Abstract
Abstract Algebra is an area of mathematics which focuses on the properties of algebraic structures. One such structure, called a Group, has properties which are applicable to puzzle solving. We provide the fundamental properties of permutation groups and discuss certain theorems which enable one to model a variety of puzzles. In addition, we demonstrate how the computational algebra program, GAP can be utilized in order to work with the large permutation groups that describe very complex puzzles. Our goal is to use the mathematics underlying these puzzles in order to understand how they can be solved.
Faculty Sponsors
Dr. Ricardo Carrera
Project Type
Event
Location
Alvin Sherman Library
Start Date
4-12-2013 1:00 PM
End Date
4-12-2013 5:30 PM
Applications of Abstract Algebra to Puzzle Modeling
Alvin Sherman Library
Abstract Algebra is an area of mathematics which focuses on the properties of algebraic structures. One such structure, called a Group, has properties which are applicable to puzzle solving. We provide the fundamental properties of permutation groups and discuss certain theorems which enable one to model a variety of puzzles. In addition, we demonstrate how the computational algebra program, GAP can be utilized in order to work with the large permutation groups that describe very complex puzzles. Our goal is to use the mathematics underlying these puzzles in order to understand how they can be solved.
