LaTeX practice: type the maths you see

Type ^ for a power and _ for a subscript. Only the next character is raised or lowered, so put anything longer in braces: x^{10}, not x^10.

1. $$x^2$$
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2. $$a_1$$
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3. $$x^{10}$$
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4. $$x_1^2$$
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5. $$e^{-x^2}$$
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6. $$a_{n+1} = 2a_n + 1$$
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\frac{top}{bottom} makes a fraction and \sqrt{x} a square root. For any other root, put its number in square brackets: \sqrt[3]{x}.

Read the guide: Fractions in LaTeX

1. $$\frac{1}{2}$$
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2. $$\frac{a+b}{c}$$
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3. $$\sqrt{2}$$
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4. $$\sqrt[3]{x}$$
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5. $$\frac{1}{1 + \frac{1}{x}}$$
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6. $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
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A Greek letter is its name after a backslash: \alpha, \theta, \pi. Start the name with a capital for the capital letter: \Delta, \Omega.

Read the guide: Greek letters in LaTeX

1. $$\alpha$$
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2. $$\theta$$
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3. $$\Delta x$$
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4. $$\lambda_1, \lambda_2$$
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5. $$\sigma^2$$
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6. $$\Omega = 2\pi f$$
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Symbols that are not on the keyboard each have a command: \times for ×, \cdot for a centred dot, \leq for ≤, \neq for ≠ and \approx for ≈.

Read the guide: LaTeX symbols

1. $$3 \times 4 = 12$$
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2. $$a \cdot b$$
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3. $$x \leq 5$$
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4. $$x \neq 0$$
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5. $$\pi \approx 3.14$$
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6. $$x \to \infty$$
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Brackets typed on their own stay small. Write \left before the opening bracket and \right before the closing one, and they grow to fit what is between them. Curly braces need a backslash: \{ and \}.

Read the guide: Brackets and delimiters in LaTeX

1. $$\left( \frac{1}{2} \right)$$
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2. $$\left[ \frac{a}{b} \right]$$
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3. $$\left| \frac{x}{2} \right|$$
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4. $$\{1, 2, 3\}$$
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5. $$\left( \sum_{i=1}^{n} x_i \right)^2$$
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6. $$\|\mathbf{v}\|$$
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\sum and \prod take their limits from _ and ^. In a formula on its own line, like these, the limits sit below and above the symbol.

Read the guide: Summation (∑)

1. $$\sum_{i=1}^{n} i$$
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2. $$\sum_{k=0}^{\infty} \frac{1}{2^k}$$
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3. $$\prod_{i=1}^{n} a_i$$
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4. $$\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$$
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5. $$\sum_{k=0}^{n} \binom{n}{k} = 2^n$$
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6. $$\sum_{i=1}^{m} \sum_{j=1}^{n} a_{ij}$$
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\int gives the integral sign, with its limits in _ and ^. A thin space, \,, before the dx is the usual style; here it is optional.

Read the guide: Integrals in LaTeX

1. $$\int x \, dx$$
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2. $$\int_0^1 x^2 \, dx$$
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3. $$\int_{-\infty}^{\infty} e^{-x^2} \, dx = \sqrt{\pi}$$
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4. $$\iint_D f(x, y) \, dA$$
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5. $$\oint_C \mathbf{F} \cdot d\mathbf{r}$$
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6. $$\frac{d}{dx} \int_a^x f(t) \, dt = f(x)$$
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Names like \sin, \log and \lim are commands, so they print upright instead of as slanted letters. \lim takes what x tends to from _, and ' gives a prime.

Read the guide: Derivatives in LaTeX

1. $$\sin x$$
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2. $$\log_2 8 = 3$$
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3. $$\lim_{x \to 0} \frac{\sin x}{x} = 1$$
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4. $$f'(x)$$
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5. $$\frac{dy}{dx}$$
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6. $$\frac{\partial f}{\partial x}$$
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\mathbf{v} makes a bold vector and \vec{v} puts an arrow over it. \mathbb{R} gives the blackboard-bold R of the real numbers, and \in, \cup and \subseteq are set symbols.

Read the guide: Vectors in LaTeX

1. $$\mathbf{v}$$
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2. $$\vec{a} \cdot \vec{b}$$
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3. $$x \in \mathbb{R}$$
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4. $$A \cup B$$
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5. $$A \subseteq B$$
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6. $$\{ x \in \mathbb{Z} : x > 0 \}$$
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A matrix goes between \begin{pmatrix} and \end{pmatrix}: & moves to the next column and \\ starts a new row. bmatrix gives square brackets, vmatrix straight bars, and cases the brace of a function in several parts.

Read the guide: Matrices in LaTeX

1. $$\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$$
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2. $$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$$
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3. $$\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc$$
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4. $$\begin{pmatrix} x \\ y \\ z \end{pmatrix}$$
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5. $$A = \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix}$$
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6. $$|x| = \begin{cases} x & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \end{cases}$$
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