\documentclass[12pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[czech]{babel}
\usepackage[T1]{fontenc}
\usepackage{amsmath} % pokud pouzivam matematiku, nahravam balicek
\usepackage{amsfonts}
\usepackage{amssymb} % pokud pouzivam matematiku, nahravam balicek
\usepackage{amsbsy} % pokud pouzivam matematiku, nahravam balicek
\usepackage{esvect} % balicek na vektory
\newcommand{\dx}{\,\mathrm{d}x} % definice matematickeho znaku
\newcommand{\dt}{\,\mathrm{d}t}
\newcommand{\e}{\mathrm{e}}
\DeclareMathOperator{\tg}{tg} % definice noveho opetartoru
\begin{document}
\begin{enumerate}
\item $ C\,(n,r)=n!/\bigl(r!(n-r)!\bigl) $
\item $ \vv{x}\cdot\vv{y}=\langle\vv{x},\vv{y}\rangle $, právě když $\vv{x}\not\perp\vv{y} $
\item $ (\forall x \in \mathbb R)(\exists y \in \mathbb R)\,y>x$
\item $ \frac{a+b}{c} $, $ \frac{a}{b+c} $, $\frac{1}{a+b+c} \ne \frac{1}{a}+\frac{1}{b}+\frac{1}{c}$
\item $ \nabla^2 f(x,y)=\frac{\partial^2f}{\partial x^2}+\frac{\partial^2f}{\partial y^2} $
\item $ \lim_{x\rightarrow 0} (1+x^2)^\frac{1}{x}=\e $
\item $ \int_0^1 3x^2\dx=1$, $\displaystyle\int\textstyle\frac{x+\sqrt{x}}{\sqrt[4]{x^2(1+\tg x)}}\dx$
\item $ \sqrt{2} $, $ \sqrt{\frac{x+y}{x-y}} $, $\sqrt[3]{10}$, $\e^{\sqrt{x}} $
\item $ \| x \|=\sqrt{x\cdot x} $
\item $ \underline{x}\quad\overline{y}\quad\underline{\overline{x+y}} $
\item $ \lim_{a\rightarrow 0} \frac{\tg \alpha}{\alpha}=1$
\item {\mathversion{bold} $ a \equiv c \pmod{\theta} $}
\item \[\biggl\{x\biggm| \int _0^x t^2\dt\leq 5\biggl\}\]
\item \[F(x)| _a^b = F(b)-F(a)\]
\item \[ \underbrace{\overbrace{a+\dots+a}^{(m-n)/2}+\underbrace{b+\dots+b}_n+\overbrace{a+\dots+a}^{(m-n)/2}}_m \]
\end{enumerate}
\end{document}