From c43a36b693b700f2fa6f19d1c58d7f5410f5d421 Mon Sep 17 00:00:00 2001
From: Enrique Andrade Gonzalez <e.andrade@udc.es>
Date: Tue, 5 Dec 2017 22:34:10 +0000
Subject: [PATCH] update tea

---
 03/solutions #3/solution #03.tex | 35 ++++++++++++++++----------------
 1 file changed, 17 insertions(+), 18 deletions(-)

diff --git a/03/solutions #3/solution #03.tex b/03/solutions #3/solution #03.tex
index 81535a0..46de6d8 100644
--- a/03/solutions #3/solution #03.tex	
+++ b/03/solutions #3/solution #03.tex	
@@ -17,14 +17,15 @@
 \item Properly typeset the following command and properly refere to it in the text
 
 \begin{align}
-(\sum_{i_1,\dots,i_m} a_{i_1,\dots,i_m} ^{2m}{m+1} ^{\frac{m+1}{2m}} \leq C\le \\
-\sup\{ |\sum_{i_1,\dots, i_m} a_{i_1,\dots,i_m} x^1_{i_1}\dots x^m_{i_m}|: \|(x_i^k)_{i=1}^n \|_\infty\leq1,\ 1\leq k\leq m\},
+(\sum_{i_1,\dots,i_m} a_{i_1,\dots,i_m} ^{2m}(m+1) ^{\frac{m+1}{2m}}) \leq C\le \\
+\sup \left\{ \left\|\sum_{i_1,\dots, i_m} a_{i_1,\dots,i_m} x^1_{i_1}\dots x^m_{i_m}\right\|: \|(x_i^k)_{i=1}^n \|_\infty\leq1,\ 1\leq k\leq m\right\},
 \end{align}
 
 %----------------------------------------------------------------------------------------------
 % ¿Es correcto?
 % ¿Is good?
-\item Properly typset the expression: \[R \in z\]
+\item Properly typset the expression: \[
+    \operatorname{Re}  z\]
 
 
 
@@ -45,20 +46,20 @@ k=2\end{subarray}}^\infty a_n^k
 %----------------------------------------------------------------------------------------------
 % ¿Es correcto?
 % ¿Is good?
-\begin{theorem}
-(Cauchy--Hadamard) \emph{The radius of convergence $R$ of the power series 
+\begin{theorem}[Cauchy--Hadamard] The radius of convergence $R$ of the power series 
 \[
-\sum_{n=0}^\infty a_n(z-z_0)^n\ \ \ \ \ |z-z_0|<R
+\sum_{n=0}^\infty a_n(z-z_0)^n\quad |z-z_0|<R
 \]
 can by calculated via the following formula
 \[
-\frac{1}{R}=limsup_{n\to\infty} \sqrt[n]{|a_n|}.
-\]}
-\begin{defn}
-(Prime numbers) A number is called prime, if it is not compound. 
-\end{defn}
+\frac{1}{R}=\limsup_{n\to\infty} \sqrt[n]{|a_n|}.
+\]
 \end{theorem}
 
+\begin{defn}[Prime numbers]
+  A number is called prime, if it is not compound. 
+\end{defn}
+
 
 
 %----------------------------------------------------------------------------------------------
@@ -67,15 +68,14 @@ can by calculated via the following formula
 
 \item Typeset the follwing matrix (display-style):
 \[
-\left\{\begin{array}{cc}
+\begin{pmatrix}
          a_{11} & a_{12}\\
          a_{21} & a_{22}
-       \end{array}
-     \right\}
-\]
+       \end{pmatrix}
+     \]
 and in the text
 $
-\left(\begin{smallmatrix}{cc}
+\left(\begin{smallmatrix}
          a_{11} & a_{12}\\
          a_{21} & a_{22}
 \end{smallmatrix}\right)
@@ -88,5 +88,4 @@ $ Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do
      sunt in culpa qui officia deserunt mollit anim id est laborum.
 
 \end{enumerate}
-\end{document}
- 
+\end{document}