Magic boxes and related topics

University of Minnesota M.S. thesis. June 2014. Major: Applied and Computational Mathematics. Advisor: Dalibor Froncek. 1 computer file (PDF); vi, 77 pages, appendix A.Magic boxes are a 3-dimensional generalization of magic rectangles, which in turn are a classical generalization of the magic square. In this paper, two new generalizations of the magic box are introduced: the magic box set and the magic hollow box. Several necessary conditions and several sufficient conditions for the existence of these structures are examined, as well as conditions which preclude the existence of these structures