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Ivan M. Niven

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Ivan M. Niven
BornOctober 25, 1915
Vancouver, Canada
DiedMay 9, 1999(1999-05-09) (aged 83)
Known forNiven number
Niven's constant
Niven's proof
Niven's theorem
Eilenberg–Niven theorem
AwardsLester R. Ford Award (1970)
Academic background
Alma mater
Doctoral advisorLeonard Eugene Dickson[1]
Academic work
InstitutionsUniversity of Oregon
Doctoral studentsMargaret Maxfield

Ivan Morton Niven (October 25, 1915 – May 9, 1999) was a Canadian-American number theorist best remembered for his work on Waring's problem. He worked for many years as a professor at the University of Oregon, and was president of the Mathematical Association of America. He wrote several books on mathematics.

Life

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Niven was born in Vancouver. He did his undergraduate studies at the University of British Columbia and was awarded his doctorate in 1938 from the University of Chicago.[1] He was a member of the University of Oregon faculty from 1947 to his retirement in 1981. He was president of the Mathematical Association of America (MAA) from 1983 to 1984.[2]

He died in 1999 in Eugene, Oregon.

Research

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Niven completed the solution of most of Waring's problem in 1944.[3] This problem, based on a 1770 conjecture by Edward Waring, consists of finding the smallest number such that every positive integer is the sum of at most -th powers of positive integers. David Hilbert had proved the existence of such a in 1909; Niven's work established the value of for all but finitely many values of .

Niven gave an elementary proof that is irrational in 1947.[4]

Niven numbers, Niven's constant, and Niven's theorem are named for Niven.

He has an Erdős number of 1 because he coauthored a paper with Paul Erdős, on partial sums of the harmonic series.[5]

Recognition

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Niven received the University of Oregon's Charles E. Johnson Award in 1981. He received the MAA Distinguished Service Award[6] in 1989.

He won a Lester R. Ford Award in 1970.[7] In 2000, the asteroid 12513 Niven, discovered in 1998, was named after him.[8][9]

Books

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  • Irrational Numbers. [Carus Mathematical Monographs]. The Mathematical Association of America. 1956. ISBN 0-88385-011-7.[10]
  • Niven, Ivan; Zuckerman, Herbert S.; Montgomery, Hugh L. (1991) [First published 1960]. An Introduction to the Theory of Numbers. New York: John Wiley & Sons. ISBN 978-81-265-1811-1.[11]
  • Calculus. Van Nostrand Reinhold Company. 1966. ISBN 978-0-442-06032-9.[12][13][14][15]
  • Numbers: Rational and Irrational. Washington DC: The Mathematical Association of America. 2011 [First published 1961]. doi:10.5948/upo9780883859193. ISBN 978-0-88385-919-3.
  • Diophantine Approximations. Mineola, N.Y: Dover Publications. 1 January 2008 [First published 1963]. ISBN 978-0-486-46267-7.[16]
  • Mathematics of Choice: How to Count without Counting. Washington, DC: Mathematical Association of America. 1965. ISBN 978-0-88385-615-4.
  • Maxima and Minima Without Calculus. Washington, D.C.: Cambridge University Press. 1981. ISBN 978-0-88385-306-1.
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See also

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References

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  1. ^ a b Ivan M. Niven at the Mathematics Genealogy Project
  2. ^ MAA presidents: Ivan Niven
  3. ^ Niven, Ivan M. (1944). "An unsolved case of the Waring problem". American Journal of Mathematics. 66 (1). The Johns Hopkins University Press: 137–143. doi:10.2307/2371901. JSTOR 2371901. MR 0009386.
  4. ^ Niven, Ivan (1947), "A simple proof that π is irrational" (PDF), Bulletin of the American Mathematical Society, vol. 53, no. 6, p. 509, doi:10.1090/s0002-9904-1947-08821-2
  5. ^ Erdős, P.; Niven, I. (1946), "Some properties of partial sums of the harmonic series", Bull. Amer. Math. Soc., 52 (4): 248–251, doi:10.1090/s0002-9904-1946-08550-x
  6. ^ "Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service". Mathematical Association of America. Retrieved 28 April 2024.
  7. ^ Niven, Ivan (1969). "Formal power series". Amer. Math. Monthly. 76 (8): 871–889. doi:10.2307/2317940. hdl:10338.dmlcz/120493. JSTOR 2317940.
  8. ^ "AstDyS-2 Asteroids – Dynamic Site – (12513) Niven". newton.spacedys.com. Retrieved 3 April 2020.
  9. ^ "Asteroids with Canadian connections" (PDF), Journal of the Royal Astronomical Society of Canada, 94 (2): 47, April 2000, archived from the original (PDF) on 2005-02-16
  10. ^ Rosenbaum, R. A. (1959). "Review: Irrational Numbers by Ivan Niven. Carus Monograph, no. 11: New York, Wiley, 1956" (PDF). Bull. Amer. Math. Soc. 64 (2): 68–69. doi:10.1090/S0002-9904-1958-10170-6.
  11. ^ Whiteman, Albert Leon (1961). "Review: An introduction to the theory of numbers, by Ivan Niven and Herbert S. Zuckerman". Bull. Amer. Math. Soc. 67 (4): 339–340. doi:10.1090/s0002-9904-1961-10603-4.
  12. ^ Kaltenborn, H. S., Reviewed Work: Calculus: An Introductory Approach. by Ivan Niven The American Mathematical Monthly, vol. 69, no. 1, 1962, pp. 69–69. JSTOR, www.jstor.org/stable/2312762.
  13. ^ Bishop, R. L., Reviewed Work: Calculus, An Introductory Approach by Ivan Niven Pi Mu Epsilon Journal, vol. 3, no. 5, 1961, pp. 236–236 [www.jstor.org/stable/24338116 JSTOR]
  14. ^ Goodstein, R. (1962). Calculus. An introductory approach. By I. Niven. Pp. 169. 36s. 1961. (D. van Nostrand, London). The Mathematical Gazette, 46(358), 333–333. doi:10.2307/3611795
  15. ^ Cobb, R. (1967). Calculus: An Introductory Approach. 2nd Edition. (University Series in Undergraduate Mathematics.) By Ivan Niven. Pp. viii, 202. 46s. 6d. 1967. (D. Van Nostrand Co. Ltd.). The Mathematical Gazette, 51(378), 330–330. doi:10.2307/3612954
  16. ^ D.S. (1959). "Review: Diophantine Approximations Interscience Publishers, New York, 1963" (PDF). Bull. Amer. Math. Soc. 64 (2): 68–69. doi:10.1090/S0002-9904-1958-10170-6.
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