CPM-7 Visualizing Abstract Algebra
Start Date
12-4-2024 9:30 AM
End Date
12-4-2024 11:30 AM
Location
University Readiness Center Greatroom
Document Type
Poster
Abstract
In upper-level mathematics courses, students begin to encounter increasingly abstract algebraic concepts such as groups, rings and vector spaces. This abstraction, along with a plethora of new terminology and notation that accompanies it, can make it difficult for students to build their intuition and follow what’s going on. The aim of our research is to bring some of these abstract algebraic ideas down to earth with some concrete visualizable examples. For example, addition and multiplication of natural numbers can be analogized with unions and Cartesian products of finite sets, and the group S_3 can be interpreted as rotations and mirror symmetries of an equilateral triangle. Not only do such examples help students navigate higher-level mathematics, they also have the potential to make such mathematics a little more accessible to those who do not consider themselves mathematically inclined.
Keywords
Algebra, categorification, group, ring, monoid
CPM-7 Visualizing Abstract Algebra
University Readiness Center Greatroom
In upper-level mathematics courses, students begin to encounter increasingly abstract algebraic concepts such as groups, rings and vector spaces. This abstraction, along with a plethora of new terminology and notation that accompanies it, can make it difficult for students to build their intuition and follow what’s going on. The aim of our research is to bring some of these abstract algebraic ideas down to earth with some concrete visualizable examples. For example, addition and multiplication of natural numbers can be analogized with unions and Cartesian products of finite sets, and the group S_3 can be interpreted as rotations and mirror symmetries of an equilateral triangle. Not only do such examples help students navigate higher-level mathematics, they also have the potential to make such mathematics a little more accessible to those who do not consider themselves mathematically inclined.