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Irrational Numbers by Ivan Morton Niven
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About this book :-
Irrational Numbers written by
Ivan Morton Niven .
The entire subject of irrational numbers cannot of course be encompassed in a single volume. In the selection of material the main emphasis has been on those aspects of irrational numbers commonly associated with number theory and Diophantine approximations. The topological facets of the subject are not included, although the introductory part of
I has a sketch of some of the simplest set-theoretic properties of the irrationals as a part of the continuum. The axiomatic basis for irrational numbers, proceeding say from the Peano postulates for the natural numbers to the construction of the real numbers, is purposely omitted, because in the first place the aim is not in the direction of the foundations of mathematics, and in the second place there are excellent treatments of this topic readily available.
The customary organization of a book with related subjects grouped together has been modified in part by consideration of the degree of difficulty of the topics, proceeding from the easiest to the most difficult.
(Ivan Morton Niven)
Book Detail :-
Title: Irrational Numbers
Author(s): Ivan Morton Niven
Publisher: The Mathematical Association of America
Series: Carus Mathematical Monographs
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About Author :-
The author Ivan Morton Niven (1915–1999) was a Canadian-American mathematician, specializing in number theory and known 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 was the author of several books on mathematics. 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. 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. He died in 1999 in Eugene, Oregon.
Niven received the University of Oregon's Charles E. Johnson Award in 1981. He received the MAA Distinguished Service Award in 1989. He won a Lester R. Ford Award in 1970. In 2000, the asteroid 12513 Niven, discovered in 1998, was named after him.
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Book Contents :-
Irrational Numbers written by
cover the following topics.
1. RATIONALS AND IRRATIONALS
2. SIMPLE IRRATIONALITIES
3. CERTAIN ALGEBRAIC NUMBERS
4. THE APPROXIMATION OF IRRATIONALS BY RATIONALS
5. CONTINUED FRACTIONS
6. FURTHER DIOPHANTINE APPROXIMATIONS
7. ALGEBRAIC AND TRANSCENDENTAL NUMBERS
8. NORMAL NUMBERS
9. THE GENERALIZED LINDEMANN THEOREM
10. THE GELFOND-SCHNEIDER THEOREM
LIST OP NOTATION
INDEX OF TOPICS
INDEX OF NAMES
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