LaTeX provides powerful tools for creating mathematical content, from simple expressions to complex equations. There are different ways of working with math in LaTeX:

• Inline Math: To include mathematical expressions within a line of text, use the dollar signs $...$
• Display Math: For equations that need to be displayed on their own line, use double dollar signs $$...$$ or the \[...\] notation

Below, I show how inline math and display math looks like in Overleaf. Math code has light green color to easily differentiate it from the normal text.

• Equation Environment: For numbered equations, use the equation environment.
• Aligning Equations: For multiple equations or aligning equations, use the align environment from the amsmath package.
• Fractions, Exponents, and Subscripts:
  • Fractions: \frac{numerator}{denominator}
  • Exponents: a^b 
  • Subscripts: a_b

Below, I present a screenshot of equation environment:

When we compile, here is how this code looks like (notice that LaTeX automatically assigns numbers to our equations within equation environment):

LaTeX supports many Greek letters and mathematical symbols. For example:

• Greek letters: \alpha, \beta, \gamma, \Delta, \Omega
• Other symbols: \sum, \int, \prod, \sqrt, \leq, \geq

Greek letters and symbols have purple color in Overleaf interface:

Which creates the following output:

• Spacing: Use \, for a small space, \: for a medium space, and \; for a large space in your equations.
• Text in Math Mode: To include text within an equation, use the \text{} command from the amsmath package.
• Common Functions: LaTeX automatically formats common functions such as \sin, \cos, \log, etc.

For example, in the following screenshot, I used spacing function:

This code produces the following: