Fraction, subscript and Greek characters

Came from CSAPP “1.9.1 Amdahl’s Law”

$$ T_{\text{new}} = (1-\alpha)T_{\text{old}} + (\alpha T_{\text{old}})/k = T_{\text{old}}[(1-\alpha) + \alpha/k] $$

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T_{\text{new}} = (1-\alpha)T_{\text{old}} + (\alpha T_{\text{old}})/k = T_{\text{old}}[(1-\alpha) + \alpha/k]

• _ is used for subscripts.
• \alpha produce the Greek letter α. Other Greek letters follow similar pattern(e.g., \beta, \gamma, \delta).
• \text{} makes the text inside appear normal text font rather than math italic.
• By default in LaTex math mode, every character is assumed to be its own variables, appearing in italics. \text makes characters to be read together as a word, apearing in normal text style.

$$ S = \frac{T_{\text{old}}}{T_{\text{new}}} = \frac{1}{(1-\alpha) + \alpha/k} $$

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S = \frac{T_{\text{old}}}{T_{\text{new}}} = \frac{1}{(1-\alpha) + \alpha/k}

• \frac{numerator}{denominator} creates a fraction.

Multiple dot

Came from Practice Problem 2.1 (solution page 179)

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n = 11 = 3 + 4 \cdot 2

$$ n = 11 = 3 + 4 \cdot 2 $$

• \cdot means the multiplication dot.

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x^n

$$ x^n $$

• x to the nth power.

Logical symbols

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A \land B \lor C \not D \wedge C \vee E \neg F \oplus G \barwedge H \; \hat{} \; I  \veebar J

$$ A \land B \lor C \not D \wedge C \vee E \neg F \oplus G \barwedge H ; \hat{} ; I \veebar J $$

Set operations

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A \cap B \cup C \bigcap_{i=1}^n A_i

$$ A \cap B \cup C \bigcap_{i=1}^n A_i $$

Vector, Sum, Equation numbering, Dot equal

came from “CSAPP 2.2.2 Unsigned Encodings”

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B2U_w(\vec{x}) \doteq \sum_{i=0}^{w-1}x_{i}2^i \qquad (2.1)

$$ B2U_w(\vec{x}) \doteq \sum_{i=0}^{w-1}x_{i}2^i \qquad (2.1) $$

• \qquad: “quad” refers to a unit of horizontal spacing (specifically a quadratically sized space). So \qquad means “quadratic space” - it creates a wide horizontal space
• \ldots: “l” stands for “low” - these are dots that appear on the baseline, as opposed to \cdots where “c” stands for “centered” dots that appear in the middle. So \ldots means “low dots”.
• $\doteq$ is commonly used in mathematics and computer science to denote a “definitional equality” - meaning it’s used when you’re defining something, rather than just stating that two things are equal.

Cases (curly brace), Condition, Greater and equal to

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T2U_{w}\left( x \right)  = \begin{cases}
x + 2^{w}, & x < 0  \\
x, & x \geq 0
\end{cases} \qquad (2.5)

$$ T2U_{w}\left( x \right) = \begin{cases} x + 2^{w}, & x < 0 \ x, & x \geq 0 \end{cases} \qquad (2.5) $$

• \\ means newline.
• & before x < 0 is an alignment operator