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Sep 26, 2022
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Things to do
-------------

- LaTeX ``array`` and ``tabular`` environments; we will cover the ``theorem`` and ``bibliography`` environments, and the ``includegraphicx`` command soon.

- Guide to finding a good topic;
  
LaTeX array and tabular
------------------------

Both environments work simliarly and we will focus on ``array``. Keep in mind, ``array`` is for `math mode` and ``tabular`` for `text mode`. 

First, let's review the ``matrix`` environments. 

.. math:: 

    \begin{bmatrix}
    1&2 \\
    3&5 \\
    8&13 
    \end{bmatrix} 
    ~\text{or}~
    \begin{pmatrix}
    1&2 \\
    3&5 \\
    8&13 
    \end{pmatrix}

To create the matrices above, we can use the following code. 

.. code-block::
    :caption: Matrix Example

    \begin{equation*} # or two dollar symbols
    \begin{bmatrix}
    1 & 2 \\
    3 & 5 \\
    8 & 13 
    \end{bmatrix} 
    ~\text{or}~
    \begin{pmatrix}
    1 & 2 \\
    3 & 5 \\
    8 & 13 
    \end{pmatrix}
    \end{equation*} # or two dollar symbols

Here, \& is a separator that separates columns. We use it for the ``align`` environments, too. 

.. note:: space in math mode

    ``\begin{bmatrix}1&2\\3&5\\8&13\end{bmatrix}`` produces the same matrix, but it is much harder to read. 

See https://www.overleaf.com/learn/latex/Matrices for the complete list of ``matrix`` options. 

Another approch is to use the ``array`` environment and delimiters. It is more felxible than the matrix environment. Here is an array way to create a matrix. 

.. code-block::
    :caption: Matrix Example by Array (Imcomplete)

    \begin{equation*} 
    \begin{array}{cc} # the {cc} after {array} denotes the number of columns and the alignment.
    1 & 2 \\
    3 & 5 \\
    8 & 13 
    \end{array} 
    \end{equation*}

Note that this code creates a matrix without parenthesis. 
The regular ``(`` and ``)`` do not provide suitble size paranthesis. 
We use the left or right delimiters with ``\left`` and ``\right`` command. 

.. code-block::
    :caption: Matrix Example by Array 

    \begin{equation*} 
    \left(              # One can use [, { and more
    \begin{array}{cc} 
    1 & 2 \\
    3 & 5 \\
    8 & 13 
    \end{array} 
    \right)             # One can use ], } and more
    \end{equation*}

The left and right combination need to be matched (I might be wrong though). If you want one of them use ``\right\.`` to ignore the right one. 

Lastly, we can decorate arrays with lines. For vertical lines, use :math:`\mid` such as ``{c|c}``. For horizontal lines, use ``\hline``. These commands can be stacked. 

.. code-block::
    :caption: Array with lines 

    \begin{equation*} 
    \begin{array}{c|c|c} 
    ~ &  \pi/2 & \pi \\
    \hline 
    \sin & 1 & 0 \\
    \hline
    \cos & 0 & -1 
    \end{array} 
    \end{equation*}

This code gives the following. 


.. math::

    \begin{array}{c|c|c} 
    ~ &  \pi/2 & \pi \\
    \hline
    \sin & 1 & 0 \\
    \hline
    \cos & 0 & -1 
    \end{array} 

----

Final Project Topics
~~~~~~~~~~~~~~~~~~~~~

We worked on chooing the final project topics. For those, who have chosen on, start working on gather background and preliminary resources. 




.. class ends here