THE LANGUAGE OF

MATHEMATICS

THE VOCABULARY OF MATHEMATICS

Mathematical Notation has assimilated symbols from many different alphabets and typefaces. Also includes symbols that are specific to mathematics such as:

Mathematics has its own brand of technical terminology

-ex: group, ring, field, category, term, factor

THE VOCABULARY OF MATHEMATICS

There are stock phrases in mathematics, used with specific meanings

- ex: “if and only if” , “necessary and sufficient” . Such phrases are known as mathematical jargon

The vocabulary of mathematics also has visual elements.

- ex: Diagrams

THE GRAMMAR OF MATHEMATICS

The grammar used for mathematical discourse is essentially the grammar of the natural language uses as substrate, but with several mathematical specific peculiarities.

Mathematical notation used for formulas has its own grammar, not dependent on a specific natural languages, but shared intentionally by mathematicians regarding their mother tongue

Mathematical Expression-finite combination of symbols that is well formed according to rules that depend on the context

Syntax -being an expression is a syntactic concept. An expression must be well formed. Strings of symbols that violate the rules of syntax are not valid mathematical expressions

THE GRAMMAR OF MATHEMATICS-ex: the expression 2 + 3 is well informed but x4+,y would not be considered an expression but only a meaningless jumble

Semantics

- an expression may be used to designate a value, which might depend on the values assigned to variables occurring in the expression. The determination of the value depends on the semantics attached to the symbols.

- these semantic rules may declare that certain expressions do not designate any value. Ex: division by 0

- have an undefined value, but they are well-formed expression - The meaning of expression is not limited to designating values