LaTeX Math Typesetting Guide

• Style Issue Basics
  • Variables
  • Vectors
  • Functions
  • Alignment and Line Breaks for Display Formulas
  • Avoid Obsolete Codes and Delimiters (eqnarray, $$ display math delimiters)
  • Use Appropriate Delimiters for Display Equations
  • mathcal vs. RSFS script
• Example I: Cases
  • Example 1-1
  • Example 1-2
  • Example 1-3
• Example II: Text Functions
  • Example 2-1
  • Example 2-2
  • Example 2-3
• Example III: Limits
  • Example 3-1
  • Example 3-2
• Example IV: Text Acronyms
  • Example 4-1
  • Example 4-2
  • Example 4-3
• Example V: Fences
  • Example 5-1
  • Example 5-2
  • Example 5-3

Style Issue Basics

Variables

Variables should always be set in italic font in both text and in equations.

Vectors

Vectors should always be in bold type.

Functions

Functions should always be set as roman type.

Alignment and Line Breaks for Display Formulas

• Break and Align on Mathematical Verbs

• Break at Mathematical Conjunctions and Align to the Right of the First Mathematical Verb

• Always Keep Expressions Visually Within Fences

Note the position of the “+” under and to the right of the parentheses surrounding the expression.

Avoid Obsolete Codes and Delimiters (eqnarray, $$ display math delimiters)

Avoid the use of outdated macros, such as eqnarray and $$ math delimiters, for display equations.

Use Appropriate Delimiters for Display Equations

• For single-line unnumbered display equations, please use only the following delimiters: \[ . . . \] or \begin{equation*} . . . \end{equation*}
• For multiline unnumbered display equations, please use only the following delimiters: \begin{align} . . . \end{align}
• For single-line numbered display equations, please use only the following delimiters: \begin{equation} . . . \end{equation}
• For multiline numbered display equations, please use only the following delimiters: \begin{align} . . . \end{align}

mathcal vs. RSFS script

Please see the RSFS documentation at https://ctan.org/pkg/rsfs for proper use.

Example I: Cases

Example 1-1

Incorrect Example: The wrong environment is used (array instead of cases), the tabs are missing, and the text is not formatted correctly (should not be italic).

\begin{equation}
  P(Y=1|\boldsymbol{X_{i}^{j}})=
  \left\lbrace
  \begin{array}{l}
    0, correct \\
    1, erroneous.
  \end{array}
  \right.
  \tag{1}
\end{equation}

Correct Example: The correct environment is used. Using the cases environment will save keystrokes (from not having to type the \left\brace{) and automatically provide the correct column alignment. The tabs have been inserted and the text formatting corrected.

\begin{equation*}
  P(Y=1|\boldsymbol{X_{i}^{j}})=
  \begin{cases}
    0, & \text{correct} \\
    1,& \text{erroneous.}
  \end{cases}
  \tag{1a}
\end{equation*}

Example 1-2

Incorrect Example: The wrong environment is used and the column alignment is incorrect. Columns in cases should be left aligned.

\begin{equation}
  {z_m(t)} = \left\lbrace {
    \begin{array}{cc}
      1,&{{\mathrm {if}}\  {{\beta }_m(t)} < \frac{\mathfrak {B}_{m}^{\max }}{{ |\mathcal {U}_m|r_{m,i}^{\min } }}},\\
      {0,}&{{\mathrm {otherwise.}}}
  \end{array}}
  \right.
  \tag{2}
\end{equation}

Correct Example: The correct environment is being used. Using the cases environment will save keystrokes (from not having to type the \left\brace{) and automatically provide the correct column alignment.

\begin{equation*}
  {z_m(t)} =
  \begin{cases}
    1,&{\mathrm {if}}\ {\beta }_m(t) < \frac{\mathfrak {B}_{m}^{\max }}{{ |\mathcal {U}_m|r_{m,i}^{\min } }},\\
    {0,}&{\mathrm {otherwise.}}
  \end{cases}
  \tag{2a}
\end{equation*}

Example 1-3

Incorrect Example: The wrong environment is used; a space is missing after the word “if.” In this instance an extra bit of space is needed.

\begin{align}
  h_{i}(x,y) &= \left\lbrace
  \begin{array}{ll}
    +1 & \mathrm{if} \xi _{i}(x)=\eta _{i}(y),\\
    -1 & \mathrm{otherwise },
  \end{array}
  \right.\nonumber \\
  &=(2 \xi _{i}(x)-1)(2\eta _{i}(y)-1),
  \tag{3}
\end{align}

Correct Example: The correct environment is being used. Using the cases environment will save keystrokes (from not having to type the \left\brace{) and automatically provide the correct column alignment. The text formatting is corrected by using \text{} to surround the textual elements “if” and “otherwise.”

\begin{align}
  h_{i}(x,y) &=
  \begin{cases}
    +1 & \mathrm{if }~ \xi _{i}(x)=\eta _{i}(y),\\
    -1 & \text{otherwise },
  \end{cases} \nonumber \\
  &=(2 \xi _{i}(x)-1)(2\eta _{i}(y)-1),
  \tag{3a}
\end{align}

Example II: Text Functions

Example 2-1

Incorrect Example: This example has incorrect text formatting and alignment issues. Please use \max, \min, and \text{...} for the conditions or text. \; should not be used for spacing: when the code is reused in other composition software, it will likely format differently than expected. Using tabs will provide concrete alignment points.

\begin{equation}
  LD(a_{x},b_{y})
  \begin{cases}
    max(x,y) \;\;\;\;\;\;\;\;\;\;\;if\; min(x,y)=0 \\
    min
    \begin{cases}
      L(a,b)(x-1,y)+1 \\
      L(a,b)(x,y-1,j)+1 & Otherwise\\
      L(a,b)(x-1,y-1)+1(a_{x}\neq b_{y})
    \end{cases}
  \end{cases}
  \tag{7}
\end{equation}

Correct Example: This example has the correct text formatting and tabs are used to correctly set column alignment. Note the use of \hfill to replace the multiple \; for alignment purposes.

\begin{equation}
  LD(a_{x},b_{y})
  \begin{cases}
    \max(x,y) \hfill \text{if } \min(x,y)=0 \\
    \min
    \begin{cases}
      L(a,b)(x-1,y)+1 & \\
      L(a,b)(x,y-1,j)+1 & \text{Otherwise} \\
      L(a,b)(x-1,y-1)+1 & (a_{x}\neq b_{y})
    \end{cases}
  \end{cases}
  \tag{7a}
\end{equation}

Example 2-2

Incorrect Example: This example has bad formatting of the function min. When coded as shown, it formats incorrectly as italic text.

\begin{equation*}
  d_{l}^{KM} = \underset {\mathbf {p}_{w}}{min} || \mathbf {p}_{f}^{l} – \mathbf {p}_{w} ||,
  \tag{12}
\end{equation*}

Correct Example: This example shows the use of \min to get the correct formatting of the function min.

\begin{equation*}
  d_{l}^{KM} = \underset {\mathbf {p}_{w}}\min || \mathbf {p}_{f}^{l} – \mathbf {p}_{w} ||,
  \tag{12a}
\end{equation*}

Example 2-3

Incorrect Example: This example has bad formatting of the function “arg min.” When coded as shown, it formats incorrectly as italic text.

\begin{equation*}
  d_{R}^{KM} = \underset {d_{l}^{KM}}{arg~{min}} \{ d_{1}^{KM},\ldots,d_{6}^{KM}\}.
  \tag{13}
\end{equation*}

Correct Example: This example shows the use of {\text{arg min}} to get the correct formatting of the function “arg min.”

\begin{equation*}
  d_{R}^{KM} = \underset {d_{l}^{KM}} {\text{arg min}} \{ d_{1}^{KM},\ldots,d_{6}^{KM}\}.
  \tag{13a}
\end{equation*}

Example III: Limits

Example 3-1

Incorrect Example: The upper and lower limits in a display formula should generally be above and below the operators.

\begin{equation*}
  c_{r_i} = \beta _0+\sum \nolimits _{j=1}^{n}{\beta _j \times c_{r_j}},
  \tag{15}
\end{equation*}

Correct Example: In this example, the \nolimits was removed as it was causing the incorrect formatting. \nolimits has appropriate uses for inline equations and in certain subelements of a display equation.

\begin{equation*}
  c_{r_i} = \beta _0+\sum_{j=1}^{n}{\beta _j \times c_{r_j}},
  \tag{15a}
\end{equation*}

Example 3-2

Incorrect Example: When limits appear in fractions within a display formula, they should be off to the side of the operator.

\begin{equation*}
  {C_{D}} = \frac {{\sum \limits _{i = 1}^{N} {\left ({{C_{D}({n_{\max }}) – {C_{D}}({n_{i}})} }\right)} }}{{ \sum \limits _{i = 1}^{N} {\left ({{C_{D}(n_{\max }^ {*}) – {C_{D}}(n_{i}^{*})} }\right)} }}
  \tag{18}
\end{equation*}

Correct Example: This example shows the proper formatting when \limits are removed. LaTeX will automatically format the limits correctly when within a fraction.

\begin{equation*}
  {C_{D}} = \frac {{\sum _{i = 1}^{N} {\left ({{C_{D}({n_{\max }}) {C_{D}}({n_{i}})} }\right)} }}{{ \sum _{i = 1}^{N} {\left ({{C_{D}(n_{\max }^ {*}) – {C_{D}}(n_{i}^{*})} }\right)} }}
  \tag{18a}
\end{equation*}

Example IV: Text Acronyms

Example 4-1

Incorrect Example: This example shows when the acronym “MSE” is not coded as text, it will appear in italic. This is inconsistent with how it appears in the text and it should be consistent.

\begin{equation*}
  MSE = \frac {1}{n}\sum _{i=1}^{n}(Y_{i} – \hat {Y_{i}})^{2}
  \tag{19}
\end{equation*}

Correct Example: This example shows where the acronym “MSE” is coded using \text{} to match how it appears in the text.

\begin{equation*}
  \text {MSE} = \frac {1}{n}\sum _{i=1}^{n}(Y_{i} – \hat {Y_{i}})^{2}
  \tag{19a}
\end{equation*}

Example 4-2

Incorrect Example: This example shows an instance where the formatting of the acronym “NCC” is inconsistent between text and its use in a formula.

\begin{equation*}
  {NCC}=\dfrac {\left |{\sum _{i=1}^{n}(a_{i}-\mu _{A})(b_{i}-\mu _{B})}\right |}{l\times \sigma _{A} \times \sigma _{B}},
  \tag{20}
\end{equation*}

Correct Example: This example shows where the acronym “NCC” is coded using \text{} to match how it appears in the text.

\begin{equation*}
  \text {NCC}=\dfrac {\left |{\sum _{i=1}^{n}(a_{i}-\mu _{A})(b_{i}-\mu _{B})}\right |}{l\times \sigma _{A} \times \sigma _{B}},
  \tag{20a}
\end{equation*}

Example 4-3

Incorrect Example: This example shows an instance where the formatting of the acronym “RMS” is inconsistent between text and its use in a formula.

\begin{equation*}
  RMS_{rs}=\sqrt {\frac {1}{N}\sum \limits _{i}^{N} {\left ({{d_{rs}(i)} }\right)^{2}}}
  \tag{32}
\end{equation*}

Correct Example: This example shows where the acronym “RMS” is coded using \text{} to match how it appears in the text.

\begin{equation*}
  \text{RMS}_{rs}=\sqrt {\frac {1}{N}\sum \limits _{i}^{N} {\left ({{d_{rs}(i)} }\right)^{2}}}
  \tag{32a}
\end{equation*}

Example V: Fences

Example 5-1

Incorrect Example: In this example, the parentheses are not growing to properly surround the content in between them.

\begin{equation*}
  \delta \approx 1 – ({e^{-\frac {d^{2}}{2 \times C^{m}_{T}}} \times e^{-\frac {d^{2}}{2 \times C^{m-1}_{T}}}})
  \tag{21}
\end{equation*}

Correct Example: In this example, the use of \left( and \right) enables the parentheses to grow to the height of the content in between them.

\begin{equation*}
  \delta \approx 1 – \left({e^{-\frac {d^{2}}{2 \times C^{m}_{T}}} \times e^{-\frac {d^{2}}{2 \times C^{m-1}_{T}}}}\right)
  \tag{21a}
\end{equation*}

Example 5-2

Incorrect Example: In this example, the square brackets are not growing to properly surround the content in between them.

\begin{equation*}
  [\sqrt {(\Delta x_{i}+d_{x})^{2}+(\Delta y_{i})^{2}} -\mu ^{k}]>\epsilon \mu ^{k}
  \tag{22}
\end{equation*}

Correct Example: In this example, the use of \left[ and \right] enables the square brackets to grow to the height of the content in between them.

\begin{equation*}
  \left[ \sqrt {(\Delta x_{i}+d_{x})^{2}+(\Delta y_{i})^{2}} -\mu ^{k}\right] >\epsilon \mu ^{k}
  \tag{22a}
\end{equation*}

Example 5-3

Incorrect Example: In this example, the parentheses are not growing to properly surround the content in between them.

\begin{equation*}
  \textrm {T} = ({\frac {c}{B}})^{2}
  \tag{34}
\end{equation*}

Correct Example: In this example, the use of \left( and \right) enables the parentheses to grow to the height of the content in between them.

\begin{equation*}
  \textrm {T} = \left({\frac {c}{B}}\right)^{2}
  \tag{34a}
\end{equation*}