Getting Started

When tasked with conveying intricate ideas or concepts, you'll likely find the need to articulate them formally. While diagrams and charts can be beneficial in illustrating your points, mathematical equations serve as the universally accepted method. For this purpose, LaTeX is the go-to system for crafting and sharing these equations. Let's begin with the initial setup:

• Install LaTeX:

  brew install --cask mactex

  On a Mac, this has been the simplest approach for me, but you may also explore:

  • TexLive (a hefty 6GB): https://www.tug.org/texlive/
  • TinyTeX is smaller but requires Perl.

• Incorporate a plugin into your IDE (I'm using VSCode), specifically the LaTeX Workshop extension.

If everything is in order, we can dive into a straightforward LaTeX example:

Make a new .tex file and type the following:

documentclass{article}

begin{document}

The sum of two variables (a) and (b) is represented by:

[ a + b ]

end{document}

The key takeaway is defining the document type with: documentclass{article} (this could also be report, book, letter, beamer, memoir, etc.) and the document's content with: begin{document}, which must be concluded with end{document}.

Next, you'll need to compile the LaTeX project (press ? ? B on Mac or the compile button), which will generate a PDF for you to preview or open:

Baby Steps

Now, let's tackle a slightly more intricate example:

documentclass{article}

begin{document}

noindent Einstein's renowned equation ( E = mc^2 ) connects energy (( E )), mass (( m )), and the speed of light (( c )).

end{document}

This should yield:

In this case, we enclose an equation with ( Equation... ), and remember that variables are enclosed in double parentheses: ( (Variable) ). Also, notice the formatting adjustments, such as removing the first line's indent using noindent and creating a line break with \.

Here are some additional basic mathematical expressions:

documentclass{article}

begin{document}

Fractions: ( frac{3}{4} )

Exponents: ( x^{2} )

Square Roots: ( sqrt{2} )

Subscripts and Superscripts: ( x_{1} )

Greek Letters: ( alpha, beta, gamma )

Summation: ( sum_{i=1}^{n} i )

Integrals: ( int_{0}^{pi} sin(x) , dx )

Limits: ( lim_{x to 0} frac{sin(x)}{x} )

Multiplication: ( 3 cdot 4 )

Divisions: ( frac{10}{2} )

end{document}

This should yield:

For a more complex equation:

documentclass{article}

begin{document}

( frac{1}{2pi i} oint_C frac{f(z)}{(z - z_0)^{n+1}} , dz = frac{f^{(n)}(z_0)}{n!} )

end{document}

This should produce:

Creating a matrix:

documentclass{article}

usepackage{amsmath}

begin{document}

$$

begin{bmatrix}

1 & 2 & 3 \

4 & 5 & 6 \

7 & 8 & 9

end{bmatrix}

$$

end{document}

Note: Matrices and arrays can be a bit tricky since each LaTeX library handles them differently. In this case, we imported the amsmath package and used $$ instead of [ ... ] for an alternative syntax.

Additionally, here's a straightforward example featuring theorems, definitions, and proofs:

documentclass{article}

usepackage{amsthm} % Required for theorem environments

theoremstyle{plain} % Style for theorems (italicized body)

newtheorem{theorem}{Theorem} % Define theorem environment

begin{document}

begin{theorem}[Fundamental Theorem of Arithmetic]

Every integer greater than 1 can be uniquely expressed as a product of prime numbers, up to the order of the factors.

end{theorem}

begin{proof}

Let ( n ) be an integer greater than 1. We'll prove the theorem by induction on ( n ).

Base Case: For ( n = 2 ), the theorem holds since 2 is itself a prime number.

Inductive Step: Assume the theorem is valid for all integers ( k ) such that ( 2 leq k leq n ). We'll demonstrate that it holds for ( n + 1 ).

If ( n + 1 ) is prime, then it can be expressed as a product of a single prime number, satisfying the theorem.

If ( n + 1 ) is composite, it can be expressed as ( n + 1 = ab ), where ( 2 leq a, b leq n ). By the induction hypothesis, both ( a ) and ( b ) can be expressed as products of prime numbers. Therefore, ( n + 1 ) can also be expressed as a product of prime numbers.

Thus, by mathematical induction, the theorem holds for all integers greater than 1.

end{proof}

end{document}

This will produce:

Going Further

By now, you should have a grasp of LaTeX. However, since everyone's projects differ, your next steps will depend on your specific goals. Here are some useful resources:

• LaTeX Wikibook: Most topics you might be interested in are covered here; consider it more of a reference than a tutorial.
• Overleaf (Learn): Overleaf is an online LaTeX editor worth trying, even if you don't use it, its documentation is exceptional, featuring numerous tutorials.
• TeX — LaTeX Stack Exchange: As a last resort, if you can't find answers to your LaTeX questions, consider searching (or even asking) in the dedicated Stack Overflow section. There’s also a subreddit: r/LaTeX.

More Features

While not covered in detail here, there are additional capabilities you can explore in LaTeX. Here are a few that piqued my interest:

Academic Paper Elements (like footnotes):

documentclass{article}

begin{document}

This is a sentence with a footnotefootnote{This is the footnote text.}.

Another sentence follows.

end{document}

This is just the beginning; there’s a wide range of features from advanced lists, cross-references, graphics, tables, and more.

Programming: LaTeX offers basic macros and a more complex low-level programming called PlainTeX, along with packages for extensive customization.

While you're here, you might also want to look into converting LaTeX to HTML (numerous options are available, just check the link).

And that wraps up this brief and hopefully straightforward introduction to LaTeX. Thank you for reading!