics Teacher 48 (5): 353–354. 
  14. ↑ Lee, Herbert L. (1955). "Review: Elements of algebra by Howard Levi". The Scientific Monthly 80 (6): 387. 
  15. ↑ Rajaratnam, Nageswari (1960). "Review: Elements of algebra by Howard Levi". The Mathematics Teacher 53 (7): 585–586. 
  16. ↑ Dickson, Douglas G. (1962). "Review: Foundations of Geometry and Trigonometry by Howard Levi". Science Magazine 137 (3533): 846–847. doi:10.1126/science.137.3533.846-d. PMID 17787326. https://www.science.org/doi/abs/10.1126/science.137.3533.846.a. 
  17. ↑ Bezuszka, S. J. (1965). "Review: Foundations of Geometry and Trigonometry by Howard Levi". The American Mathematical Monthly 72 (5): 565. doi:10.2307/2314158. 
  18. ↑ Chakerian, G. D. (1969). "Review: Topics in Geometry by Howard Levi". The American Mathematical Monthly 76 (8): 962. doi:10.2307/2317992. 



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