==============
Oct 10th, 2022
==============

.. Prep for the course
.. ~~~~~~~~~~~~~~~~~~~

Review
------

* ``array`` environment: align, hline, left, right
* ``theorem`` environment: named theorem

Things to do
-------------

- ``bibliography``; minimal
  
  - Overleaf document https://www.overleaf.com/learn/latex/Bibtex_bibliography_styles
  - MathSciNet https://mathscinet.ams.org/mathscinet/ use ``Select Alternative Format`` then ``BibTex``
  - arXiv https://arxiv.org/help/hypertex/bibstyles use ``Export Bibtex Citation``
  - the ``bibtex`` package provides additional features, but it is different from ``bibtex``, https://www.overleaf.com/learn/latex/Bibliography_management_with_biblatex

- ``includegraphicx`` https://www.overleaf.com/learn/latex/Inserting_Images
- ``itemize`` environments; ``enumitem`` package https://ctan.org/pkg/enumitem?lang=en 

Referencing in LaTeX 
--------------------

Cross Referencing
~~~~~~~~~~~~~~~~~~

- Overleaf https://www.overleaf.com/learn/latex/Cross_referencing_sections%2C_equations_and_floats

- Chapters, sections, subsections, theorems, equations, etc

To cross-reference in LaTeX, we use ``\label{<name>}`` to create an anchor point and ``\ref{<label name>}`` to point to that anchor. 
Here is an example of referring to a section. 

.. code-block:: latex
    :caption: label, ref commands example

    \section{Good section to be referred} \label{goodSection}
    ...
    ...
    ...
    In Section~\ref{goodSection} ...

It will produce ``In Section N ...``, where N is the corresponding section number for ``Good section to be referred``. 
Similarly, we can refer to equations. Recall generally we do not put an equation number, but to refer an equation `properly`, one needs to use ``\begin{equation}`` and ``\end{equation}`` (or the ``\align`` environment). 

.. code-block:: latex
    :caption: equation theorem label example

    \begin{equation} \label{importantFormula}
    F = ma
    \end{equation}
    ...
    ...
    By eq.~\ref{importantFormula}, we are done.

Here one sees a drawback that ``\label`` and ``\ref`` commands only return a number not the name of the environment. 
This can be solved with the package ``cleveref`` https://ctan.org/pkg/cleveref?lang=en. 
With this package, one can use ``\Cref`` and ``\cref`` in place of ``\ref``. The former makes the first letter in uppercase and the latter makes it in lowercase, respectively. 


.. code-block:: latex
    :caption: cref label example

    # in preamble
    \usepackage{cleveref}
    ...
    ...
    # in body
    \section{Good section to be referred} \label{goodSection}

    \begin{equation} \label{importantFormula}
    F = ma
    \end{equation}
    ...
    ...
    Now, the following two lines produce the same outcome. \\
    
    By eq.~(\ref{importantFormula}) in Section~\ref{goodSection}, we are done. \\
    By \cref{importantFormula} in \Cref{goodSection}, we are done.

Of course, this package shines most when used with theorems. 

.. code-block:: latex
    :caption: theorems cref

    \begin{theorem}[{My Statement}] \label{myThm}
    Great!
    \end{theorem}

    \Cref{myThm} # This will print Theorem N. 

    \begin{proposition}[{My Statement}] \label{myProp}
    Great!
    \end{propotision}

    \Cref{myProp} # This will print Proposition N+1. 

When one switches ``theorem`` and ``proposition``, ``\Cref`` takes care of the changes.

We cannot use ``\label`` to cite papers as ``\label`` can be only put with the existing text. 
To this end, we use LaTeX bibliography tools. 

Bibliography Referencing
~~~~~~~~~~~~~~~~~~~~~~~~~

We will learn the following.

- How to create a bib file; this is the file that contains the bibliography data. 
- How to load the bib file in LaTeX
- This is one way and somewhat minimal; for instance, https://www.overleaf.com/learn/latex/Bibliography_management_with_bibtex provides more powerful tools. 

.. note:: 

    The goal is to do the least to maintain your bib file. 
    That means we will minimize typing entries manually. 
    To do this, we need to use the appropriate search tools.  

When it is done, we can simply use the ``\cite`` command, which is similar to ``\ref``. 

Suppose we have the following in our sample.bib file. 

.. code-block:: latex
    :caption: sample bib file

    @article {wiles95,    % <- this is the name we need to use in \cite{<name>} %%%% Warning you need to delete this commment in the bib file %%%%%
      AUTHOR = {Wiles, Andrew},
      TITLE = {Modular elliptic curves and {F}ermat's last theorem},
      JOURNAL = {Ann. of Math. (2)},
      FJOURNAL = {Annals of Mathematics. Second Series},
      VOLUME = {141},
      YEAR = {1995},
      NUMBER = {3},
      PAGES = {443--551},
      ISSN = {0003-486X},
      MRCLASS = {11G05 (11D41 11F11 11F80 11G18)},
      MRNUMBER = {1333035},
      MRREVIEWER = {Karl Rubin},
      DOI = {10.2307/2118559},
      URL = {https://doi.org/10.2307/2118559},
    }

Then in our main tex file, we add the following two lines. Then we are ready to refer to this article by calling ``\cite{wiles95}``.


.. code-block:: latex

    ...
    ... # at the end of the file

    \bibliographystyle{alpha} % this provides the style of reference displayed
    \bibliography{sample} % we declare that we use sample.bib for our bib file.  

Also, in the tex file, one needs to add the following two lines, often at the end of the tex file. 

.. note:: 
    
    Later, I will add how to search on `MathSciNet` and `arXiv`. 


Lastly, if you want ``References`` to be included in your table of contents (use ``\tableofcontents`` to create one), add the following in your preamble.

.. code-block:: latex
    :caption: References in Table of contents

    %%%% In preamble
    \usepackage[nottoc]{tocbibind}

Check out our thesis template bibliography section, https://www.overleaf.com/read/prmnfsqfxmzr. 




.. class ends here