Mathematical Notation

A clear and consistent notation system improves reviewability and reproducibility. Follow the conventions below, especially italics for variables, roman units, and consistent equation numbering.

General principles

• Define symbols at first use and keep notation consistent throughout (case, subscripts, boldness).
• Avoid reusing the same symbol for different meanings; if unavoidable, clarify explicitly.
• Consider adding a Notation subsection listing key variables and units.

Typography conventions

• Use italics for variables/symbols; use roman type for units, function names, and operators.
• Use bold symbols for vectors/matrices; keep scalars non-bold.
• Use roman subscripts for descriptors (e.g., max, in, out) and italic subscripts for variables.

Equations: editing, numbering, and referencing

• Create equations with an equation editor; avoid images or manual character hacks.
• Number equations consecutively with right-aligned numbers in parentheses, e.g., (1).
• Refer to equations as “(1)” (not “Eq. (1)”) except at sentence start where “Equation (1)” is acceptable.
• Punctuate equations when they are part of a sentence.
• Define all symbols before the equation appears or immediately after it.

Units, dimensions, and numerical style

• Provide units for physical quantities and prefer SI units; place a space between number and unit (e.g., 30 km/h).
• Avoid mixing unit systems; if non-SI is used, provide conversions or clear notes.
• Write decimals as 0.25 (not .25) and state significant digits/uncertainty when relevant.

Algorithms & pseudocode

• Number algorithms and provide short titles; format them distinctly from body text.
• Use consistent notation; specify inputs/outputs and hyperparameters.

Clarity tips

• Use parentheses, solidus (/), or exp() to avoid ambiguous denominators/exponents.
• Avoid long, subscript-heavy formulas in titles; keep them short if unavoidable.
• When notation is dense, add a symbol/parameter table in the paper or appendix.