Writing

$\TeX$

$\TeX$ is a typesetting program specialized for expressing formulas, considered an essential markup language for writing papers in fields close to formal sciences. $\TeX$ is pronounced as “Tech,” not “Tex.” Likewise, $\LaTeX$ is pronounced as “Lay-tech,” not “La-tex.”

The default font used in $\LaTeX$ is ‘Computer Modern.’

Basics

• Installing $\TeX$ and Using it with VS Code
• Writing Korean in $\TeX$
• Writing $\TeX$ Code in Gmail (Email)
• Using Quotation Marks

Functions

• Creating a New Command to Use \begin{}...\end{} Syntax as a Single Function \newcommand{\eq}[1]{\begin{equation}#1\end{equation}}
• Differences between \mathrm, \text, and \operatorname

Visualization

• Drawing Subplots
• Inserting GIF Animations
• Inserting Code Blocks

Tricks

• Using Large Brackets on One Side Only \left., \right.
• Increasing Line Spacing \\[1em] \\[1pt]
• Customizing Chapter and Section Numbering \setcounter{chapter}{}
• How to render text, formulas, pictures, and more transparently \phantom

Documentation

• Referencing Equations
• Hiding the Date with \maketitle

TikZ

• Drawing Universal Property Diagrams

English

The language of science is mathematics, and the language of mathematics is English. People studying formal sciences mostly study and write papers in English. Here, confusing grammar points are clarified and useful tips are introduced.

Grammar

• After Every and Each, a Singular Noun Must Follow
• After All, Either a Countable Noun in Plural Form or an Uncountable Noun in Singular Form Follows
• After Let, a Base Form Verb Must Follow

Sentence Structures

• To V with a probability of $a$

Dictionary for Science and Engineering

F

• Filtration: Formally, in various fields of mathematics, a set of sets $F = \left\{ X_{\alpha} \right\}{\alpha \in \forall}$ is called a filtration if for all $t < s$, the following inclusion relationship holds: $$ X{t} \subset X_{s} $$
  • (Probability Theory) Filtration of sigma fields
  • (Algebraic Topology) Filtration of complexes

S

• Support: Generally in mathematics, it refers to the set $\operatorname{supp} f$ that makes the function value non-zero. In geometry, points located on the boundary are also referred to as supports.
  • (Functional Analysis): Support of a function
  • (Mathematical Statistics): Support of a random variable
  • (Machine Learning): Support Vector Machines
  • (Geometry): Minimum Enclosing Disk Problem

Symbols and Abbreviations

• How to Read and Write Greek Letters and Their Significance in Mathematics and Science
• Differentiating Between Double-u $w$ and Omega $\omega$ in Mathematics and Physics Textbooks
• Common Symbols and Abbreviations Used in Mathematics