LINGG 1 language of mathematics.pptx
Transcript of LINGG 1 language of mathematics.pptx
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