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Topics in the Theory of Numbers

By: Contributor(s): Material type: TextTextLanguage: English Series: Undergraduate Texts in MathematicsPublication details: USA Springer 2003Description: xviii, 287p. illISBN:
  • 0387953205 (HB)
Subject(s):
Contents:
1. Divisibility, the Fundamental Theorem of Number Theory. 2. Congruences. 3. Rational and irrational numbers. Approximation of numbers by rationals. (Diophantine approximation.). 4. Geometric methods in number theory. 5. Properties of prime numbers. 6. Sequences of integers. 7. Diophantine problems. 8. Arithmetic functions.
Summary: Number theory, the branch of mathematics which studies the properties of the integers, is a repository of interesting and quite varied problems, sometimes impossibly difficult ones. The authors have gathered together a collection of problems from various topics in number theory that they find beautiful, intriguing, and from a certain point of view instructive. In addition to revealing the beauty of the problems themselves, they have tried to give glimpses into deeper, related mathematics. The book presents problems whose solutions can be obtained using elementary methods. No prior knowledge of number theory is assumed.
Item type: BOOKS
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IMSc Library 511 ERD (Browse shelf(Opens below)) Available 48920

Includes index

Includes bibliography (p. 275-281) and references

1. Divisibility, the Fundamental Theorem of Number Theory. 2. Congruences. 3. Rational and irrational numbers. Approximation of numbers by rationals. (Diophantine approximation.). 4. Geometric methods in number theory. 5. Properties of prime numbers. 6. Sequences of integers. 7. Diophantine problems. 8. Arithmetic functions.

Number theory, the branch of mathematics which studies the properties of the integers, is a repository of interesting and quite varied problems, sometimes impossibly difficult ones. The authors have gathered together a collection of problems from various topics in number theory that they find beautiful, intriguing, and from a certain point of view instructive. In addition to revealing the beauty of the problems themselves, they have tried to give glimpses into deeper, related mathematics. The book presents problems whose solutions can be obtained using elementary methods. No prior knowledge of number theory is assumed.

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The Institute of Mathematical Sciences, Chennai, India