Notation
How to read math symbols and Greek letters, and what they mean
This page lists the math symbols used on this site, with how to read them and what they mean. The ideas behind them are explained gently in “0.2 Reading math notation”. “Main lessons” shows where each symbol mainly appears (including lessons still to be published).
Basic symbolsProbability & statisticsDerivatives & vectorsGreek letters
Basic symbols
| Symbol | How to read it | Meaning | Main lessons |
|---|---|---|---|
| \(\sum\) | sigma (capital) | Add everything up | 0.2, 1.4 |
| \(\prod\) | pi (capital) | Multiply everything together | 2.4 |
| \(f(x)\) | f of x | Function: give it x, get one answer | 0.2, 2.1 |
| \(\arg\min_{\theta}\) | arg min over theta | The θ that makes the expression smallest | 2.1, 2.2 |
| \(\mathrm{MSE}\) | M S E | Mean squared error: the average of the squared prediction gaps | 2.2 |
| \(\leftarrow\) | left arrow (“gets”) | Replace the left side with the value on the right (update) | 2.3 |
| \(\sigma(z)\) | sigma of z | Sigmoid function: squeezes any value into 0–1 (not the σ of standard deviation) | 2.4 |
| \(\mathrm{TP},\ \mathrm{FN},\ \mathrm{FP},\ \mathrm{TN}\) | T P, and so on | The four cells of a confusion matrix: correct detection, miss, false alarm, correct rejection | 2.7 |
| \(\mathrm{ReLU}(z) = \max(0, z)\) | ReLU (“ray-loo”) | Activation function: 0 if z is negative, z itself if positive | 3.1 |
| \(\mathrm{softmax}(\mathbf{z})\) | softmax | Turns a list of scores into probabilities (weights) that are at least 0 and add up to 1 | 2.4, 3.5 |
| \(\mathrm{ECE}\) | E C E | Expected calibration error: the average gap between confidence and actual accuracy | 3.7 |
| \(\mathrm{sign}(a)\) | sign of a | +1 if a is positive, −1 if negative | 3.8 |
| \(x_i\) | x sub i | Subscript: the i-th x | 0.2 |
| \(\bar{x}\) | x bar | The average of the data (sample mean) | 0.2, 1.4 |
| \(\hat{y}\) | y hat | An estimate or prediction | 1.6, 2.2 |
| \(e^{x},\ \exp(x)\) | e to the x | Exponential function (e ≈ 2.718) | 1.3, 1.8 |
| \(\ln x\) | natural log of x | Natural logarithm: the power of e that gives x | 1.8, 2.4 |
| \(n!\) | n factorial | n × (n − 1) × … × 1 (0! = 1) | 1.3 |
| \(\binom{n}{k}\) | n choose k | The number of ways to choose k items from n | 1.3 |
| \(\lvert x \rvert\) | absolute value of x | The size of x without its sign | Throughout |
| \(\approx\) | approximately equal to | Nearly equal | Throughout |
Probability & statistics
| Symbol | How to read it | Meaning | Main lessons |
|---|---|---|---|
| \(P(A)\) | P of A | The probability that A happens | 1.1 |
| \(P(B \mid A)\) | P of B given A | Conditional probability: the probability of B when A has happened | 1.2 |
| \(P(A \cap B)\) | P of A and B | The probability that both A and B happen | 1.2 |
| \(A \cup B\) | A union B | Everything in A or B (\(A \cap B\) is the overlap) | 3.4, 4.1 |
| \(\bar{A}\) | A bar (not A) | A does not happen (the complement) | 1.2 |
| \(X \sim N(\mu, \sigma^2)\) | X follows N of mu, sigma squared | X follows a normal distribution with mean μ and variance σ² | 1.3 |
| \(E[X]\) | E of X | Expected value (mean) | 1.4 |
| \(\mathrm{Var}(X)\) | variance of X | Variance | 1.4 |
| \(\mu\) | mu | Mean | 1.3, 1.4 |
| \(\sigma\) | sigma (lowercase) | Standard deviation (the size of the spread) | 1.3, 1.4 |
| \(\lambda\) | lambda | Rate (e.g. accidents per km) | 1.3, 1.8 |
| \(\chi^2\) | chi-squared | Chi-square distribution (used, for example, to compute confidence bounds) | 1.8 |
| \(\mathrm{SE}\) | S E (standard error) | Standard error: the spread of an average (or proportion), \(\sigma/\sqrt{n}\) | 1.5, 1.6 |
| \(s,\ s^2\) | s, s squared | Sample standard deviation and sample variance (dividing by n − 1) | 1.4, 1.6 |
| \(t\) | t | Value from the t-distribution (used instead of the “2” when data are few) | 1.6, 1.7 |
| \(\alpha\) | alpha | Significance level (the confidence level is 1 − α) | 1.6, 1.7 |
| \(H_0,\ H_1\) | H zero, H one | Null hypothesis (no difference) and alternative hypothesis (a difference) | 1.7 |
| \(z\) | z | How many standard errors the observed value lies from the assumed value | 1.7 |
Derivatives & vectors
| Symbol | How to read it | Meaning | Main lessons |
|---|---|---|---|
| \(\frac{dy}{dx}\) | d y d x | Derivative: the slope (how fast y changes when x changes slightly) | 0.2, 2.3 |
| \(\frac{\partial L}{\partial w}\) | partial L partial w | Partial derivative: the slope when only one input moves | 0.2, 2.3, 3.2, 3.9 |
| \(\nabla L\) | nabla L / grad L | Gradient: the partial derivatives lined up as a vector | 0.2, 2.3, 3.2, 3.8 |
| \(\mathbf{x}\) | vector x | A list of numbers (a vector) | 0.2, 3.1 |
| \(\mathbf{w} \cdot \mathbf{x}\) | w dot x | Dot product: multiply matching elements and add them up | 0.2, 2.2, 3.1 |
| \(W\) | W (capital) | Matrix: numbers arranged in rows and columns | 3.1 |
| \(\mathbf{x}^{\top}\) | x transpose | Transpose: swap rows and columns | 3.1, 3.5 |
Greek letters
| Letter | How to read it | Main use on this site |
|---|---|---|
| \(\alpha\) | alpha | Significance level |
| \(\beta\) | beta | Regression coefficients; probability of a type II error |
| \(\delta,\ \Delta\) | delta | A small change / an amount of change |
| \(\varepsilon\) | epsilon | A small value / an error |
| \(\eta\) | eta | Learning rate (step size) |
| \(\theta\) | theta | Model parameters |
| \(\lambda\) | lambda | Rate; strength of regularization |
| \(\mu\) | mu | Mean |
| \(\xi\) | xi | How heavy a tail is (extreme value theory) |
| \(\pi\) | pi | The circle constant (3.14…) |
| \(\sigma,\ \Sigma\) | sigma | Standard deviation (lowercase); sum (capital) |
| \(\chi\) | chi | Chi-square distribution |
As with capital \(\Sigma\) (sum) and lowercase \(\sigma\) (standard deviation), the same name can mean completely different things in capital and lowercase.
Further reading
- The ideas behind the symbols: 0.2 Reading math notation
- What the terms mean: Glossary