Background
Buell, Duncan Alan was born on October 17, 1950 in Detroit, Michigan, United States. Son of David Newcomb and Verna May (Lusk) Buell.
(The first coherent exposition of the theory of binary qua...)
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.
http://www.amazon.com/gp/product/1461288703/?tag=2022091-20
(An elementary and computationally explicit introduction t...)
An elementary and computationally explicit introduction to the theory of binary quadratic forms. Where possible, the emphasis is on explicit, algorithmically sensible proofs and examples. Constructive proofs are preferred over existence proofs. The author offers a contemporary discussion of the classical theory and a survey of computations and applications. The text should be understandable by advanced undergraduates in mathematics and computer science, and the expert in number theory will likely find the computational emphasis rewarding.
http://www.amazon.com/gp/product/0387970371/?tag=2022091-20
Buell, Duncan Alan was born on October 17, 1950 in Detroit, Michigan, United States. Son of David Newcomb and Verna May (Lusk) Buell.
Bachelor of Science, University Arizona, 1971. Master of Arts, University Michigan, 1972. Doctor of Philosophy, University Illinois, Chicago, 1976.
Research associate, Carleton U., Ottawa, Ontario., Canada, 1976-1977; assistant professor, Bowling Green State University, Bowling Green, Ohio., 1977-1979; assistant professor, Louisiana State University, Baton Rouge, 1979-1982; associate professor, Louisiana State University, 1982-1986; research staff member, Center for Computing Sciences, Bowie, Maryland., 1986-1987; director algorithms research, Center for Computing Sciences, Bowie, 1987-1990; senior research scientist, Center for Computing Sciences, Bowie, Maryland., since 1990.
(The first coherent exposition of the theory of binary qua...)
(An elementary and computationally explicit introduction t...)
Member state board American Civil Liberties Union, Louisiana, 1983-1985. Member American Mathematics Society, Association for Computing Machinery, Institute of Electrical and Electronics Engineers, American Association for the Advancement of Science, Phi Beta Kappa, Phi Kappa Phi.
Married Mary Ann Grandjean, October 31, 1986.