PREFACE :
In 1990 we introduced a one-semester applications of algebra course at
North Carolina State University for students who had successfully completed
semesters of linear and abstract algebra.We intended for the course
to give students more exposure to basic algebraic concepts, and to show
students some practical uses of these concepts.The course was received
enthusiastically by both students and faculty and has become one of the
most popular mathematics electives at NC State.
When we were originally deciding on material for the course, we knew
that we wanted to include several topics from coding theory, cryptography,
and counting (what we call Polya theory).With this in mind, at the suggestion
of Michael Singer, we used George Mackiw’s book Applications of
Abstract Algebra for the first few years, and supplemented as we saw fit.
After several years, Mackiw’s book went out of print temporarily.Rather
than search for a new book for the course, we decided to write our own notes
and teach the course from a coursepack.Ab out the same time, NC State
incorporated the mathematics software package Maple VTM1 into its calculus
sequence, and we decided to incorporate it into our course as well.The
use of Maple played a central role in the recent development of the course
because it provides a way for students to see realistic examples of the topics
discussed without having to struggle with extensive computations.With
additional notes regarding the use of Maple in the course, our coursepack
evolved into this book.In addition to the topics discussed in this book, we
have included a number of other topics in the course.Ho wever, the present
material has become the constant core for the course.
Our philosophy concerning the use of technology in the course is that
it be a useful tool and not present new problems or frustrations.Consequently,
we have included very detailed instructions regarding the use of Maple in this book.It is our hope that the Maple discussions are thorough
enough to allow it to be used without much alternative aid.As alternative
aids, we have included a basic Maple tutorial in Appendix A, and an
introduction to some of Maple’s linear algebra commands in Appendix B.
Although we do not require students to produce the Maple code used in
the course, we do require that they obtain a level of proficiency such that
they can make basic changes to provided worksheets to complete numerous
Maple exercises.So that this book can be used for applications of algebra
courses in which Maple is not incorporated, we have separated all Maple
material into sections
Title : Applications of Abstract Algebra with MAPLE
author(s) : Richard E. Klima, Neil Sigmon, Ernest Stitzinger
size : 1 Mb
file type : PDF
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