The Queen of Mathematics: An Introduction to Number Theory

Overview

Like other introductions to number theory, this one includes the usual curtsy to divisibility theory, the bow to congruence, and the little chat with quadratic reciprocity. It also includes proofs of results such as Lagrange's Four Square Theorem, the theorem behind Lucas's test for perfect numbers, the theorem that a regular n-gon is constructible just in case phi(n) is a power of 2, the fact that the circle cannot be squared, Dirichlet's theorem on primes in arithmetic ...

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Paperback (Softcover reprint of the original 1st ed. 1995)
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Overview

Like other introductions to number theory, this one includes the usual curtsy to divisibility theory, the bow to congruence, and the little chat with quadratic reciprocity. It also includes proofs of results such as Lagrange's Four Square Theorem, the theorem behind Lucas's test for perfect numbers, the theorem that a regular n-gon is constructible just in case phi(n) is a power of 2, the fact that the circle cannot be squared, Dirichlet's theorem on primes in arithmetic progressions, the Prime Number Theorem, and Rademacher's partition theorem.
We have made the proofs of these theorems as elementary as possible.
Unique to The Queen of Mathematics are its presentations of the topic of palindromic simple continued fractions, an elementary solution of Lucas's square pyramid problem, Baker's solution for simultaneous Fermat equations, an elementary proof of Fermat's polygonal number conjecture, and the Lambek-Moser-Wild theorem.

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Editorial Reviews

Booknews
A textbook for first-year graduate or honors undergraduate students of mathematics. The only prerequisite for most of the book is pre-calculus mathematics, but many of the problems are not accessible to someone without several undergraduate mathematics course. Includes the standard topics of introductions to number theory, including divisibility theory, congruence, and quadratic reciprocity. Also proves that the circle cannot be squared. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9789401041263
  • Publisher: Springer Netherlands
  • Publication date: 12/31/2013
  • Series: Texts in the Mathematical Sciences (closed) Series
  • Edition description: Softcover reprint of the original 1st ed. 1995
  • Pages: 390
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.83 (d)

Table of Contents

Preface. 1. Propaedeutics. 2. Simple Continued Fractions. 3. Congruence. 4. x2—Ry2 = C. 5. Classical Construction Problems. 6. The Polygonal Number Theorem. 7. Analytic Number Theory. Bibliography. A Appendix: Answers to Selected Exercises. Index.

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