Free Samples from Exploring Abstract Algebra with Mathematica

These labs are a sampling of what is available in Exploring Abstract Algebra with Mathematica, published by TELOS/Springer-Verlag. More details regarding this book are available at other subsections of this EAAM section.

Note that the labs are not functional (capable of being evaluated) unless you have installed the underlying AbstractAlgebra packages, but they can still be read as they are. You are encouraged, however, to download the AbstractAlgebra packages to allow for full experimentation within the labs.

For each lab, there are several choices of viewing the notebook. Note: if you receive a 404 error (file not found), it may be cause your web server does not accept documents with extension .ma and/or .nb. In this case, ask the IT person in charge of the server to allow these types or contact us.

Group Lab 5. Subversively Grouping Our Elements

This lab explores the notion of a subgroup, including looking at the subgroups of Zn and Un, calculating the probability that a random subset of Zn is a subgroup and determining what elements in a subset are necessary so that the closure yields the whole group.

Group Lab 8. Isomorphisms

Here we look at the definition of an isomorphism and then use various visual mechanisms to try to determine when two groups are or are not isomorphic.

Ring Lab 4. What Does Z[i]/< a+bi > Look Like?

This lab focuses on the Gaussian integers mod an ideal generated by some Gaussian integer.

Ring Lab 6. Polynomial Rings

Some basic properties of polynomial rings are introduced and explored.

To view the .pdf files, one needs a pdf reader. One application for all platforms, Adobe Acrobat Reader, is free. One can download this from http://www. adobe.com/prodindex/acrobat/readstep.html.

 

Prepared by Al Hibbard. Most recent update: 6/16/2006. This page has been viewed 304 times since June 16, 2006. The entire EAAM web site has had 669,528 hits since July 23, 2002.