%HW01.tex
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% First Homework for Honors Algebra I  (415H)
% Frank Sottile
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\begin{document}
\LARGE 
\noindent
Algebra 415H \ \ Autumn 2026\vspace{2pt}\\
{\color{magenta}Your Name}\vspace{2pt}\\
\Large 25 August 2025 \hfill
\sf
 First Homework\makebox[40pt][l]{\ }
\normalsize\vspace{10pt}

\noindent
Write your answers neatly, in complete sentences.  
I highly recommend recopying your work before handing it in.
Correct and crisp proofs are greatly appreciated; oftentimes your work can be shortened and made clearer.

\noindent
\barsn

\noindent\Maroon{{\sf Hand in at the start of class, Thursday 27 August:}} 

Either read Section 0 of Fraleigh and Brand or review Math 300 (or both).

Recall, in particular, the following notions.
Write clean, precise, and crisp definitions for each of them.

\begin{enumerate}

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\item
  Cartesian product $A\times B$ of sets $A$ and $B$.
  
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\item
  Function $f\colon A\to B$ with domain the set $A$ and codomain the set $B$.
  
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\item 
  Equivalence relation $\sim$ on a set $A$.
  
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\item
  For $n$ a positive integer, $\ZZ/n\ZZ$ (or $\ZZ_n$), the set of integers modulo $n$.
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\item
  Addition on $\ZZ_n$ (as a function).
  (This may require a tiny proof that what you describe is well-defined.)
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\end{enumerate}
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\end{document}
