Advanced search options

Advanced Search Options 🞨

Browse by author name (“Author name starts with…”).

Find ETDs with:

in
/  
in
/  
in
/  
in

Written in Published in Earliest date Latest date

Sorted by

Results per page:

You searched for +publisher:"University of North Carolina – Greensboro" +contributor:("Brett Tangedal"). One record found.

Search Limiters

Last 2 Years | English Only

No search limiters apply to these results.

▼ Search Limiters

1. Shepherd, Rick L. Binary quadratic forms and genus theory.

Degree: 2013, University of North Carolina – Greensboro

The study of binary quadratic forms arose as a natural generalization of questions about the integers posed by the ancient Greeks. A major milestone of understanding occurred with the publication of Gauss's Disquisitiones Arithmeticae in 1801 in which Gauss systematically treated known results of his predecessors and vastly increased knowledge of this part of number theory. In effect, he showed how collections of sets of binary quadratic forms can be viewed as groups, at a time before group theory formally existed. Beyond that, he even defined and calculated genus groups, which are essentially quotient groups, that explain which congruence classes of numbers can be represented by given sets of forms. This thesis examines Gauss's main results as interpreted and refined over two centuries. Also code has been created to implement many of the algorithms used in studying the relationships of such forms to each other, to generate examples, and to provide a small toolkit of software for analyzing the corresponding algebraic structures.; Binary quadratic forms, Class groups, Class number, Genus theory, PARI code Advisors/Committee Members: Brett Tangedal (advisor).

Subjects/Keywords: Forms, Binary; Forms, Quadratic; Group theory

Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Page 7

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Shepherd, R. L. (2013). Binary quadratic forms and genus theory. (Masters Thesis). University of North Carolina – Greensboro. Retrieved from http://libres.uncg.edu/ir/listing.aspx?styp=ti&id=15057

Chicago Manual of Style (16th Edition):

Shepherd, Rick L. “Binary quadratic forms and genus theory.” 2013. Masters Thesis, University of North Carolina – Greensboro. Accessed July 15, 2020. http://libres.uncg.edu/ir/listing.aspx?styp=ti&id=15057.

MLA Handbook (7th Edition):

Shepherd, Rick L. “Binary quadratic forms and genus theory.” 2013. Web. 15 Jul 2020.

Vancouver:

Shepherd RL. Binary quadratic forms and genus theory. [Internet] [Masters thesis]. University of North Carolina – Greensboro; 2013. [cited 2020 Jul 15]. Available from: http://libres.uncg.edu/ir/listing.aspx?styp=ti&id=15057.

Council of Science Editors:

Shepherd RL. Binary quadratic forms and genus theory. [Masters Thesis]. University of North Carolina – Greensboro; 2013. Available from: http://libres.uncg.edu/ir/listing.aspx?styp=ti&id=15057

.