Download Theses (pdf)
  • Sonja Wieck
  • Evelyn Manalo

  • Honors Theses
    Submitted to the UCSD Mathematics Department in Spring 2001

    Sonja Willis    (now Sonja Wieck)
    Hamiltonian Paths and Cayley Digraphs of Algebraic Groups

    Ms. Willis uses procedures she has written in Maple to investigate the Cayley Digraphs of groups. Her work was inspired by a section in the textbook "Contemporary Abstract Algebra" by Joseph Gallian. She developed a program to find Hamiltonian Paths in a group; she extended the Maple "draw" program to appropriately display Cayley digraphs; and she conducted a study of Hamiltonian paths for all groups of orders 1-32 (using Groups32 to import the data to Maple). She has supplied computer proofs of some of the assertions found in the literature.  A Maple worksheet will appear for those who want to run her procedures.

    Evelyn Manalo   
    Group Properties and Group Isomorphism

    Ms. Manalo investigates efficient ways to determine whether or not two groups are isomorphic. Her goal is to find easily computed properties of groups of low order which can be used to distinguish them. In this thesis she develops an algorithm which, for an abelian group, produces the canonical decomposition of a group as a product of cyclic subgroups of prime power order given the number of elements of various orders. This thesis contains the algorithm with examples and the necessary support theorems. Groups32 was used to examine examples.  The Powerpoint version of her talk, a downloadable copy of Groups32, and some supplementary programs for Groups32 used in this work will appear.