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Examples of Math Expressions



1.
Binomial coefficient

\begin{displaymath}\left( \begin{array}{c} m+n \\ n \end{array} \right) \end{displaymath}

or simply

\begin{displaymath}{m+n}\choose{n}\end{displaymath}

2.
Integral

\begin{displaymath}\int_{a}^{b+c} f(x) d x \end{displaymath}

3.
Limit

\begin{displaymath}\lim_{n \rightarrow \infty} a_{n} = \ell \end{displaymath}

4.
Summation

\begin{displaymath}R = \sum_{i=k}^{l} a_{i} \end{displaymath}

5.
Step function

\begin{displaymath}y = \left\{ \begin{array}{lll} 1 & \mbox{if $x \geq 1$ } \\ ... ...0 \leq x < 1$ } \\ 0 & \mbox{otherwise} \end{array} \right. \end{displaymath}

6.
Fraction

\begin{displaymath}f(x,y) = \frac{x}{1 + y} \end{displaymath}

7.
The above 1-6 are in ``displayed formula" mode. Examples of in-text formula are: \( \int_{a}^{b+c} f(x) d x \); \( \lim_{n \rightarrow \infty} a_{n} = \ell \); \( R = \sum_{i=k}^{l} a_{i} \); \( f(x,y) = \frac{x}{1 + y} \).
8.
Roots
Square root: \( \sqrt{x+y} \) and nth root: \( \sqrt[n]{2} \)
9.
To number a displayed formula

\begin{displaymath}\log xy = \log x + \log y \end{displaymath} (1)

The ``displayed formula" mode is the same as the equation environment except it does not generate equation numbers.
10.
Multiline formula
x = 17y (2)
y > a + b + c + d + e + f + g + h + i + j +  
    k + l + m + n + o + p (3)

The eqnarray$\star$ environment is the same as the eqnarray except it does not generate equation numbers.
Tex File to Produce Math Examples 
\documentstyle[12pt]{article}
\input tex-set
\begin{document}
%
\begin{center}
subsection{Examples of Math Expressions} \vspace{.2in}
\end{center}
%
\begin{itemize}
%
\item[1.] Binomial coefficient 
     \[ \left( \begin{array}{c} m+n \\ n \end{array} \right) \]
or simply
 \[{m+n}\choose{n}\]
%
\item[2.] Integral
     \[ \int_{a}^{b+c} f(x) d x \]
%
\item[3.] Limit
     \[ \lim_{n \rightarrow \infty} a_{n} = \ell \]
%
\item[4.] Summation
     \[ R = \sum_{i=k}^{l} a_{i} \]
%
\item[5.] Step function
     \[ y = \left\{ \begin{array}{lll}
                     1    & \mbox{if $x \geq 1$} \\      
                     2x   & \mbox{if $0 \leq x < 1$} \\
                     0    & \mbox{otherwise}
                    \end{array}
            \right. \]
%
\item[6.] Fraction
     \[ f(x,y) = \frac{x}{1 + y} \]
%
\item[7.] The above 1-6 are in ``displayed formula" mode. Examples of
     in-text formula are:  \( \int_{a}^{b+c} f(x) d x \);
                           \( \lim_{n \rightarrow \infty} a_{n} = \ell \);
                           \( R = \sum_{i=k}^{l} a_{i} \);
                           \( f(x,y) = \frac{x}{1 + y} \).
%
\item[8.] Roots 
\begin{center}
Square root: \( \sqrt{x+y} \) \hspace{.5in} and \hspace{.5in}
$n$th root: \( \sqrt[n]{2} \)
\end{center}
%
\item[9.] To number a displayed formula
     \begin{equation}
        \log xy = \log x + \log y
     \end{equation}
     {\em The ``{\rm displayed formula}" mode is the same as the {\rm equation} 
     environment except it does not generate equation numbers.}
%
\item[10.] Multiline formula
     \begin{eqnarray}
        x & = & 17y\\
        y & > & a + b + c + d + e + f + g + h + i + j + \nonumber  \\
          &   & k + l + m + n + o + p 
     \end{eqnarray}
     {\em The {\rm eqnarray$\star$} environment is the same as the 
     {\rm eqnarray} except it does not generate equation numbers.}
\end{itemize}
%

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Next: Examples of Tables Up: Writing Math Articles Previous: Math Symbols Commonly Used