Scientific reporting attention points

On this page, I collect a list of attention points for scientific reporting. These attention points are based on issues observed in reports I have received from students. Next to highlighting the issues, I will also give pointers on how to correct them, with a focus on LaTeX. Feedback on this document is appreciated. EQ

Font style for mathematical symbols

The typeface for mathematical symbols are standardized to avoid confusion with, e.g., symbols for units, and to distinguish variables and constants. Often, these conventions are not followed. Sometimes the conventions are followed in equations, but not in the text, creating a situation where two typographically distinct symbols are used for the same thing. Basically, the standard tells us to write

• variables and quantities in italic (or at least slanted), and
• mathematical constants, units, and descriptive terms in roman (or at least upright).

Some examples:

• The value of the mathematical constant $$\mathrm{e}$$ is approximately $$2.72$$.
• The established value for the electron charge $$e$$—a physical constant but mathematical variable—is approximately $$1.6\cdot10^{-19}~\textrm{C}$$.
• The function generically denoted by $$f$$ is here defined for all real-values $$x$$ by $$f(x)=x^2+1$$.
• We will need the coefficients $$c_{\text{dry}}$$ and $$c_{\text{wet}}$$.
• Is the sum $$\sum_{k=1}^\infty\frac{1}{k}$$ well-defined?

Multiplication symbols

There is a difference between symbols used in programming languages and those in written texts. The former are essentially constrained by the keys available on keyboards, the latter are not. This is especially relevant for multiplication symbols:

• standard multiplication does not always need to be indicated using a symbol, juxtaposition may be enough ($$ab$$);
• $$\cdot$$ can be used for the scalar product (inner product) of vectors ($$\vec{u}\cdot\vec{v}$$) or for standard multiplication ($$1.6\cdot10^6$$);
• $$\times$$ is used for multiplication (Cartesian product) of sets ($$\mathcal{C}\times\mathcal{D}$$), (outer) vector product ($$\vec{u}\times\vec{v}$$), or standard multiplication ($$1.6\times10^6$$);
• $$*$$ is used for convolution of functions ($$f*g$$) and never for standard multiplication.

In any case, usage must be consistent.

Units

The notation for units is standardized as well; they should be written in roman (or at least upright). The positioning of units is also standardized; they should be separated from the value by a single—non-breaking—space (apart from a few exceptions).

Some examples:

• The temperature of $$-273.15~\mathrm{K}$$ is equal to $$0~°\mathrm{C}$$.
• Delft lies as a latitude of $$52°\,00′\,24″$$ North and a longitude of $$4°\,21′\,20″$$ East.

Values

The number of digits shown in a text should not be arbitrary. For example, it should not be based on the number of digits output from a computation tool. Only the significant digits should be shown. If the number of significant digits is difficult to determine: showing fewer is better than showing more and any significant digit (certainly beyond the second) should be justified.

Walls of text

Paragraphs should not be overly long, as this makes it hard to follow the argument. There are no hard rules, but paragraphs more than six sentences, say, should be evaluated for splitting. (Each of these sentences should of course also be of reasonable length; beware the ‘run-on sentence’.)

Apart from splitting them, there are other ways to fix overly long paragraphs, such as

• using ordered or un-ordered lists, or
• presenting the content in another way, e.g., using tables or figures.

Placement of mathematical expressions

Mathematical expressions should be part of the flowing text, even if the expression is displayed and not in-line. This means in particular that punctuation rules must be followed. So never end a sentence before an expression and keep it hanging.

An example: The quantites $$a$$ and $$b$$ are inversely proportional; namely $a=\gamma\frac{1}{b},$ where $$\gamma$$ is a proportionality constant.

Introduction of symbols

Symbols should always be introduced on first usage. It is not enough to put them in a list of symbols. Actually, it is good practice to re-introduce a symbol briefly (e.g., by referring back to the first time it was introduced) when it has not been used for a while or when one cannot assume the original introduction is fresh in the mind of the reader (e.g., in a new chapter that is read later or that can be read separately).

Functions vs. values

Functions and values should not be confused. Their distinction should be clear from the notation used.

For example: the airfoil chord length $$c$$ is a function of the radial position $$r$$ on the blade; crudely, $$c(r)\propto1/r$$. (Only if there is only one, fixed radial position considered can one write $$c\propto1/r$$.)