Latex

Sources

You can find some additional information here:

• http://tex.imm.uran.ru/tex/2e/lshort2e/node52.html;

• https://ido.tsuab.ru/mod/book/view.php?id=62&chapterid=23;

• https://ru.overleaf.com/learn/latex/List_of_Greek_letters_and_math_symbols.

Comparison

\leq - \(\leq\), \geq - \(\geq\), \approx - \(\approx\), \neq - \(\neq\), \sim - \(\sim\).

Proofs symbols

\forall - \(\forall\), \Leftarrow - \(\Leftarrow\), \Rightarrow - \(\Rightarrow\), \Leftrightarrow - \(\Leftrightarrow\), \boxtimes - \(\boxtimes\).

Greek alphabet

Here is a list of the Greek alphabet and the corresponding LaTeX for each letter:

Name	LaTeX	Rendered	LaTeX	Rendered
Alpha	\alpha	\(\alpha\)	A	\(A\)
Beta	\beta	\(\beta\)	B	\(B\)
Gamma	\gamma	\(\gamma\)	\Gamma	\(\Gamma\)
Delta	\delta	\(\delta\)	\Delta	\(\Delta\)
Epsilon	\epsilon	\(\epsilon\)	E	\(E\)
Zeta	\zeta	\(\zeta\)	Z	\(Z\)
Eta	\eta	\(\eta\)	H	\(H\)
Theta	\theta	\(\theta\)	\Theta	\(\Theta\)
Iota	\iota	\(\iota\)	I	\(I\)
Kappa	\kappa	\(\kappa\)	K	\(K\)
Lambda	\lambda	\(\lambda\)	\Lambda	\(\Lambda\)
Mu	\mu	\(\mu\)	M	\(M\)
Nu	\nu	\(\nu\)	N	\(N\)
Xi	\xi	\(\xi\)	\Xi	\(\Xi\)
Omicron	o	\(o\)	O	\(O\)
Pi	\pi	\(\pi\)	\Pi	\(\Pi\)
Rho	\rho	\(\rho\)	P	\(P\)
Sigma	\sigma	\(\sigma\)	\Sigma	\(\Sigma\)
Tau	\tau	\(\tau\)	T	\(T\)
Upsilon	\upsilon	\(\upsilon\)	\Upsilon	\(\Upsilon\)
Phi	\phi	\(\phi\)	\Phi	\(\Phi\)
Chi	\chi	\(\chi\)	X	\(X\)
Psi	\psi	\(\psi\)	\Psi	\(\Psi\)
Omega	\omega	\(\omega\)	\Omega	\(\Omega\)

Note: Some rendering engines interpret special commands for symbols that are identical to modern English letters — e.g., \Alpha for the symbol $A$. However, some interpreters (including browsers) do not recognize these commands, so it is recommended to use regular characters instead.

There are some special forms for classical letters:

\varphi: \(\varphi\);\varepsilon: \(\epsilon\).

Popular functions

TeX has special commands for popular mathematical functions. If a command is used to render a function, the result may look slightly different.

The LaTeX code $\sin \& sin$ will be rendered as: \(\sin \& sin\).

The following table shows some of the functions that have corresponding commands in TeX.

LaTeX Command	Rendered Output	Description
\arccos	\(\arccos\)	Inverse cosine
\arcsin	\(\arcsin\)	Inverse sine
\arctan	\(\arctan\)	Inverse tangent
\cos	\(\cos\)	Cosine
\cosh	\(\cosh\)	Hyperbolic cosine
\cot	\(\cot\)	Cotangent
\coth	\(\coth\)	Hyperbolic cotangent
\csc	\(\csc\)	Cosecant
\deg	\(\deg\)	Degree (angle)
\det	\(\det\)	Determinant
\dim	\(\dim\)	Dimension
\exp	\(\exp\)	Exponential function
\gcd	\(\gcd\)	Greatest common divisor
\hom	\(\hom\)	Homomorphism
\inf	\(\inf\)	Infimum
\ker	\(\ker\)	Kernel
\lg	\(\lg\)	Logarithm base 10
\lim	\(\lim\)	Limit
\liminf	\(\liminf\)	Limit inferior
\limsup	\(\limsup\)	Limit superior
\ln	\(\ln\)	Natural logarithm
\log	\(\log\)	Logarithm
\max	\(\max\)	Maximum
\min	\(\min\)	Minimum
\Pr	\(\Pr\)	Probability operator
\sec	\(\sec\)	Secant
\sin	\(\sin\)	Sine
\sinh	\(\sinh\)	Hyperbolic sine
\sup	\(\sup\)	Supremum
\tan	\(\tan\)	Tangent
\tanh	\(\tanh\)	Hyperbolic tangent

Upper excreta

• \tilde{ffff} - \(\tilde{ffff}\), \widetilde{ffff} - \(\widetilde{ffff}\);

• \hat{ffff} - \(\hat{ffff}\), \widehat{ffff} - \(\widehat{ffff}\);

• \bar{ffff} - \(\bar{ffff}\), \overline{ffff} - \(\overline{ffff}\).

Operations with sets

• A \in B - \(A \in B\);

• A \subset B - \(A \subset B\);

• A \supset B - \(A \supset B\);

• A \subseteq B - \(A \subseteq B\);

• A \supseteq B - \(A \supseteq B\);

• A \cup B - \(A \cup B\);

• A \cap B - \(A \cap B\).

Binary operators

• A \times B - \(A \times B\);

• A \pm B = \(A \pm B\).

Existance

• \exists a - \(\exists a\);

• \nexists a - \(\nexists a\).

Ellipses

Ellipses is a symbol that looks like three dots in a row. They are typically used to show that some elements are omitted from the notation. These hidden elements follow a pattern that should be obvious from the explicitly stated ones.

The following tables shows typical ellipsis symbols:

Command	Rendered	Description	Example
\ldots	\(\ldots\)	Low dots are used to skip some elements of the sequnce	\(a_1, a_2, \ldots, a_n \)
\cdots	\(\cdots\)	Centered dots	\(\begin{array}{c} a_1 & a_2 & \cdots & a_n & \end{array}\)
\vdots	\(\vdots\)	Vertical dots	\(\begin{array}{ccc} a_1 \\ \vdots \\ a_2 \end{array}\)
\ddots	\(\ddots\)	Diagonal patterns
\dotsc	\(\dotsc\)	With commas
\dotsb	\(\dotsb\)	Binary operations
\dotsm	\(\dotsm\)	Multiplication
\dotsi	\(\dotsi\)	Integrals, sums
\dotso	\(\dotso\)	Miscellaneous

Vertical bar

There is a lot of cases when vertical bars in mathematical notation can be used. And there is a set of options how you can peform that:

• Defining conditions for sets \(\{x \in \mathbb{R} \mid x>0 \}\).

• Conditional probability \(P(A \mid B)\).

• It can be used as brackets for an expression; a typical expression for the Euclidean norm is \(\| A \|\).

There are few ways to create such symbol:

• Just use | symbol: $A|B$-\(A|B\).

• Use \mid keyword, the most typical option, create some extra spacing for symbols before and after: $A|B \mid C$- \(A|B \mid C\)

• Use \vert keyword, I haven’t found difference with using | symbol yet: $A|B \vert C$ - \(A|B \vert C\).

• For creating brackets as two close positioned vertical lines use \|: $\|A\|$ - \(\|A\|\).

Joining case

The following instructions are used to create a parenthesis in latex:

• \begin{cases} <expression>  \\end{cases} - will put expression under the bracket;

• \\ - to jump to a new line for an expression under a bracket.

For example expression:

$$\begin{cases}
      line1; \\
      line2.
\end{cases}$$

Will show markdown:

\[\begin{split}\begin{cases} line1; \\ line2. \end{cases}\end{split}\]

Expression numbers

Using command \tag

For example:

$$\frac{\delta}{\gamma} \tag{hello}$$

\[\frac{\delta}{\gamma} \tag{hello}\]

Brakets

Rounding

• Floor \lfloor a \rfloor - \(\lfloor a \rfloor\);

• Ceil \lceil a \rceil - \(\lceil a \rceil\);

• Note \(\lfloor 5.31 \rfloor = 5, \lfloor -5.31 \rfloor = -6, \lceil 5.31 \rceil = 6, \lceil -5.31 \rceil=-5\).

To wrap in brackets

Expression like:

$$[\frac{\sum_i^n}{\prod_i^n}]$$

Will be interpreted like:

\[[\frac{\sum_i^n}{\prod_i^n}]\]

The problem is that a square bracket does not completely close the expression it surrounds. To fix this, you need to put the tag $\left$ before the opening bracket and $\right$ before the closing bracket. That is, the expression:

$$\left[\frac{\sum_i^n}{\prod_i^n}\right]$$

Which will be interpreted like this:

\[\left[\frac{\sum_i^n}{\prod_i^n}\right]\]

You can even use it with types of parentheses defined by other keywords. For example expression:

\left\lceil \frac{a}{b} \right\rceil

will look like:

\[\left\lceil \frac{a}{b} \right\rceil\]

Matrices

To create the matrix, you will need:

• Opening and closing brackets \left(, \right);

• The \betting{array} \end{array} instruction will allow you to create table elements inside the bracket. (in order to start the wod after opening \begin{array}, you will have to put \\);

• The & symbol is used to move to the next element of the string;

• To move to the next line element, the \\ is used;

• To fill in the intermediate places between matrix elements, you may need to use multipo dots:

  • Horizontal dots \cdots - \(\cdots\);

  • Vertical dots \vdots - \(\vdots\);

  • Dianal polynomial dots - \(\ddots\):

Thus an entry of the form:

$$
\left(\begin{array}{cccc}
    a_{11} & a_{12} & \cdots & a_{1n} \\ 
    a_{21} & a_{22} & \cdots & a_{2n} \\ 
    \vdots & \vdots & \ddots & \vdots \\
    a_{n1} & a_{n2} & \cdots & a_{nn} 
\end{array}\right)
$$

Will allow you to form an expression of the form:

\[\begin{split} \left(\begin{array}{cccc} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{n1} & a_{n2} & \cdots & a_{nn} \end{array}\right) \end{split}\]

Letters with empty space

Usually used to denote moieties. To write a letter in this way, use the command \mathbb{...}.

$$\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz}$$- \(\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz}\)