AAR Preface

\(\newcommand{\ds}{\displaystyle} \newcommand{\la}{\langle} \newcommand{\ra}{\rangle} \newcommand{\ba}{\left[\begin{array}} \newcommand{\ea}{\end{array}\right]} \newcommand{\normal}{\trianglelefteq} \newcommand{\Span}{\operatorname{Span}} \newcommand{\Null}{\operatorname{Null}} \renewcommand{\Im}{\operatorname{Im}} \newcommand{\nullity}{\operatorname{nullity}} \newcommand{\rank}{\operatorname{rank}} \newcommand{\range}{\operatorname{range}} \newcommand{\tr}{\operatorname{tr}} \newcommand{\proj}{\operatorname{proj}} \newcommand{\col}{\operatorname{Col}} \newcommand{\row}{\operatorname{Row}} \newcommand{\diag}{\operatorname{diag}} \newcommand{\rref}{\operatorname{rref}} \newcommand{\lcm}{\operatorname{lcm}} \newcommand{\sgn}{\operatorname{sgn}} \newcommand{\0}{\mathbf 0} \newcommand{\E}{\mathbf E} \newcommand{\e}{\mathbf e} \newcommand{\bdot}{\boldsymbol \cdot} \newcommand{\C}{\mathbb C} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \newcommand{\Z}{\mathbb Z} \newcommand{\cB}{\mathcal B} \newcommand{\cC}{\mathcal C} \newcommand{\cE}{\mathcal E} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} \)

Preface Preface

These notes are not intended as a first or second course in abstract algebra, though they assume the reader has seen the material in a basic algebra course, covered for example in [1].

These notes will undertake a review of many basic topics from a typical first course, often taking the opportunity to interleave more advanced concepts with simpler ones when convenient. It will refresh the reader’s memory of definitions, structural results, core examples, and provide some computational tools to help the reader come to a deeper appreciation of the ideas first met perhaps a long time ago.

Computations in these notes uses Sage (sagemath.org) which is a free, open source, software system for advanced mathematics. Sage can be used either on your own computer, a local server, or on SageMathCloud (cocalc.com).

Thomas R. Shemanske
Hanover, NH
2020

Prev Top Next