Mathematics for Data Science 1 (BSMA1001) formula sheet

$\mathbb{Q} = \left\{ \frac{p}{q} \mid p, q \in \mathbb{Z}, q \neq 0 \right\}$

$2 \in \{1, 2, 3, 4, 6, 8, 12, 24\}$

$|S|$

$A \subseteq B$

$\mathcal{P}(S)$

$A \cup B$

$A \cap B$

$A \setminus B$

$R \subseteq A \times B$

$f: X \to Y$

$f \text{ is injective if } f(x_1) = f(x_2) \Rightarrow x_1 = x_2$

$f \text{ is surjective if } \forall y \in Y, \exists x \in X \text{ such that } f(x) = y$

$\frac{m}{n} = \frac{x - x_1}{x_2 - x}$

$\frac{m}{n} = \frac{y - y_1}{y_2 - y}$

$x = \frac{m x_2 + n x_1}{m + n}, \quad y = \frac{m y_2 + n y_1}{m + n}$

$A_{\text{triangle}} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|$

$y - y_0 = m(x - x_0)$

$\frac{x}{-3} + \frac{y}{3} = 1$

$\frac{x}{a} + \frac{y}{b} = 1$

$m_1 = m_2 \iff l_1 \parallel l_2$

$m_1 \cdot m_2 = -1 \iff l_1 \perp l_2$

$a_1 b_2 = a_2 b_1 \iff l_1 \parallel l_2$

$a_1 a_2 + b_1 b_2 = 0 \iff l_1 \perp l_2$

$\frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}$

$\frac{|C_1 - C_2|}{\sqrt{A^2 + B^2}}$

$SSE = \sum_{i=1}^{n} (y_i - mx_i - c)^2$

$g(x) = 2 a x + b$

$x_{\text{vertex}} = -\frac{b}{2a}$

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$p(x) + q(x) = \sum_{k=0}^{\max(m,n)} (a_k + b_k) x^k$

$p(x) - q(x) = \sum_{k=0}^{\max(m,n)} (a_k - b_k) x^k$

$p(x) \cdot q(x) = \sum_{k=0}^{m+n} \left( \sum_{j=0}^{k} a_j b_{k-j} \right) x^k$