Free tuition of LaTeX

Work in Progress

Available in French in February Archive

The software needed
It’s imperative to download the software LaTeX from the website LaTeX or from a platform Ubuntu
available to the users of this program.
1. using Windows
Many programs are needed of whom Ghost Script (software able to transform a file .tex in a
file .pdf)
2. using Linux
One program is needed, but one can choose between two programs similars :
• TeX Studio
• TeX Maker
The beginning
First you have to describe the type of the document (article, book, ...), the size of the print (11
points or 12 points generally), the syze of the paper (letterpaper or A4 , A5 [Continental Europe])
and the packages used to write an article of mathematics. You can also use the type of document
defined by the American Mathematical Society (\documentclass{amsart}). Here you are for the
most casual forms (That you can copy-glue)
\documentclass{amsart}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,amsfonts,amssymb}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{mathrsfs}
\usepackage{stmaryrd}
\usepackage{graphicx}
\usepackage{enumitem}
\usepackage{comment}
\usepackage[parfill]{parskip}
\usepackage{array}
remark : in some cases it is possible that the package {babel} is needed
So one can add it in this manner :
\usepackage{babel}[english]

The new commands
A new command allow us to type a shorter text. For example :
\newcommand{\Z}{\mathbb{Z}}
This new command replace the second writing \mathbb{Z} of the ring Z by \Z , a shorter writing.
What you can’t miss
What you can’t miss, after protocols and new commands is to begin by \begin{document} and at
the end of the document is to finish by \end{document}. Otherwise the template would be
impossible, exempla gratia you can’t transform the file nameofthefile.tex in afile nameofthefile.pdf
Here you are what you must copy-glue in order to realize an article :
\begin{document}
\title{write the title}
\author{write your name}
\date{write the date or the place and the date}
\maketitle
\end{document}

The LaTeX formula
In math mode the formula are preceded by $. For Example $\int_{a}^{b} f(x) dx$ what we can read
as : integration from a to b of f(x) dx.
The usefull LaTeX formulae are :
• \int_{0}^{\infty} = integration from zero to infinity
• \Sum_{i=1}^{n} ou \Sigma_{i=1}^{n} = Addition from i=1 to n
• \Pi_{i, i\neq j} e_{i} e_{j} = Product on i , i different to j, of ei ej
• A \times B = Cartesian Product of A and B
• f \circ g (x) = f(g(x))
• A \cup B = union of A and B
• A \cap B = intersection of A and B
• a \in A = a belong to A
• \forall x = forall x
• \exists \epsilon = exists epsilon
• \emptyset = emptyset
• \overline{n} = n with a straight line above it (element of a division ring)
• \overrightarrow{v} = vector v
• \rightarrow (resp. \leftarrow) = simple arrow to the right (resp. the left)
• Rightarrow (resp. \Leftarrow) = double arrow to the right (resp. the left)
• LeftRightarrow = double implication
• \quad = big space between two expressions
example : x = \quad 3 mod \quad 5
x = 3 mod 5
• \mathbb{R} = set of reals
• \mathfrak{a} = ideals of a ring
• \frac{3}{4} = rationnal number three quarter
• \geq = grand or equal
• \leq = less or equal
• > = grand
• < = less
• A \subset B = A is a subset of B
• \sqrt = square root of
• x_{i} = x indice i
• a^{n} = a exposant n
• \Aleph_{0} = Aleph zero
• \cong = congru modulo
• \bigotimes = tensor product
• \rond{\frac{\partial f}{\partial t}} = partial derivative of f by à t
• \nabla f = gradient of f

Later developpement in LaTeX
By developpement, we understand expressions like equation system, matrix, déterminants, ...

• Express a matrix with coefficients aij
A possible manner is this :
$\left(\begin{matrix}
a_{11}& a_{12}\\
a_{21}&a_{22}
\end{matrix}\right)$.
An other manner is those :
$\left(\begin{array}{cc}
a_{11}& a_{12}\\
a_{21}&a_{22}
\end{array} \right )$

• Express a determinant with coefficients aij
$\left | \begin{array}{rrr}
a_{11}& a_{12}& a_{13}\\
a_{21}& a_{22}& a_{23}\\
a_{31}& a_{32}& a_{33}
\end{array} \right | $

• Express an equation systems of modular congruences
$\left\{ \begin{array}{lll}
x\cong\quad a_{1}\ mod\quad \mathfrak{a}_{1}\\
....\\
x\cong\quad a_{n}\ mod\quad \mathfrak{a}_{n}
\end{array}\right.$
The indications {cc}, {rrr} ou {lll} design an alignement on the centre {c} , on the right {r} or
on the left {l}. One need use so many c, r or l that exists lines.

Template
When you wrote a part of the text, you need to template.
• using TeX Studio
Unscrolling Box Tools, then template or F1
• using TeX Maker
Unscrolling box Toolss, then template or F1
One needn't waiting to type all the text to template. On the contrary, it's better to template paragraph after paragraph, because if the template fails you will need to go back until the moment the template succeed and after going slowly line by line in ordrer to detect your error.