| Symbol | Meaning | Example |
|---|---|---|
| \(+\) | Addition | \(2 + 3 = 5\) |
| \(-\) | Subtraction | \(7 - 4 = 3\) |
| \(\times\) | Multiplication | \(2 \times 3 = 6\) |
| \(\div\) | Division | \(6 \div 2 = 3\) |
| \(\%\) | Percentage | \(25\% \text{ of } 80 = 20\) |
| Symbol | Meaning | Example |
|---|---|---|
| \(=\) | Equal to | \(5 = 5\) |
| \(\neq\) | Not equal to | \(4 \neq 5\) |
| \(<\) | Less than | \(3 < 5\) |
| \(>\) | Greater than | \(7 > 5\) |
| \(\leq\) | Less than or equal to | \(3 \leq 3\) |
| \(\geq\) | Greater than or equal to | \(5 \geq 5\) |
| \(\approx\) | Approximately equal to | \(\pi \approx 3.14\) |
| \(\equiv\) | Identical to | \(x \equiv x\) |
| \(\sim\) | Similar to | \(\triangle ABC \sim \triangle DEF\) |
| \(\propto\) | Proportional to | \(y \propto x\) |
| Symbol | Meaning | Example |
|---|---|---|
| \(\in\) | Element of | \(2 \in \mathbb{Z}\) |
| \(\notin\) | Not an element of | \(\pi \notin \mathbb{Q}\) |
| \(\ni\) | Contains as an element | \(\mathbb{R} \ni \pi\) |
| \(\subset\) | Proper subset | \(\{1,2\} \subset \{1,2,3\}\) |
| \(\subseteq\) | Subset | \(\{1,2\} \subseteq \{1,2,3\}\) |
| \(\supset\) | Proper superset | \(\{1,2,3\} \supset \{1,2\}\) |
| \(\supseteq\) | Superset | \(\{1,2,3\} \supseteq \{1,2\}\) |
| \(\cup\) | Union | \(A \cup B\) |
| \(\cap\) | Intersection | \(A \cap B\) |
| \(\setminus\) | Set difference | \(A \setminus B\) |
| \(\emptyset\) | Empty set | \(\{x \in \mathbb{N} : x < 0\} = \emptyset\) |
| Symbol | Meaning | Example |
|---|---|---|
| \(\wedge\) | And | \(p \wedge q\) |
| \(\vee\) | Or | \(p \vee q\) |
| \(\neg\) | Not | \(\neg p\) |
| \(\Rightarrow\) | Implies | \(p \Rightarrow q\) |
| \(\Leftrightarrow\) | If and only if | \(p \Leftrightarrow q\) |
| \(\forall\) | For all | \(\forall x \in \mathbb{R}\) |
| \(\exists\) | There exists | \(\exists x \in \mathbb{R}\) |
| \(\therefore\) | Therefore | \(A=B, B=C, \therefore A=C\) |
| \(\because\) | Because | \(\because A=B \text{ and } B=C, \therefore A=C\) |
| Symbol | Meaning | Example |
|---|---|---|
| \(\angle\) | Angle | \(\angle ABC\) |
| \(\perp\) | Perpendicular | \(l_1 \perp l_2\) |
| \(\parallel\) | Parallel | \(l_1 \parallel l_2\) |
| \(\cong\) | Congruent | \(\triangle ABC \cong \triangle DEF\) |
| \(\sim\) | Similar | \(\triangle ABC \sim \triangle DEF\) |
| \(\triangle\) | Triangle | \(\triangle ABC\) |
| \(\square\) | Square | \(\square ABCD\) |
| \(\circ\) | Degree | \(90^\circ\) |
| \(\pi\) | Pi | \(\pi r^2\) |
| Symbol | Meaning | Example |
|---|---|---|
| \(\int\) | Integral | \(\int_a^b f(x) dx\) |
| \(\oint\) | Contour integral | \(\oint_C f(z) dz\) |
| \(\partial\) | Partial derivative | \(\frac{\partial f}{\partial x}\) |
| \(\nabla\) | Gradient | \(\nabla f\) |
| \(\lim\) | Limit | \(\lim_{x \to \infty} f(x)\) |
| \(\sum\) | Summation | \(\sum_{i=1}^n i\) |
| \(\prod\) | Product | \(\prod_{i=1}^n i\) |
| \(\frac{d}{dx}\) | Derivative | \(\frac{d}{dx} f(x)\) |
| \(\iint\) | Double integral | \(\iint_D f(x, y) dx dy\) |
| Symbol | Meaning | Example |
|---|---|---|
| \(\sqrt{}\) | Square root | \(\sqrt{4} = 2\) |
| \(\sqrt[n]{}\) | nth root | \(\sqrt[3]{8} = 2\) |
| \(\|x\|\) | Absolute value | \(\|-5\| = 5\) |
| \(n!\) | Factorial | \(5! = 120\) |
| \(\binom{n}{k}\) | Binomial coefficient | \(\binom{5}{2} = 10\) |
| \(\oplus\) | Exclusive or | \(1 \oplus 1 = 0\) |
| \(\otimes\) | Kronecker product | \(A \otimes B\) |
| Symbol | Meaning | Example |
|---|---|---|
| \(\mid\) | Divides | \(3 \mid 9\) |
| \(\nmid\) | Does not divide | \(3 \nmid 10\) |
| \(\pmod{}\) | Modulo operation | \(7 \pmod{3} \equiv 1\) |
| \(\gcd\) | Greatest common divisor | \(\gcd(12,18) = 6\) |
| \(\text{lcm}\) | Least common multiple | \(\text{lcm}(4,6) = 12\) |
| \(\infty\) | Infinity | \(\lim_{x \to 0} \frac{1}{x} = \infty\) |
| Symbol | Meaning | Example |
|---|---|---|
| \(\det\) | Determinant | \(\det(A)\) |
| \(\text{tr}\) | Trace of a matrix | \(\text{tr}(A)\) |
| \(A^T\) | Matrix transpose | \((A^T)_{ij} = A_{ji}\) |
| \(A^{-1}\) | Matrix inverse | \(AA^{-1} = I\) |
| \(\ker\) | Kernel | \(\ker(T)\) |
| \(\text{Im}\) | Image | \(\text{Im}(T)\) |
| \(\text{rank}\) | Rank | \(\text{rank}(A)\) |
| \(\dim\) | Dimension | \(\dim(V)\) |
| \(\text{span}\) | Span | \(\text{span}\{v_1, v_2, \ldots, v_n\}\) |
| \(\cdot\) | Dot product | \(\mathbf{a} \cdot \mathbf{b} = a_1 b_1 + a_2 b_2 + a_3 b_3\) |
| \(\times\) | Cross product | \(\mathbf{a} \times \mathbf{b} = (a_2 b_3 - a_3 b_2, a_3 b_1 - a_1 b_3, a_1 b_2 - a_2 b_1)\) |
| \(\otimes\) | Kronecker product | \(A \otimes B\) |
| \(\mathbf{0}\) | Zero vector | \(\mathbf{0} = (0, 0, \ldots, 0)\) |
| Symbol | Meaning | Example |
|---|---|---|
| \(i\) | Imaginary unit | \(i^2 = -1\) |
| \(z^*\) | Complex conjugate | \((a+bi)^* = a-bi\) |
| \(\|z\|\) | Modulus | \(\|3+4i\| = 5\) |
| \(\arg(z)\) | Argument | \(\arg(1+i) = \frac{\pi}{4}\) |
| Symbol | Meaning | Example |
|---|---|---|
| \(\mu\) | Population mean | \(\mu = \frac{1}{N}\sum_{i=1}^N x_i\) |
| \(\sigma\) | Standard deviation | \(\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^N (x_i - \mu)^2}\) |
| \(\sigma^2\) | Variance | \(\sigma^2 = \frac{1}{N}\sum_{i=1}^N (x_i - \mu)^2\) |
| \(\rho\) | Correlation coefficient | \(-1 \leq \rho \leq 1\) |
| \(\chi^2\) | Chi-squared | \(\chi^2 = \sum \frac{(O-E)^2}{E}\) |
| Symbol | Meaning | Example |
|---|---|---|
| \(e\) | Euler's number | \(\lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n = e\) |
| \(\pi\) | Pi | \(\pi \approx 3.14159\) |
| \(i\) | Imaginary unit | \(i^2 = -1\) |
| \(\gamma\) | Euler-Mascheroni constant | \(\gamma \approx 0.57721\) |
| \(\phi\) | Golden ratio | \(\phi = \frac{1 + \sqrt{5}}{2} \approx 1.618\) |
| \(\zeta(3)\) | Apéry's constant | \(\zeta(3) = \sum_{n=1}^{\infty} \frac{1}{n^3} \approx 1.20206\) |
| \(\ln(2)\) | Natural logarithm of 2 | \(\ln(2) \approx 0.69315\) |
| \(\delta\) | Khinchin's constant | \(\delta \approx 2.68545\) |
| \(\lambda\) | Lemniscate constant | \(\lambda \approx 2.62205\) |
| \(K\) | Catalan's constant | \(K \approx 0.91596\) |
| \(M\) | Meissel-Mertens constant | \(M \approx 0.261497\) |
| Symbol | Meaning | Example |
|---|---|---|
| \(\nabla\) | Gradient, divergence, or curl | \(\nabla f\) |
| \(\Box\) | End of proof | \(\therefore x = 2 \quad \Box\) |
| \(\sim\) | Distributed as | \(X \sim N(\mu, \sigma^2)\) |
| \(\asymp\) | Asymptotically equivalent | \(f(x) \asymp g(x)\) |
| \(\ll\) | Much less than | \(1 \ll 1000\) |
| \(\gg\) | Much greater than | \(1000 \gg 1\) |
| \(\to\) | Tends to | \(x \to \infty\) |
| \(\mapsto\) | Maps to | \(f: x \mapsto x^2\) |
| Symbol (Lowercase) | Symbol (Uppercase) | Pronunciation | Meaning | Example |
|---|---|---|---|---|
| \(\alpha\) | \(A\) | Alpha | Angle, coefficient | \(\alpha = 45^\circ\) |
| \(\beta\) | \(B\) | Beta | Angle, coefficient | \(\beta = 0.5\) |
| \(\gamma\) | \(\Gamma\) | Gamma | Gamma function | \(\Gamma(x)\) |
| \(\delta\) | \(\Delta\) | Delta | Delta function, change | \(\Delta x = x_2 - x_1\) |
| \(\epsilon\) | \(E\) | Epsilon | Small quantity, permittivity | \(\epsilon > 0\) |
| \(\zeta\) | \(Z\) | Zeta | Zeta function | \(\zeta(s)\) |
| \(\eta\) | \(H\) | Eta | Efficiency, viscosity | \(\eta = 0.8\) |
| \(\theta\) | \(\Theta\) | Theta | Angle | \(\theta = 30^\circ\) |
| \(\iota\) | \(\iota\) | Iota | Small quantity, index | \(\iota_n\) |
| \(\kappa\) | \(K\) | Kappa | Curvature | \(\kappa = \frac{1}{R}\) |
| \(\lambda\) | \(\Lambda\) | Lambda | Eigenvalue, wavelength | \(\lambda = 500 \, \text{nm}\) |
| \(\mu\) | \(M\) | Mu | Mean, magnetic moment | \(\mu = 10\) |
| \(\nu\) | \(N\) | Nu | Frequency | \(\nu = 60 \, \text{Hz}\) |
| \(\xi\) | \(\Xi\) | Xi | Random variable | \(\xi \sim N(0, 1)\) |
| \(o\) | \(O\) | Omicron | Omicron | \(o(n)\) |
| \(\pi\) | \(\Pi\) | Pi | Pi, product | \(\pi \approx 3.14\) |
| \(\rho\) | \(P\) | Rho | Density, resistivity | \(\rho = 1000 \, \text{kg/m}^3\) |
| \(\sigma\) | \(\Sigma\) | Sigma | Standard deviation, sum | \(\sigma = 2\) |
| \(\tau\) | \(T\) | Tau | Tau, torque | \(\tau = 5 \, \text{Nm}\) |
| \(\upsilon\) | \(\Upsilon\) | Upsilon | Upsilon | \(\Upsilon(x)\) |
| \(\phi\) | \(\Phi\) | Phi | Phi, potential | \(\phi = 10 \, \text{V}\) |
| \(\chi\) | \(X\) | Chi | Chi, chi-squared | \(\chi^2\) |
| \(\psi\) | \(\Psi\) | Psi | Psi, wave function | \(\Psi(x, t)\) |
| \(\omega\) | \(\Omega\) | Omega | Omega, angular frequency | \(\omega = 2\pi f\) |