Mathematical notation

Mathematical notation is a system in mathematics that uses symbols to represent objects and ideas. In mathematics and other exact sciences like physics or computer science, problems often need to be presented in some way. In such representations, different symbols have different meanings:

• There are numbers, like 1 and 2, or variables that stand for such numbers (like x and y)
• There are functions that act on numbers and variables. Such function take a predetermined number of elements, and do something with them. An example is +, which adds two numbers
• There are concepts of advanced mathematics such as limits and derivatives

Some mathematical notations use diagrams, or small drawings to show the underlying concepts. One example is the Penrose graphical notation which is used to show tensors. Another examples are Coxeter–Dynkin diagram which are used for certain problems of geometry.

There are different ways to write down an equation like two and three

• Infix notation: The functions and the symbols they act on, are mixed, this gives 2 + 3
• Prefix notation: First there is the function, and then the values it operates on. This gives + 2 3. Computer languages influenced by lambda calculus, like LISP use this notation. Sometimes this is called polish notation
• Postfix notation: First there are the numbers, and then the function. 2 3 +. Postscript uses this. It is also generally known as reverse polish notation

Related software

• KaTeX - JavaScript library that shows mathematical notation on any web browser
• LaTeX - Free software to output mathematical notations on a PDF