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Binary Quadratic Forms

Classical Theory and Modern Computations

Authors: Buell, Duncan A.

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  • ISBN 978-1-4612-4542-1
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About this book

The first coherent exposition of the theory of binary quadratic forms was given by Gauss in the Disqnisitiones Arithmeticae. During the nine­ teenth century, as the theory of ideals and the rudiments of algebraic number theory were developed, it became clear that this theory of bi­ nary quadratic forms, so elementary and computationally explicit, was indeed just a special case of a much more elega,nt and abstract theory which, unfortunately, is not computationally explicit. In recent years the original theory has been laid aside. Gauss's proofs, which involved brute force computations that can be done in what is essentially a two­ dimensional vector space, have been dropped in favor of n-dimensional arguments which prove the general theorems of algebraic number the­ ory. In consequence, this elegant, yet pleasantly simple, theory has been neglected even as some of its results have become extremely useful in certain computations. I find this neglect unfortunate, because binary quadratic forms have two distinct attractions. First, the subject involves explicit computa­ tion and many of the computer programs can be quite simple. The use of computers in experimenting with examples is both meaningful and enjoyable; one can actually discover interesting results by com­ puting examples, noticing patterns in the "data," and then proving that the patterns result from the conclusion of some provable theorem.

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook 67,40 €
price for Spain (gross)
  • ISBN 978-1-4612-4542-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 124,79 €
price for Spain (gross)
Softcover 83,19 €
price for Spain (gross)
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Bibliographic Information

Bibliographic Information
Book Title
Binary Quadratic Forms
Book Subtitle
Classical Theory and Modern Computations
Authors
Copyright
1989
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York Inc.
eBook ISBN
978-1-4612-4542-1
DOI
10.1007/978-1-4612-4542-1
Hardcover ISBN
978-0-387-97037-0
Softcover ISBN
978-1-4612-8870-1
Edition Number
1
Number of Pages
X, 248
Topics

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