Howard Levi
Howard Levi | |
---|---|
Born | November 9, 1916 New York City |
Died | September 11, 2002(2002-09-11) (aged 85) New York City |
Nationality | American |
Alma mater | Columbia University |
Known for | Levi's reduction process |
Scientific career | |
Fields | Mathematics: differential algebra |
Institutions | Columbia University City University of New York |
Doctoral advisor | Joseph 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) Archived 2016-03-04 at the Wayback Machine
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
- ^ Notices of the AMS, June/July 2003, Volume 50, Number 6, p. 705.
- ^ Howard Levi at the Mathematics Genealogy Project
- ^ a b Melvin Fitting – The Four Color Theorem Archived 2015-02-12 at the Wayback Machine
- ^ 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).
- ^ Sinclair, Nathalie (2008). The History of the Geometry Curriculum in the United States. IAP. p. 64. ISBN 978-1-59311-697-2.
- ^ Sitomer, H. – Coordinate geometry with an affine approach, Mathematics Teacher 57 (1964), 404–405.
- ^ C. Ray Wylie, An Affine Approach to Euclidean Geometry (p. 237 from the PDF document, p. 231 from the document itself)
- ^ Levi, Howard — An Experimental Course in Analysis for College Freshmen
- ^ Gillman, Leonard (1993). "An Axiomatic Approach to the Integral" (PDF). The American Mathematical Monthly. 100 (1): 16–25. doi:10.2307/2324809. JSTOR 2324809.
- ^ Gillman, Leonard (1974). "Review: Polynomials, Power Series, and Calculus by Howard Levi". The American Mathematical Monthly. 81 (5): 532–533. doi:10.2307/2318616. JSTOR 2318616.
- ^ Mead, D. G. (December 1973). "The Equation of Ramanujan-Nagell and [y2]" (PDF). Proceedings of the American Mathematical Society. 41 (2): 333–341. doi:10.2307/2039090. JSTOR 2039090.
- ^ 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.
- ^ Lott, Fred W. (1955). "Review: Elements of algebra by Howard Levi". The Mathematics Teacher. 48 (5): 353–354. JSTOR 27954922.
- ^ Lee, Herbert L. (1955). "Review: Elements of algebra by Howard Levi". The Scientific Monthly. 80 (6): 387. JSTOR 21575.
- ^ Rajaratnam, Nageswari (1960). "Review: Elements of algebra by Howard Levi". The Mathematics Teacher. 53 (7): 585–586. JSTOR 27956256.
- ^ 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.
- ^ Bezuszka, S. J. (1965). "Review: Foundations of Geometry and Trigonometry by Howard Levi". The American Mathematical Monthly. 72 (5): 565. doi:10.2307/2314158. JSTOR 2314158.
- ^ Chakerian, G. D. (1969). "Review: Topics in Geometry by Howard Levi". The American Mathematical Monthly. 76 (8): 962. doi:10.2307/2317992. JSTOR 2317992.