Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Publication
- Publication Type
Articles 1 - 2 of 2
Full-Text Articles in Set Theory
Difference Sets In Non-Abelian Groups Of Order 256, Taylor Applebaum
Difference Sets In Non-Abelian Groups Of Order 256, Taylor Applebaum
Honors Theses
This paper considers the problem of determining which of the 56092 groups of order 256 contain (256; 120; 56; 64) difference sets. John Dillon at the National Security Agency communicated 724 groups which were still open as of August 2012. In this paper, we present a construction method for groups containing a normal subgroup isomorphic to Z4 Z4 Z2 . This construction method was able to produce difference sets in 643 of the 649 unsolved groups with the correct normal subgroup. These constructions elimated approximately 90% of the open cases, leaving 81 remaining unsolved groups.
Advanced Portfolio Theory: Why Understanding The Math Matters, Tom Arnold
Advanced Portfolio Theory: Why Understanding The Math Matters, Tom Arnold
Finance Faculty Publications
The goal of this paper is to motivate the use of efficient set mathematics for portfolio analysis [as seen in Roll, 1977] in the classroom. Many treatments stop at the two asset portfolio case (avoiding the use of matrix algebra) and an alarming number of treatments rely on illustration and templates to provide a heuristic sense of the material without really teaching how efficient portfolios are generated. This is problematic considering that the benefits of understanding efficient set mathematics go beyond portfolio analysis and into such topics as regression analysis (as demonstrated here).