( This self-contained treatment originated as a series of...)
This self-contained treatment originated as a series of lectures delivered to the Mathematical Association of America. It covers basic results on homogeneous approximation of real numbers; the analogue for complex numbers; basic results for nonhomogeneous approximation in the real case; the analogue for complex numbers; and fundamental properties of the multiples of an irrational number, for both the fractional and integral parts. The author refrains from the use of continuous fractions and includes basic results in the complex case, a feature often neglected in favor of the real number discussion. Each chapter concludes with a bibliographic account of closely related work; these sections also contain the sources from which the proofs are drawn.
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mathematician university professor
Niven completed the solution of most of Waring"s problem in 1944.
He did his undergraduate studies at the University of British Columbia and was awarded his doctorate in 1938 from the University of Chicago. He received the University of Oregon"s Charles East. Johnson Award in 1981. This problem, based on a 1770 conjecture by Edward Waring, consists of finding the smallest number g(n) such that every positive integer is the sum of at most g(n) nth powers of positive integers.
David Hilbert had proved the existence of such a g(n) in 1909.
Niven"s work established the value of g(n) for all but finitely many values of n. He was president of the Mathematical Association of America (MAA) from 1983 to 1984.
He died in 1999 in Eugene, Oregon. He was honored by being selected to write the Carus Monograph Number 11, entitled Irrational Numbers.
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 has coauthored a paper with Paul Erdőson
( This self-contained treatment originated as a series of...)
He was a member of the University of Oregon faculty from 1947 to his retirement in 1981.