From 278fed27ca07bff386d830e2142d207d904703fc Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Tue, 23 Feb 2021 19:58:40 +0100
Subject: new slides chapter 3

---
 vorlesungen/slides/3/polynome.tex | 9 +++++++++
 1 file changed, 9 insertions(+)
 create mode 100644 vorlesungen/slides/3/polynome.tex

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

diff --git a/vorlesungen/slides/3/polynome.tex b/vorlesungen/slides/3/polynome.tex
new file mode 100644
index 0000000..6ca0009
--- /dev/null
+++ b/vorlesungen/slides/3/polynome.tex
@@ -0,0 +1,9 @@
+%
+% polynome.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\begin{frame}
+\frametitle{Polynome}
+
+\end{frame}
-- 
cgit v1.2.1


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


From 67addea9bf154558ca3bbc14703c2b0fef8fc60c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Mon, 1 Mar 2021 08:18:59 +0100
Subject: phases, typos

---
 vorlesungen/slides/3/polynome.tex | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

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

diff --git a/vorlesungen/slides/3/polynome.tex b/vorlesungen/slides/3/polynome.tex
index 161a4ed..d7179a0 100644
--- a/vorlesungen/slides/3/polynome.tex
+++ b/vorlesungen/slides/3/polynome.tex
@@ -20,9 +20,9 @@ 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}: $a_n=1$
+\item<2-> {\em Grad} des Polynoms: $\deg a(X) = \deg a = n$
+\item<3-> $\deg 0 = -\infty$
+\item<4-> {\em normiertes Polynom}: $a_n=1$
 \end{itemize}
 
 
-- 
cgit v1.2.1