“Ivan M. Niven”的意思、由来-开放百科全书

Ivan Morton Niven (October 25, 1915 – May 9, 1999) was a Canadian-American mathematician, specializing in number theory. He 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 received the University of Oregon's Charles E. Johnson Award in 1981.

Niven completed the solution of most of Waring's problem in 1944. 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

He was president of the Mathematical Association of America (MAA) from 1983 to 1984.^[2] He received the MAA Distinguished Service Award in 1989.

He was honored by being selected to write the Carus Monograph Number 11, entitled Irrational Numbers.^[3] He won a Lester R. Ford Award in 1970.^[4] Niven numbers, Niven's constant, and Niven's theorem are named in his honor; also, in 2000, the asteroid 12513 Niven, discovered in 1998, was named after him. He has an Erdős number of 1 because he coauthored a paper with Paul Erdős ^[5]

Popular works by Niven

See also

References

1. ^{{MathGenealogy|id=6349}}
2. ^MAA presidents: Ivan Niven
3. ^{{cite journal|author=Rosenbaum, R. A.|title=Review: Irrational Numbers by Ivan Niven. Carus Monograph, no. 11: New York, Wiley, 1956|journal=Bull. Amer. Math. Soc.|year=1959|volume=64|issue=2|pages=68–69|url=http://www.ams.org/journals/bull/1958-64-02/S0002-9904-1958-10170-6/S0002-9904-1958-10170-6.pdf|doi=10.1090/S0002-9904-1958-10170-6}}
4. ^{{cite journal|author=Niven, Ivan|title=Formal power series|journal=Amer. Math. Monthly|volume=76|year=1969|pages=871–889|url=http://www.maa.org/programs/maa-awards/writing-awards/formal-power-series|doi=10.2307/2317940}}
5. ^{{citation|last=Erdős|first= P.|last2=Niven|first2=I.|date=1946|title=Some properties of partial sums of the harmonic series|journal=Bull. Amer. Math. Soc. |volume=52|pages=248–251|doi=10.1090/s0002-9904-1946-08550-x}}
6. ^{{cite journal|author=Whiteman, Albert Leon|title=Review: An introduction to the theory of numbers, by Ivan Niven and Herbert S. Zuckerman|journal=Bull. Amer. Math. Soc.|year=1961|volume=67|issue=4|pages=339–340|url=http://www.ams.org/journals/bull/1961-67-04/S0002-9904-1961-10603-4/|doi=10.1090/s0002-9904-1961-10603-4}}
7. ^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.
8. ^Bishop, R. L., Reviewed Work: Calculus, An Introductory Approach by Ivan Niven Pi Mu Epsilon Journal, vol. 3, no. 5, 1961, pp. 236–236. JSTOR, www.jstor.org/stable/24338116.
9. ^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
10. ^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