A collection of some ideas about mathematical notation, especially as it relates to J.
Standard Mathematical Notation
There is no such thing. However, many people think there is.
An example of an idiosyncratic notation, perhaps invented by the author. This sort of thing is not uncommmon. This is from Bayesian Nets and Causality by Jon Williamson (Oxford University Press, 2005).
Order of Operations
In programming languages, this is often exemplified by C or C++. See http://www.cppreference.com/operator_precedence.html for an example. This is rather complex and fails to address some issues, particularly that of multiple uses of a variable within a single line.
What is more, this is not the only order of operations that gets used: see http://support.microsoft.com/kb/25189 for Microsoft Excel's take on this.
See NYCJUG/notationFAQ for an explanation about why right-to-left order of execution is substantially more useful than the reverse.