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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Symmetric Designs, Difference Sets, And A New Way To Look At Macfarland Difference Sets, John Bowen Polhill Jr.
Symmetric Designs, Difference Sets, And A New Way To Look At Macfarland Difference Sets, John Bowen Polhill Jr.
Honors Theses
In this paper, the topics of symmetric designs and difference sets are discussed both separately and in relation to each other. Then an approach to MacFarland Difference Sets using the theory behind homomorphisms from groups into the complex numbers is introduced. This method is contrasted with the method of finding this type of difference set used by E.S. Launder in his book Symmetric Designs: An Algebraic Approach.
Topics In Cyclotomic And Quadratic Fields, Pam Mellinger
Topics In Cyclotomic And Quadratic Fields, Pam Mellinger
Honors Theses
This paper introduces cyclotomic and quadratic fields and explores some of their properties and applications to problems in number theory. After some preliminary definitions and theorems, the paper looks at the relationship between quadratic and cyclotomic fields, at Kummer's lemma on units in the pth cyclotomic field, and at the Quadratic Reciprocity Law and its applications to diophantine equations.