A special feature of Nagell's well-known text is the rather extensive treatment of Diophantine equations of second and higher degree. A large number of non-routine problems are given.
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9 of 9 people found the following review helpful:
5.0 out of 5 stars
Elementary, but deep,
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This review is from: Introduction to Number Theory (Hardcover)
Nagell accomplishes a lot in 300 pages. He concentrates on interesting and deep results that can be obtained by elementary methods. In this respect, Nagell's text resembles Hardy and Wright's, but he includes 180 exercises. The exercises, he writes, "are not of a routine character but are really intended to supplement the theory with known and new results ...." Thus the book is for the serious student of mathematics. Some highlights: In the first chapter, Nagell proves the irrationality of e and pi. In chapters 2 and 8, he introduces the reader to asymptotic methods and gives an elementary proof of the Prime Number Theorem. Other chapters include very good introductions to cyclotomic polynomials and Diophantine equations of the second degree. In chapter 5, he determines the values of quadratic Gauss sums. In the context of Diophantine equations, Nagell also proves some results about unique factorization in several imaginary quadratic number fields.
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1. Divisors. - The elementary theory of numbers deals primarily with the properties of the positive integers or natural numbers 1, 2, 3, 4, 5, ... Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hence Theorem, Euclid's Elementa New!
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1. Divisors. - The elementary theory of numbers deals primarily with the properties of the positive integers or natural numbers 1, 2, 3, 4, 5, ... Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hence Theorem, Euclid's Elementa New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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- Disquisitiones Arithmeticae by Carl F. Gauss in Front Matter
- Fermat's Last Theorem for Amateurs by Paulo Ribenboim on page 63, and Back Matter
- Number Theory: Proceedings of the First Conference of the Canadian Number Theory Association Held at the Banff Center, Banff, Alberta ([De Gruyter Proceedings in Mathematics]) by Richard A. Mollin on page 91
- Elements of the Theory of Numbers by Thomas P. Dence on page 321
- A Tribute to Paul Erdos by A. Baker on page 443
- The Higher Arithmetic: An Introduction to the Theory of Numbers by H. Davenport in Back Matter
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