Mathematical notation
As a mathematical notation is called in mathematics, logic and computer science, the representation of equations, and other mathematical objects using mathematical symbols. The mathematical notation corresponds to a language that is more formal than many natural languages , while still retaining some ambiguity as they are characteristic of natural languages.
- 3.1 infix notation
- 3.2 prefix notation
- 3.3 postfix
- 3.4 Other variants
Components
The mathematical notation uses special symbols.
- As, for mathematical objects, such as functions or numbers,
- For assignment purposes, ie brackets,
- And for the development of templates.
The names of mathematical objects, a distinction
- Constants ( fixed values), that is generally accepted labels for commonly used objects such as, , and
- Variables ( variable values), so for example names for objects that have yet to be found or you would like some general statements.
Mathematical signs
Variable names
In mathematics, letters are used as a sign when it is mutable objects in general. Usually a serif font is used for the text block.
Examples of rule instances of the alphabet used and the text set:
- Scalars: in italics:
- Vectors: partly as scalars, some with übergesetztem arrow or semi-bold (DIN 1303):
- Complex variables: how real scalars, in the engineering sciences often by horizontal line under the sign (DIN 1304 and DIN 5483 ):
- Quantities: ordinary capital letters or sets of numbers with double lines ( blackboard bold ):
- Matrices preferably uppercase, occasionally semi-bold (DIN 1303):
Other characters
Other characters include instructions for example, get special mathematical symbols assigned to the (originally ) only come in part from alphabets.
Examples:
Operator notation
In addition to determining which characters are used for the individual operators ( eg for addition ), the determination of the sequence of operators and their operands is important. In today's conventional mathematical notation, many variants are mixed:
Infix notation
In arithmetic, the most common is the infix notation, where the operator is placed between the operands. For her the computing sequence is determined by the valence of operations ( " point before line calculation "). By setting the brackets you can define subexpressions that must be calculated first. example:
Another example of an infix notation is the Peano Russell notation used in the logic of:
Prefix notation
Expressions in infix notation can quickly become confusing. In the 1920s, the Polish logician and philosopher therefore January Łukasiewicz developed the Polish notation, a prefix notation, which does not require brackets. The operators are denoted by capital letters, eg for the material implication ( sufficient condition ) and for disjunction ( alternative). In Polish notation to write the above logic term as:
Postfix
In postfix notation to write the operator according to the arguments to be linked; it is therefore also called Reverse Polish Notation (RPN ). Occasionally attributed to the Australian philosopher Charles Hamblin, she was very likely also already known Łukasiewicz. In the logic of the UPN was never used, but they gained by working Hamblin of some importance in the early computer science and the early compilers, because let expressions in UPN execute machine very easy. For the same reason they took over the company Hewlett -Packard in the 60s for their scientific calculators.
Other variants
Other notations are the staple- free Begriffsschrift notation of Gottlob Frege, the spelling of the first predicate logic system at all, and the Existential Graphs of Charles S. Peirce. Both also extremely different from the notations in use today because it is graphical, two-dimensional notations.
Explore mathematical notation
Mathematical notation is object of study among others in the following areas:
- Semiotics
- History of Mathematics
- Standardisation (DIN, ISO)
- Computer Algebra
- Programming languages
- Artificial intelligence
- Formal concept analysis and lattice theory
- Mathematics Education