Hibbard, Al

Mathematics & Computer Science Central College

Pella, IA 50219



hibbarda@central.edu



Exploring Abstract Algebra with Mathematica



I am currently trying to extend and improve some work that I had formerly 

prepared for Mathematica in a non-notebook environment. One the major 

overriding goals is to provide a graphical perspective to algebraic 

concepts, whenever possible. Since many algebraic notions can be visualized 

using the groups of symmetry of various geometric objects, these groups in 

particular will be exploited. I am also interested in providing a structure 

to explore the groups of smaller order (somewhat akin to what is done in 

the program Exploring Small Groups by Ladnor Geissinger). I intend to 

provide a variety of packages that can be used as a basis for developing 

labs, as well as providing a number of exploratory labs based on these 

packages (which can be modified, extended, or redirected). Most of the 

overall structure is in place for group theory and several packages and 

labs are finished. Other areas of abstract algebra have not yet been 

explored very thoroughly. I have also started some "pre-algebra" topics, 

such as modular arithmetic. 



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