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Ivan M. Niven

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

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

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

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

  • 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. Anneli Lax New Mathematical Library. Vol. 1. 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.

See also

References

  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.
Quelle: https://en.wikipedia.org/wiki/Ivan_M._Niven