Introduction
Formulas are commonly used in STEM papers to represent mathematical relationships, calculations, equations, and other quantitative expressions. While formulas allow authors to concisely capture complex quantitative concepts, writing them properly takes some care. This article provides guidance on how to write, display, and reference formulas within a research paper from both a technical and readability perspective.
Technical Considerations
The first consideration when including formulas is choosing a system for writing them. LaTeX is commonly used for its precise typesetting abilities and integration with word processors and citation managers. Equations written in LaTeX can be copy-pasted directly into papers. Other options include MathType or the equation editor in Microsoft Word. Consistency is key – use only one system throughout the paper.
Regardless of the system, there are standard notations to follow:
Use upright or roman font for variables (e.g. x, y, not x, y) unless they represent vectors, matrices or other objects that require bold or italic.
Write subscripts and superscripts at the correct level – don’t raise/lower them.
Enclose operators like summation (+,-,=) within the appropriate symbols like ∑, ∫ etc. rather than writing them out as words.
Make sure the formatting of fractions, radicals, logarithms etc. follow the correct syntax of the system used.
Use appropriate formatting for vectors, matrices, partial derivatives, limits etc.
Define any non-standard functions or operators the first time they are used.
Formulas should be readable at native size without zooming. Consider line breaks, brackets, decimals and other punctuation that might affect readability on screens of different sizes. Formulas may need to be broken into multiple lines for complex expressions.
In Text Referencing
Once the technical layout is correct, consider how formulas will be referenced in the text for clarity. The first instance should be referred to in both words and symbols, for example “The function f(x) represents…”. Subsequent references can use just the symbol or word depending on context and flow.
Place important formulas inline where they are first discussed for emphasis. Less important or supportive formulas can be displayed in their own numbered lines. Consider using words like “given by”, “as shown in” etc. to smoothly introduce formulas in sentences.
Numbering and Layout
Long formulas or ones requiring future reference should be given numbers. Numbering allows identification and disambiguation when discussed later. Use consistent formatting like [(Formula number)] or Equation (1).
Place numbered formulas either inline with the text or in distinct math mode on separate lines centered using $$ $(Formula)$ $. Long blocks of multiple line formulas are better placed in an appendix for readability.
Consider splitting complex concepts across multiple simpler formulas to aid understanding. Use spaces, line breaks and formatting as needed to enhance readability of long or multi-line displays. Explanatory text can be included for clarity when referring to parts of numbered formulas.
Referencing Formulas
Refer back to previously defined formulas by number when building on a concept or in proofs. Phrases like “per Equation (3)” or “as shown in (1)” clearly direct the reader without repeating the full formula.
In subsequent references, the numbers alone may suffice but include words if adding context. “As (5) grows larger” is clearer than just “(5)”. Cross referencing between text and formulas aids readability.
Always include the formula number and page number when citing a formula from external sources to disambiguate from internal formulas, for example “As in Equation 2.7 on p.18 of [3]”.
Conclusions
Properly writing, numbering and referencing formulas using consistent notation and layout aids reader understanding of quantitative concepts in research papers. Following technical and readability best practices can help convey complex ideas through clear and accessible expression of mathematical relationships.