preface.tex

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This was originally a collection of notes for abstract algebra, but it has since
evolved into a textbook. We will cover the theory of groups, rings, fields as
well as modules. 

The main motivation for writing such a textbook was to discuss the techniques
used in the study of abstract algebra, as well as the motivations behind the
concepts discussed. As such, we have adopted the more ambitious approach of
discussing the ideas and motivations behind the topics while leaving proofs
short and concise. We hope that the reader should come away with feeling that
all the concepts here are the most natural thing you could possibly think of.

The only prerequisite for this book is good mathematical maturity and the
techniques for writing proofs. It would help slightly if you have had
linear algebra, as some of our examples depend on linear algebra. Of course,
plenty of exercises and problems are included for the reader to practice
their skills. The author recommends that the reader do every exercise (even
the tedious ones!) and at at least attempt every problem. In general, the
average problem will be slightly harder than the average exercise.

At the end of the book, we include references to some other good abstract
algebra books, for those who wish to delve deeper into the theory.

This is a work in progress. Corrections and improvements are always
appreciated. Please email any corrections to robert [dot] xiu [at] mail
[dot] utoronto [dot] ca. 

\section*{Acknowledgements}
Writing a book is not a solo activity. I wish to thank some of my first readers:
Robert Chung, Jae Hyeon Hyeoh, Eddison Pham who offered feedback and suggestions
on exercises. Additionally, I would also like to thank other reviewers like
Yulong Liu who has offered feedback regarding notations, typography and
mathematical contents.

I'm also greatly indebted to other resources from which I've learnt this content
from. In no particular order: \cite{Gallian_2020}, \cite{Dummit_Foote_2004},
\cite{Jacobson_2009}. Readers are greatly encouraged to check out these other
books for a more thorough treatment on algebra.

August 2024\\
Toronto
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