Exploring Abstract Algebra with Mathematica

Al Hibbard - Central College - e-mail homepage

Ken Levasseur - UMass-Lowell - e-mail homepage

The first graphic illustrates the quotient structure of Z[12]/{0,4,8} and the second illustrates the commutators of D[5] (the dihedral group of order 10).

What is `AbstractAlgebra`?

AbstractAlgebra is a collection of Mathematica packages that enable one to work with concepts from abstract algebra (including groups, rings, fields, and morphisms). In particular, an emphasis is made to create an environment in which the packages can also be suitable for pedagogical purposes. To this end, in addition to the computation, many functions have a Textual mode (providing an explanation of the resulting computation) and a Visual mode (providing a graphic to illustrate the computation). The packages may be freely downloaded and used. More details are available, if interested.

What is Exploring Abstract Algebra with Mathematica?

The packages in AbstractAlgebra form the foundation for a series of 14 group labs and 13 ring labs designed to help students conceptualize abstract algebra. These are combined with the documentation (user's guide) for AbstractAlgebra in a book entitled Exploring Abstract Algebra with Mathematica (EAAM) published by Springer Verlag (as part of the TELOS imprint). This book is now available from TELOS/Springer-Verlag or your bookstore (ISBN 0-387-98619-7). More details regarding the book are available, if interested. In particular,for those who have already purchased the book, you are encouraged to visit the EAAM update page.

Further Information

(EAAM refers to the book Exploring Abstract Algebra with Mathematica.)