Ivan M. Niven

Ivan Morton Niven ( born October 25, 1915 in Vancouver, † 9 May 1999 in Eugene ) was an American- Canadian mathematician who has been dealing with number theory ( Diophantine approximation, additive number theory, Irrationalitäts and transcendence questions ) and combinatorics.

Biography

Niven studied at the University of British Columbia (Master 's degree in 1936 ) and his doctorate in 1938 at the University of Chicago with Leonard Dickson (A Waring problem). 1938/39, he was with Hans Rademacher at the University of Pennsylvania. He then spent three years at the University of Illinois, and five years at Purdue University before he went in 1947 to the University of Oregon, where he remained until his retirement in 1982. In 1957/58 he was a visiting professor at Stanford University and 1964/65 at the University of California, Berkeley.

In 1947, he gave a simple proof of the irrationality of ( already by Johann Heinrich Lambert proved in 1760 ). He was also known for a work on the Waring problem ( about which he already received his doctorate ). This problem, which goes back to an Edward Waring in 1770 established presumption asks for the smallest natural number such that every natural number is the sum of at most - th powers of natural numbers. David Hilbert had in 1909 already demonstrated the existence of such. Niven joined in his work from 1944 from a series of works of his teacher Dickson, of Pillai and Rubugunday. As a result of their work could be given for a formula for the exponent:

He wrote a number of books on mathematics (including a well-known introduction to elementary number theory) and also traveled in the 1960s regularly on behalf of the Mathematical Association of America ( MAA) to keep popular lectures on mathematics. 1974/75, he was Vice President of the MAA and 1983/84 its president. In 1989 he received the highest award of the MAA, the Award for Distinguished Service to Mathematics. For his article on formal power series in the American Mathematical Monthly in 1969, he received the 1970 Lester R. Ford Award from the MAA.

In 1981, he received the Charles E. Johnson Award from the University of Oregon. In 1962 he was invited speaker at the International Congress of Mathematicians in Stockholm ( On the covering of lattice points in 3 -space ).

Niven worked several times with Paul Erdős.

Niven numbers and the Niven 's constant is named after him; Also in 1998 discovered asteroid ( 12513 ) Niven was named after him in 2000.

Writings

  • With Herbert Samuel Zuckerman, Hugh Montgomery: Introduction to the theory of numbers, 5th edition, Wiley, 1991 ( first English Wiley 1960, German Niven, Zuckerman: Introduction to Number Theory, BI Publisher 1976, 2 volumes)
  • Maxima and Minima without Calculus, MAA, Dolciani Mathematical Expositions, 1981
  • Diophantine Approximations, Interscience 1963
  • Irrational Numbers, Carus Mathematical Monograph 1956
  • Numbers: Rational and Irrational, Random House 1961
  • Mathematics of Choice -how to count without counting, MAA 1965
  • Calculus - an introductory approach, Princeton, Van Nostrand, 1961, 1965
May 9 Eugene (Oregon) Leonard Eugene Dickson Harshad number Niven's constant (12513) Niven Integrated Authority File
421580
de