Aug 29, 2022
==============

More on LaTeX
-------------

Resources/References:

- Overleaf file_ used in the lecture
- `The Not So Short Introduction to LATEX <https://tobi.oetiker.ch/lshort/lshort.pdf>`_
- `OverLeaf Mathematical Expressions <https://www.overleaf.com/learn/latex/Mathematical_expressions>`_

.. _file: https://www.overleaf.com/read/pnjfsjgwjnyv

Overleaf support multi-user editiong mode. 

In math mode, having space does not do anything. 
To create proper spacing between expressions, 
there are two approaches, 
direct (absolute) and relative. 
I suggest getting used to the relative method. 
Here are the spaces created by the following commands in math mode.

* ~
* \\, 
* \\;
* \\:
* \\quad
* \\qquad

These are rendered as follows.

.. math:: 

  A~B\\
  A\,B\\
  A\;B\\
  A\:B\\
  A\quad B\\
  A\qquad B

With the **\hspace{<option>}** command, you may use the absolute spacing value. Here is one with ``1 in`` option.

.. math:: 

  A\hspace{1in}B %A\hspace{1in}B

Vertical spacing can be done in a similar manner. 
However, often it is done in text mode. 
The three basic ones are \\smallskip, \\medskip, and \\bigskip. 

.. code-block:: latex

  some interesting paragraph.

  \medskip

The **\vspace{<option>}** corresponds to hspace. Useage is similar, and both hspace and vsapce support negative offsets.

Sometimes our calculation requires more than one line. 
In general, without proper multiline command, math expressions may go out of the page margins.

.. math:: 

  11^11 + 22^22 + 33^33 = 285311670611 + 341427877364219557396646723584 + 129110040087761027839616029934664535539337183380513

We use multi-line math mode. One popular option is the **align** environment (**align\*** for non-numbered multi-line math mode).

.. code-block:: latex

  \begin{align}
  11^11 + 22^22 + 33^33 % there is no line break here. The new line is for humans.
    = 285311670611 + 341427877364219557396646723584 \\
    + 129110040087761027839616029934664535539337183380513
  \end{align}

This code produces

.. math:: 

  \begin{align}
  11^11 + 22^22 + 33^33 
    &= 285311670611 + 341427877364219557396646723584 \\
    &+ 129110040087761027839616029934664535539337183380513
  \end{align}

**Underset** and **overset**

When using inline math mode, sometimes we want to override the format. 
The \\displaymath command makes inline math into math mode. 
However, it often creates unnecessary vertical line spaces. 
For commands like :math:`\lim` or :math:`\sum`, one can use the **underset** and **overset** commands.

.. code-block:: latex

  \lim_{x \to c} f(x) \text{or}
  \underset{x \to c}{\lim} f(x)

For insatnce, compare :math:`\lim_{x \to c} f(x)` with :math:`\underset{x \to c}{\lim} f(x)`.

We may need to use long or complicated expressions. When using such several times, it is desired to make an alias. In LaTeX, this can be done by using the **renewcommand** for text and **DeclareMathOperator** for math functions. 
These need to be declared in the preamble that is before the begin{document} command. 
We have not touched upon this but see the tex example file. 

.. code-block:: latex

  # In preamble

  \renewcommand{\math6000}{{MATH 6000. Communicating Mathematics.}}
  \DeclareMathOperator{\boldLim}{\mathbf{\lim}}

Once the above lines are added, the LaTeX compiler will replace \\math6000 with 
''MATH 6000. Communicating Mathematics.'' 

.. note:: 

  These commands can have arguments, i.e., inputs. 

In math mode, the command \\operatorname does the job for DeclareMathOperator. But one needs to add it every time.

.. code-block:: latex

  \text{lim}_{x\to \infty} f(x) ~\text{vs.}~ \lim_{x\to \infty} f(x) \\
  \text{image} \Phi ~\text{vs.}~ \operatorname{image} \Phi

This code will to shown as 

.. math:: 

  &\text{lim}_{x\to \infty} f(x) ~\text{vs.}~ \lim_{x\to \infty} f(x) \\
  &\text{image} \Phi ~\text{vs.}~ \operatorname{image} \Phi.

See https://tex.stackexchange.com/questions/67506/newcommand-vs-declaremathoperator for more information.

Recall that the curly brakets \{ and \} are used for grouping. An example is \\frac function. It takes two arguments (inputs) that is \\frac AB produces :math:`\frac AB`. 
Sometimes expressions such as A or B is more than one character. 
We use \{ expression \} to group. 
To express :math:`\frac{40}{50}`, we use \\frac{40}{50}. 


---------

.. After class
.. ~~~~~~~~~~~
.. HW2; Short math exercise with align, matrix, tag, 

.. HW3 (2-week project); Form a group of 2-3 people, read one of the articles. 

.. - Who was the author  
.. - What was the level of the article? You could say something like, it was easy or (hard) to follow. We liked it because xx and yy were there.  
.. - What were the things that are different to your previous understanding?  
.. - Based on your article, what are the things you want to update? 
..   - Are there any improvments you can make for your HW1? If so, why don't you revised and include them. 

.. - You will submit them to Gradescope (or Canvas) and make a small presentation in class.