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    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
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Binary Quadratic Forms: Classical Theory and Modern Computations

Binary Quadratic Forms: Classical Theory and Modern Computations

Buell, Duncan A.

Paperback

General Mathematics

ISBN10: 1461288703
ISBN13: 9781461288701
Publisher: Springer
Published: Sep 26 2011
Pages: 248
Weight: 0.82
Height: 0.55 Width: 6.14 Depth: 9.21
Language: English
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 quadraticforms 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.

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