LaTeX Practically II
Content
of the lesson:
- Assignment of the Problem
- Typesetting
Assignment of the Problem
Our task is to create a one-sided document in LaTeX which will contain several mathematical symbols. The final document can be seen in the following image.
The Fifth Paragraph
Take a look at the fifth paragraph. You can see a combinatorial number inside. We have to find out how to write such a symbol:
- combinatorial number - {text above \choose text below} (do not forget to use the braces, otherwise the command will not be functional)
- three dots - you cannot use three classical dots, use the command \ldots instead
A factorial can be added as a simple exclamation mark, the rest of this paragraph should be clear from the previous lesson.
Pravděpodobnost výhry při losování $k$ čísel z $n$ možných lze vypočítat pomocí kombinačního čísla ${n \choose k} $. Například při losování $6$ čísel ze $49$ je
$${49 \choose 6} =\frac{49!}{43!6!} =\frac{49\cdot 48\cdot \ldots \cdot 44}{6!} =49\cdot 4\cdot 47\cdot 46\cdot 3\cdot 11\doteq 14\cdot 10^6$$
tedy 1 : 14 milionům.
The Sixth Paragraph
The last paragraph is remaining. You have to add limits, an inequality and a function g(ξ). For the first part you need to know:
- notation of the Greek letter delta which is easy - \Delta (be aware of the first upper-case letter, \delta returns lower-case delta)
- to be able to add numbers inside the function, you have to use \begin{equation} ... \end{equation} again
- notation of the set of real numbers ℜ - \Re
In the following part we get to a more complex inequality. Imagine it as a table (array) which consists of three rows and three columns. We will use another environment - array, concretely its mathematical form eqnarray (this array centers lines according to the sign):
- inequality should be bordered with commands \begin{eqnarray} and \end{eqnarray}, the sign should be placed between symbols &, every row should be ended by 2 backslashes
- logarithm can be written by \log number
- special brackets can be written by commands \lceil (left) and \rceil (right)
In case you generate the PDF file now, you can see 2 problems:
- rows of inequality are numbered, you can remove this by adding the symbol * behind the parameter eqnarray - \begin{eqnarray*} ... \end{eqnarray*}
- brackets do not have proper size - you should let the compiler compute the size according to inner text when compiling - add \left before \lceil and \right before \rceil
We have this code at this moment:
Co je derivace $f'(x)$? Je to limita
\begin{equation}
\lim_{n\to 0} \frac{f(x)-f(x+\Delta x)}{\Delta x} ,
\end{equation}
což je v geometrické interpretaci směrnice tečny v bodě x. Pro výpočet bitové šířky $x$ desítkového čísla $C \in \Re $ řešíme nerovnici:
\begin{eqnarray*}
C&\le& 2^x \\
\log{C} &\le&x\cdot \log{2} \\
x&=&\left \lceil \frac{\log{C} }{\log{2} } \right \rceil \\
\end{eqnarray*}
We can continue with the last equation. There are several problems in this part:
- Greek letter ξ (ksi) which can be written by \xi.
- Size of the braces should be optimized by command \left and the single brace should be written by \{ .
- The rest of the equation should be inserted between \begin{array} and \end{array}.
- The word "pro" is written using a common font, not in italics. You have to insert it inside the command \textrm{pro}. Textrm should contain every non-mathematical text (serif font).
- Symbol ∈ ("in") can be written by \in.
- Broken brackets cannot be written as < or >, you have to use the commands \langle and \rangle instead.
The environment array contains an optional parameter which can be inserted into braces behind \begin{array}. In this case we used {ll} to allign the text to the left.
- the number of letters inside braces sets the number of columns
- you can use these letters: l - allign to left, c - allign to center, r - allign to right.
Nespojitá funkce $g(\xi )$ je definována takto:
$$g(\xi )=\left\{
\begin{array}{ll}
0&\textrm{pro $\xi < 0$} \\
\xi &\textrm{pro }\xi \in \langle 0;1) \\
1&\textrm{pro $\xi > 1$} \\
\end{array}
$$
The whole source code is available here: Zdrojovy_kod.txt and you can also view the PDF version here: prepsany_dokument.pdf.
Congratulations, you have created your first mathematical text.
Additional Texts
Questions
- How can you insert more equations in LaTeX?
- How can you find help articles for LaTeX in the Internet?
- How can you find a way to write a concrete specific symbol?
- What is the meaning of $ or $$ in LaTeX?
- Where can you use LaTeX in the Internet in case you do not want to install any software to your computer?