Intro to LaTeX **Full Tutorial** Part II (Equations, Tables, Figures, Theorems, Macros and more)

Introduction to LaTeX for Beautiful Mathematics

Overview of LaTeX

• LaTeX is a markup language ideal for writing mathematical documents, converting messy code into beautifully formatted equations.

• This video builds on a previous introduction to LaTeX, providing tips and tricks for creating homework or project documents.

Getting Started with Overleaf

• To write in LaTeX, you need software; Overleaf is recommended as the best web-based editor that operates in the cloud.

• The creator expresses pride in being officially sponsored by Overleaf to produce this educational series aimed at novices transitioning to mastery in LaTeX.

Basic Formatting Techniques

Emphasizing Mathematical Expressions

• The video demonstrates basic formatting techniques such as making text bold using textbf within curly braces.

• Users can also utilize Overleaf's rich text features, like italics (textit), through a contextual menu instead of memorizing commands.

Underlining Text

• Another formatting option shown is underlining text with underline, which wraps the desired expression in curly braces.

Creating and Numbering Equations

Display Math Environment

• To create more complex equations, users can use the display math environment with [ ... ] or beginequation ... endequation for automatic numbering.

Referencing Equations

Creating and Referencing Equations in LaTeX

Internal Label Creation

• The speaker discusses creating an internal label in LaTeX that is not displayed but can be referenced later. Instead of manually typing "1" for equation references, they use ref to reference the label named "limit".

Understanding Equation References

• The first equation is automatically numbered as "1" because it is the first equation in the document. This demonstrates how referencing works without manual input.

Constructing Limits with LaTeX

• The speaker explains how to create a limit expression using lim, including formatting elements like braces and arrows to denote limits approaching zero.

Aligning Multiple Equations

• To manage multiple equations, the speaker shifts from an equation environment to an align environment, which allows for better alignment of equations across multiple lines.

Enhancing Equation Layout

• By using `` at the end of lines within the align environment, LaTeX recognizes line breaks. The speaker removes unnecessary labels since there are now two equations being presented together.

Aligning Equal Signs in Equations

Using Ampersands for Alignment

• An ampersand (&) is introduced before equal signs in both equations to ensure they are aligned vertically, akin to columns in a table format.

Adding Text Within Equations

• The speaker shows how to insert text into equations using text, ensuring that it appears correctly formatted rather than disrupting mathematical notation.

Combining Equations into One Reference

Transitioning Back to Equation Environment

• To treat two aligned expressions as one single equation, the speaker returns to using the equation environment combined with a split structure: beginsplit and endsplit.

Maintaining Visual Consistency

• This method visually maintains the layout while allowing for a single reference number for what is conceptually one equation despite having multiple parts.

Utilizing Overleaf Features for Efficiency

Streamlined Typing with Overleaf

• The speaker highlights Overleaf's convenience features that auto-complete environments when typing commands like beginequation, saving time and reducing errors during coding.

Compiling Complex Expressions

How to Format Long Equations and Create Tables in LaTeX

Formatting Long Equations

• When equations are too long, use beginmultline instead of beginequation to allow for multiple lines.

• To indicate line breaks within the equation, use ``, which tells LaTeX where to end a line. This provides better control over the layout.

• The precision of LaTeX allows mathematicians to format their work effectively, despite the initial learning curve associated with its coding.

Creating Tables in LaTeX

• Start creating tables using begintable and then begintabular, which sets up the table environment with standard formatting.

• The syntax c | c centers columns and adds vertical lines between them; use & to separate columns and `` to end rows.

• You can add more vertical bars by adjusting the column specifications (e.g., adding bars on both sides), and horizontal lines can be added using hline.

Enhancing Table Appearance

• If there's a syntax error, Overleaf will highlight it; ensure that commands like hline are placed correctly after ending a row with ``.

• Adjust column alignment (left/right/center); for example, right-aligning numbers can improve readability.

Centering Tables and Adding Captions

• Wrap your table in a centering environment using begincenter and endcenter for better visual placement on the page.

• Use captions (caption) for clarity about what each table represents; labels (label) allow you to reference tables easily throughout your document.

Managing Page Layout

• LaTeX automatically positions tables based on available space; if needed, you can manually force content onto new pages using commands like newpage.

Adding Graphics and Custom Environments in LaTeX

Introduction to Including Graphics

• The speaker discusses adding graphics in LaTeX, specifically using the includegraphics command within a figure environment.

• An image file named "100k.png" is uploaded for inclusion, but an error occurs due to a missing package requirement.

• The necessary package graphicx is added to handle graphics, resolving the initial error upon recompilation.

Adjusting Image Size

• The issue of an "overfull horizontal box" arises because the image is too large; parameters can be adjusted within square brackets.

• Setting the width of the image to textwidth ensures it fits perfectly on the page, maintaining visual consistency.

Figure Environment Features

• The figure environment allows for captions and labels similar to tables, enhancing organization and reference capabilities in documents.

• The speaker transitions into discussing mathematical environments such as theorems and definitions, emphasizing their importance in academic writing.

Creating Custom Theorem Environments

• To create custom theorem environments, packages like amsthm are introduced alongside amsfonts, which are standard in mathematical typesetting.

• A new theorem environment is defined using newtheorem, specifying how it will be referenced and displayed throughout the document.

Implementing Theorems

• By using begintheorem, users can easily insert formatted statements that automatically number themselves (e.g., "Theorem 1").

• Each theorem's title appears bolded with its content italicized, ensuring consistent styling without manual formatting adjustments.

Additional Options for Theorems

• Users can add titles to theirorems by placing them in square brackets during definition; this enhances clarity when referencing multiple statements.

Understanding Theorem Numbering in LaTeX

Section and Theorem Numbering

• The speaker discusses the organization of theorems within sections, emphasizing that theorem numbering can be adjusted to reflect the current section.

• By specifying "section number," theorems are numbered according to their respective sections, resulting in formats like 2.1 and 2.2 for section two.

Corollaries and Their Numbering

• Corollaries are introduced as related results stemming from theorems; however, they typically follow a different numbering system based on their associated theorem rather than the section.

• An example is provided where a corollary is labeled as Corollary 2.2.1, indicating its connection to Theorem 2.2.

Proof Structure

• The speaker highlights that every theorem must be accompanied by a proof, which is presented in a standardized format with an italicized body followed by a QED symbol.

Creating Custom Commands in LaTeX

Simplifying Common Symbols

• A demonstration of creating custom commands begins with simplifying frequently used symbols like the real numbers represented by mathbbR.

• A new command R is created to replace mathbbR, allowing for quicker typing without losing clarity or meaning.

Advanced Command Creation

• The speaker explains how to create more complex commands that accept parameters, such as generating column vectors using a new command called cv.

• This command allows users to input values dynamically into a matrix format without needing to rewrite lengthy code each time.

Conclusion on Macros

LaTeX Tips and Tricks

Overview of Upcoming Content

• The series on LaTeX will feature several tips and tricks aimed at tackling more complex LaTeX tasks.

• Viewers are encouraged to check the description for links to Overleaf, a cloud-based software that simplifies writing in LaTeX.

• Additional documentation guides related to LaTeX are also provided in the description for further learning.