Mathematics Textbook

Textbook: Abstract Algebra for Polynomial Operations (Download)

Author: Maya Mohsin Ahmed

Table of contents

To forget one's purpose is the commonest form of stupidity - Nietzsche.

I have been asked, time and again, what the purpose is of learning Abstract Algebra. I wrote this book to answer this perennial question. Traditionally, Algebra books begin with definitions and theorems and applications might appear as examples. Many students are not inclined to learn without a purpose. The beautiful subject of Algebra closes doors on them. The responses of many students to Abstract Algebra remind me of Gordan's reaction to the proof of the Hilbert's basis Theorem - "This is not Mathematics. This is Theology".

The focus of this book is applications of Abstract Algebra to polynomial systems. The first five chapters explore basic problems like polynomial division, solving systems of polynomials, formulas for roots of polynomials, and counting integral roots of equations. The sixth chapter uses the concepts developed in the book to explore coding theory and other applications.

This book could serve as a textbook for a beginning Algebra course, a student takes immediately after a Linear Algebra course. Linear Algebra is not a prerequisite but will provide the basis for the natural progression to nonlinear Algebra. This book could also be used for an elective course after an Abstract Algebra course to focus on applications. This book is suitable for third or fourth year undergraduate students.