It is common to utilize LaTex symbols for mathematics formulas, the symbols lists for the Calculus, Linear Algebra, and Discrete Mathematics with examples is as following.
Calculus
- Add-subtract (Plus-minus) / Times / Divide
- \(\pm\) / \(\times\) / \(\div\):
\pm/\time/\div - \(\pm\infty\) / \(n!=n(n-1)\cdots2\times1\) / \(n\div d\):
\pm\infty/n!=n(n-1)\cdots2\times1/n\div d
- Composite
- \(\circ\):
\circ - \((f\circ g)(x)=f[g(x)]\):
(f\circ g)(x)=f[g(x)]
- Deleted neighborhood
- \(\mathring{}\):
\mathring{} - \(\mathring{U}(x_0,\delta)\):
\mathring{U}(x_0,\delta)
- Fraction
- \(\frac{}{}\):
\frac{}{} - \(\frac{dy}{dx}=-\frac{F_x}{F_y}\):
\frac{dy}{dx}=-\frac{F_x}{F_y}
- Limit
- \(\lim\):
\lim - \(\lim\limits_{x \to \infty}f(x)=A\):
\lim\limits_{x\to\infty}f(x)=A
- Square root / Power root
- \(\sqrt{}\) / \(\sqrt[n]{}\):
\sqrt{}/\sqrt[n]{} - \(ds=\sqrt{1+y'^2}dx\) / \(\lim_{n\to\infty}\sqrt[n]{n}=1\):
ds=\sqrt{1+y'^2}dx/\lim_{n\to\infty}\sqrt[n]{n}=1
- Not Equal to / Approximately equal to
- \(\neq\) / \(\approx\):
\neq/\approx - \(f'(x_0)\neq0\) / \(\Delta y\approx f'(x_0)\Delta x\):
f'(x_0)\neq0/\Delta y\approx f'(x_0)\Delta x
- Less than or equal to / Greater than or equal to / Much less than / Much greater than
- \(\leq\) / \(\geq\) / \(\ll\) / \(\gg\):
\leq/\geq/\ll/\gg - \(\ln x\leq x-1\) / \(e^x\geq 1+x\) / \(|y'|\ll1\) / \(1\ll|y'|\):
\ln x\leq x-1/e^x\geq 1+x/|y'|\ll1/1\ll|y'|
- Partial derivative
- \(\partial\):
\partial - \(\frac{\partial^2z}{\partial x\partial y}=f_{xy}(x,y)\):
\frac{\partial^2z}{\partial x\partial y}=f_{xy}(x,y)
- Integral
- \(\int\):
\int - \(\int f(x)dx=F(x)+C\):
\int f(x)dx=F(x)+C
- Double integral
- \(\iint\):
\iint - \(\iint\limits_Df(x,y)d\sigma=\iint\limits_Df(x,y)dxdy\):
\iint\limits_Df(x,y)d\sigma=\iint\limits_Df(x,y)dxdy
- Average
- \(\overline{}\):
\overline{} - \(\overline{y}=\frac{1}{b-a}\int_a^by(x)dx\):
\overline{y}=\frac{1}{b-a}\int_a^by(x)dx
Linear Algebra
- Determinant
- \(\begin{vmatrix}\end{vmatrix}\):
\begin{vmatrix}\end{vmatrix} -
\(D=
\begin{vmatrix}
a_{11}&a_{12}&\cdots&a_{1n}\\
a_{21}&a_{22}&\cdots&a_{2n}\\
\vdots&\vdots&\vdots&\vdots\\
a_{n1}&a_{n2}&\cdots&a_{nn}
\end{vmatrix}\):
D= \begin{vmatrix} a_{11}&a_{12}&\cdots&a_{1n}\\ a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\vdots&\vdots&\vdots\\ a_{n1}&a_{n2}&\cdots&a_{nn} \end{vmatrix}
- Explanation on equal sign
- \(\xlongequal{}\):
\xlongequal{} -
\(\begin{vmatrix}
a_{11}&a_{12}&\cdots&a_{1n}\\
\vdots&\vdots&\vdots&\vdots\\
ka_{i1}&ka_{i2}&\cdots&ka_{in}\\
\vdots&\vdots&\vdots&\vdots\\
a_{n1}&a_{n2}&\cdots&a_{nn}
\end{vmatrix}
\xlongequal{r_i\div k}k
\begin{vmatrix}
a_{11}&a_{12}&\cdots&a_{1n}\\
\vdots&\vdots&\vdots&\vdots\\
a_{i1}&a_{i2}&\cdots&a_{in}\\
\vdots&\vdots&\vdots&\vdots\\
a_{n1}&a_{n2}&\cdots&a_{nn}
\end{vmatrix}\):
\begin{vmatrix} a_{11}&a_{12}&\cdots&a_{1n}\\ \vdots&\vdots&\vdots&\vdots\\ ka_{i1}&ka_{i2}&\cdots&ka_{in}\\ \vdots&\vdots&\vdots&\vdots\\ a_{n1}&a_{n2}&\cdots&a_{nn} \end{vmatrix} \xlongequal{r_i\div k}k \begin{vmatrix} a_{11}&a_{12}&\cdots&a_{1n}\\ \vdots&\vdots&\vdots&\vdots\\ a_{i1}&a_{i2}&\cdots&a_{in}\\ \vdots&\vdots&\vdots&\vdots\\ a_{n1}&a_{n2}&\cdots&a_{nn} \end{vmatrix}
- Continuous multiplication
- \(\prod\):
\prod -
\(\begin{vmatrix}
1&1&\cdots&1\\
x_1&x_2&\cdots&x_n\\
x_1^2&x_2^2&\cdots&x_n^2\\
\vdots&\vdots&\vdots&\vdots\\
x_1^{n-1}&x_2^{n-1}&\cdots&x_n^{n-1}\\
\end{vmatrix}
=
\prod_{1\leq i<j\leq n}(x_j-x_i)\):
\begin{vmatrix} 1&1&\cdots&1\\ x_1&x_2&\cdots&x_n\\ x_1^2&x_2^2&\cdots&x_n^2\\ \vdots&\vdots&\vdots&\vdots\\ x_1^{n-1}&x_2^{n-1}&\cdots&x_n^{n-1}\\ \end{vmatrix} = \prod_{1\leq i<j\leq n}(x_j-x_i)
- Matrix
- \(\begin{pmatrix}\end{pmatrix}\):
\begin{pmatrix}\end{pmatrix} -
\(A=\begin{pmatrix}
a_{11}&a_{12}&\cdots&a_{1n}\\
a_{21}&a_{22}&\cdots&a_{2n}\\
\vdots&\vdots&\vdots&\vdots\\
a_{m1}&a_{m2}&\cdots&a_{mn}
\end{pmatrix}\):
A=\begin{pmatrix} a_{11}&a_{12}&\cdots&a_{1n}\\ a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\vdots&\vdots&\vdots\\ a_{m1}&a_{m2}&\cdots&a_{mn} \end{pmatrix}
- Left curly bracket
- \(\begin{cases}\end{cases}\):
\begin{cases}\end{cases} -
\(\begin{cases}
a_{11}x_1+a_{12}x_2+\cdots+a_{1n}x_n=b_1,\\
a_{21}x_1+a_{22}x_2+\cdots+a_{2n}x_n=b_2,\\
\cdots\ \cdots\ \cdots\ \cdots\\
a_{m1}x_1+a_{m2}x_2+\cdots+a_{mn}x_n=b_m,
\end{cases}\):
\begin{cases} a_{11}x_1+a_{12}x_2+\cdots+a_{1n}x_n=b_1,\\ a_{21}x_1+a_{22}x_2+\cdots+a_{2n}x_n=b_2,\\ \cdots\ \cdots\ \cdots\ \cdots\\ a_{m1}x_1+a_{m2}x_2+\cdots+a_{mn}x_n=b_m, \end{cases}
- Equivalence / Contract
- \(\cong\) / \(\simeq\):
\cong/\simeq - \(A\cong B\) / \(A\simeq B\):
A\cong B/A\simeq B
Discrete Mathematics
- Conjunction / Disjunctions / Exclusive or
- \(\land\) / \(\lor\) / \(\oplus\):
\land/\lor/\oplus - \(p\land q\) / \(p\lor q\) / \(p\oplus q\):
p\land q/p\lor q/p\oplus q
- Continuous conjunction / Continuous disjunctions
- \(\bigwedge\) / \(\bigvee\):
\bigwedge/\bigvee - \(\neg(\underset{j=1}{\overset{n}\bigwedge}p_j)\equiv\underset{j=1}{\overset{n}\bigvee}\neg p_j\):
\neg(\underset{j=1}{\overset{n}\bigwedge}p_j) \equiv \underset{j=1}{\overset{n}\bigvee}\neg p_j
- Implication / Bidirectional implication
- \(\to\) / \(\leftrightarrow\):
\to/\leftrightarrow - \(p\to q\) / \(p\leftrightarrow q\):
p\to q/p\leftrightarrow q
- Universal quantifier / Existential quantifier
- \(\forall\) / \(\exists\):
\forall/\exists - \(\forall xp(x)\) / \(\exists xp(x)\):
\forall xp(x)/\exists xp(x)
- Therefore
- \(\therefore\):
\therefore -
\(\begin{align}
&p\\
&\underline{p\to q}\\
\therefore\ &q
\end{align}\):
\begin{align} &p\\ &\underline{p\to q}\\ \therefore\ &q \end{align}
- Belong to / Not belong to
- \(\in\) / \(\notin\):
\in/\notin - \(a\in A\) / \(a\notin A\):
a\in A/a\notin A
- Subset / Parent set / Proper subset / Proper parent set
- \(\subseteq\) / \(\supseteq\) / \(\subset\) / \(\supset\):
\subseteq/\supseteq/\subset/\supset - \(A\subseteq B\) / \(B\supseteq A\) / \(A\subset B\) / \(B\supset A\):
A\subseteq B/B\supseteq A/A\subset B/B\supset A
- Empty set / Aleph zero
- \(\varnothing\) / \(\aleph_0\):
\varnothing/\aleph_0 - \(\varnothing\subseteq S\) / \(|S|=\aleph_0\):
\varnothing\subseteq S/|S|=\aleph_0
- Union / Intersection
- \(\cup\) / \(\cap\):
\cup/\cap - \(A\cup B\) / \(A\cap B\):
A\cup B/A\cap B
- Continuous union /Continuous intersection
- \(\bigcup\) / \(\bigcap\):
\bigcup/\bigcap - \(\underset{i=1}{\overset{n}\bigcup}A_i\) / \(\underset{i=1}{\overset{n}\bigcap}A_i\):
\underset{i=1}{\overset{n}\bigcup}A_i/\underset{i=1}{\overset{n}\bigcap}A_i
- Boolean product
- \(\odot\):
\odot - \(A\odot B\):
A\odot B
- Sum
- \(\sum\):
\sum - \(\sum_{k=1}^{n}k=\frac{n(n+1)}{2}\):
\sum_{k=1}^{n}k=\frac{n(n+1)}{2}
- Curly bracket below
- \(\underbrace{}\):
\underbrace{} - \(A^R=\underbrace{AAA\cdots A}_{(multiply\ r\ A's)}\):
A^R=\underbrace{AAA\cdots A}_{(multiply r A's)}
- The largest integer not greater than x / The smallest integer not less than x
- \(\lfloor x\rfloor\) / \(\lceil x\rceil\):
\lfloor x\rfloor/\lceil x\rceil - \(\lfloor \log_2n\rfloor+1\) / \(\lceil \log_2(n+1)\rceil\):
\lfloor \log_2n\rfloor+1/\lceil \log_2(n+1)\rceil