Mark/handouts
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Fixed a few errors

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Mark 2023-01-23 16:11:45 -08:00
parent a632bf0029
commit 6761863358
3 changed files with 4 additions and 4 deletions
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4
Advanced/Group Theory/parts/00 review.tex
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@ -70,11 +70,11 @@ Not all elements of $\mathbb{Z}_n$ have an inverse. Those that do are called \te
\vspace{2mm} \vspace{2mm}
The set of all units in $\mathbb{Z}_n$ is written $(\mathbb{Z}_n)^\times$ \\ The set of all units in $\mathbb{Z}_n$ is written $\mathbb{Z}_n^\times$ \\
Read this as \say{$\mathbb{Z}$ mod $n$ cross} Read this as \say{$\mathbb{Z}$ mod $n$ cross}
\problem{} \problem{}
What are the elements of $(\mathbb{Z}_5)^\times$? What are the elements of $\mathbb{Z}_5^\times$?
\begin{solution} \begin{solution}
$\{1, 2, 3, 4\}$ $\{1, 2, 3, 4\}$

2
Advanced/Group Theory/parts/01 groups.tex
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@ -1,6 +1,6 @@
\section{Groups} \section{Groups}
Group theory gives us a set tools for understanding complex systems. We can use groups to solve the Rubik's cube, to solve problems in physics and chemistry, and to understand complex geometric symmetries. It's also worth noting that all modern crypography relies heavily on group theory. Group theory gives us a set tools for understanding complex systems. We can use groups to solve the Rubik's cube, to solve problems in physics and chemistry, and to understand complex geometric symmetries. It's also worth noting that all modern cryptography relies heavily on group theory.
\definition{} \definition{}
A \textit{group} $(G, \ast)$ consists of a set $G$ and an operator $\ast$. \\ A \textit{group} $(G, \ast)$ consists of a set $G$ and an operator $\ast$. \\

2
Advanced/Group Theory/parts/03 bonus.tex
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@ -11,7 +11,7 @@ Find the inverse of 19 in $\mathbb{Z}_{23}$ \\
\vfill \vfill
\problem{} \problem{}
Prove Lagrange's theorem: Prove Fermat's little theorem:
$$ $$
a^p = a \text{ (mod p)} a^p = a \text{ (mod p)}