From 69c5a77e6f008330327f2697f9c77cea6f2e1c3a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 16 Feb 2021 22:05:38 +0100 Subject: chapter 1 slides --- vorlesungen/slides/1/algebrastruktur.tex | 73 ++++++++++++++++++++++++++++++++ 1 file changed, 73 insertions(+) create mode 100644 vorlesungen/slides/1/algebrastruktur.tex (limited to 'vorlesungen/slides/1/algebrastruktur.tex') diff --git a/vorlesungen/slides/1/algebrastruktur.tex b/vorlesungen/slides/1/algebrastruktur.tex new file mode 100644 index 0000000..9647c04 --- /dev/null +++ b/vorlesungen/slides/1/algebrastruktur.tex @@ -0,0 +1,73 @@ +% +% algebrastruktur.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup + +\definecolor{darkgreen}{rgb}{0,0.6,0} + +\begin{frame}[t] +\frametitle{Algebra über $\Bbbk$} +\begin{center} +\begin{tikzpicture}[>=latex,thick] +\pgfmathparse{atan(7/4)} +\xdef\a{\pgfmathresult} +\fill[color=red!40,opacity=0.5] + ({-4-2.5},{2+1.0}) + -- + ({-2.5},{-3-1.0}) + -- + ({2.5},{-3-1.0}) + -- + ({-4+2.5},{2+1.0}) + -- cycle; +\fill[color=blue!40,opacity=0.5] + ({4-2.5},{2+1.0}) + -- + ({-2.5},{-3-1.0}) + -- + ({2.5},{-3-1.0}) + -- + ({4+2.5},{2+1.0}) + -- cycle; +\fill[color=darkgreen!40,opacity=0.5] + ({-4-2.5},{2+1.0}) + -- + ({-4-2.5+2*(4/7)},{2-1}) + -- + ({+4+2.5-2*(4/7)},{2-1}) + -- + ({+4+2.5},{2+1}) + -- + cycle; +\node at ({-3-0.5},2) {Skalarmultiplikation}; + +\node at (3.5,2.2) {Multiplikation}; +\node at (3.5,1.8) {\tiny Halbgruppe}; + +\node at (0,-2.8) {Addition}; +\node at (0,-3.2) {\tiny Gruppe}; + +\node[color=blue] at (4.8,-0.5) [rotate=\a] {Ring\strut}; +\node[color=red] at (-4.8,-0.5) [rotate=-\a] {Vektorraum\strut}; + +\node[color=darkgreen] at (0,2.6) {$(\lambda a)b=\lambda(ab)$}; + +\node[color=red] at (-2.5,-0.5) {$\displaystyle +\begin{aligned} +\lambda(a+b)&=\lambda a + \lambda b\\ +(\lambda+\mu)a&=\lambda a +\mu a +\end{aligned}$}; + +\node[color=blue] at (2.5,-0.5) {$\displaystyle +\begin{aligned} +a(b+c)&=ab+ac\\ +(a+b)c&=ac+bc +\end{aligned}$}; + +\end{tikzpicture} +\end{center} +\end{frame} + +\egroup -- cgit v1.2.1 From 95c9a63dbb58815be30d393a0a1891b0bddc8ae8 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Mon, 22 Feb 2021 11:19:24 +0100 Subject: phases --- vorlesungen/slides/1/algebrastruktur.tex | 102 ++++++++++++++++++------------- 1 file changed, 61 insertions(+), 41 deletions(-) (limited to 'vorlesungen/slides/1/algebrastruktur.tex') diff --git a/vorlesungen/slides/1/algebrastruktur.tex b/vorlesungen/slides/1/algebrastruktur.tex index 9647c04..d7794a3 100644 --- a/vorlesungen/slides/1/algebrastruktur.tex +++ b/vorlesungen/slides/1/algebrastruktur.tex @@ -13,34 +13,43 @@ \begin{tikzpicture}[>=latex,thick] \pgfmathparse{atan(7/4)} \xdef\a{\pgfmathresult} -\fill[color=red!40,opacity=0.5] - ({-4-2.5},{2+1.0}) - -- - ({-2.5},{-3-1.0}) - -- - ({2.5},{-3-1.0}) - -- - ({-4+2.5},{2+1.0}) - -- cycle; -\fill[color=blue!40,opacity=0.5] - ({4-2.5},{2+1.0}) - -- - ({-2.5},{-3-1.0}) - -- - ({2.5},{-3-1.0}) - -- - ({4+2.5},{2+1.0}) - -- cycle; -\fill[color=darkgreen!40,opacity=0.5] - ({-4-2.5},{2+1.0}) - -- - ({-4-2.5+2*(4/7)},{2-1}) - -- - ({+4+2.5-2*(4/7)},{2-1}) - -- - ({+4+2.5},{2+1}) - -- - cycle; +\uncover<2->{ + \fill[color=red!40,opacity=0.5] + ({-4-2.5},{2+1.0}) + -- + ({-2.5},{-3-1.0}) + -- + ({2.5},{-3-1.0}) + -- + ({-4+2.5},{2+1.0}) + -- cycle; +} + +\uncover<4->{ + \fill[color=blue!40,opacity=0.5] + ({4-2.5},{2+1.0}) + -- + ({-2.5},{-3-1.0}) + -- + ({2.5},{-3-1.0}) + -- + ({4+2.5},{2+1.0}) + -- cycle; +} + +\uncover<6->{ + \fill[color=darkgreen!40,opacity=0.5] + ({-4-2.5},{2+1.0}) + -- + ({-4-2.5+2*(4/7)},{2-1}) + -- + ({+4+2.5-2*(4/7)},{2-1}) + -- + ({+4+2.5},{2+1}) + -- + cycle; +} + \node at ({-3-0.5},2) {Skalarmultiplikation}; \node at (3.5,2.2) {Multiplikation}; @@ -49,22 +58,33 @@ \node at (0,-2.8) {Addition}; \node at (0,-3.2) {\tiny Gruppe}; -\node[color=blue] at (4.8,-0.5) [rotate=\a] {Ring\strut}; -\node[color=red] at (-4.8,-0.5) [rotate=-\a] {Vektorraum\strut}; +\uncover<4->{ + \node[color=blue] at (4.8,-0.5) [rotate=\a] {Ring\strut}; +} + +\uncover<2->{ + \node[color=red] at (-4.8,-0.5) [rotate=-\a] {Vektorraum\strut}; +} -\node[color=darkgreen] at (0,2.6) {$(\lambda a)b=\lambda(ab)$}; +\uncover<6->{ + \node[color=darkgreen] at (0,2.6) {$(\lambda a)b=\lambda(ab)$}; +} -\node[color=red] at (-2.5,-0.5) {$\displaystyle -\begin{aligned} -\lambda(a+b)&=\lambda a + \lambda b\\ -(\lambda+\mu)a&=\lambda a +\mu a -\end{aligned}$}; +\uncover<3->{ + \node[color=red] at (-2.5,-0.5) {$\displaystyle + \begin{aligned} + \lambda(a+b)&=\lambda a + \lambda b\\ + (\lambda+\mu)a&=\lambda a +\mu a + \end{aligned}$}; +} -\node[color=blue] at (2.5,-0.5) {$\displaystyle -\begin{aligned} -a(b+c)&=ab+ac\\ -(a+b)c&=ac+bc -\end{aligned}$}; +\uncover<5->{ + \node[color=blue] at (2.5,-0.5) {$\displaystyle + \begin{aligned} + a(b+c)&=ab+ac\\ + (a+b)c&=ac+bc + \end{aligned}$}; +} \end{tikzpicture} \end{center} -- cgit v1.2.1 From 3eb564bb021d51d6a8201ec3069e0acd08554f98 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 26 Feb 2021 13:07:53 +0100 Subject: typos --- vorlesungen/slides/1/algebrastruktur.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'vorlesungen/slides/1/algebrastruktur.tex') diff --git a/vorlesungen/slides/1/algebrastruktur.tex b/vorlesungen/slides/1/algebrastruktur.tex index d7794a3..fd474eb 100644 --- a/vorlesungen/slides/1/algebrastruktur.tex +++ b/vorlesungen/slides/1/algebrastruktur.tex @@ -53,7 +53,7 @@ \node at ({-3-0.5},2) {Skalarmultiplikation}; \node at (3.5,2.2) {Multiplikation}; -\node at (3.5,1.8) {\tiny Halbgruppe}; +\node at (3.5,1.8) {\tiny Monoid}; \node at (0,-2.8) {Addition}; \node at (0,-3.2) {\tiny Gruppe}; -- cgit v1.2.1