From cddeab74130c3814acd49c8ac7d03041b2a7b85d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sun, 28 Feb 2021 22:37:26 +0100
Subject: add new slides

---
 vorlesungen/slides/3/polynome.tex | 22 +++++++++++++++++++++-
 1 file changed, 21 insertions(+), 1 deletion(-)

(limited to 'vorlesungen/slides/3/polynome.tex')

diff --git a/vorlesungen/slides/3/polynome.tex b/vorlesungen/slides/3/polynome.tex
index 6ca0009..161a4ed 100644
--- a/vorlesungen/slides/3/polynome.tex
+++ b/vorlesungen/slides/3/polynome.tex
@@ -3,7 +3,27 @@
 %
 % (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
 %
-\begin{frame}
+\begin{frame}[t]
 \frametitle{Polynome}
+$R$ ein Ring, z.~B.~$\mathbb{Z}$, $\mathbb{Q}$, $\mathbb{R}$
+
+\begin{definition}
+Polynome in $X$ mit Koeffizienten in $R$:
+\[
+R[X]
+=
+\{
+a(X)\;|\;
+a(X) = a_nX^n+a_{n-1}X^{n-1} + \dots a_2X^2+a_1X + a_0, a_k\in R
+\}
+\]
+\end{definition}
+
+\begin{itemize}
+\item {\em Grad} des Polynoms: $\deg a(X) = \deg a = n$
+\item $\deg 0 = -\infty$
+\item {\em normiertes Polynom}: $a_n=1$
+\end{itemize}
+
 
 \end{frame}
-- 
cgit v1.2.1

