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  2. Language of mathematics - Wikipedia

    en.wikipedia.org/wiki/Language_of_mathematics

    The consequence of these features is that a mathematical text is generally not understandable without some prerequisite knowledge. For example, the sentence "a free module is a module that has a basis" is perfectly correct, although it appears only as a grammatically correct nonsense, when one does not know the definitions of basis, module, and free module.

  3. Principles and Standards for School Mathematics - Wikipedia

    en.wikipedia.org/wiki/Principles_and_Standards...

    The Principles and Standards for School Mathematics was developed by the NCTM. The NCTM's stated intent was to improve mathematics education. The contents were based on surveys of existing curriculum materials, curricula and policies from many countries, educational research publications, and government agencies such as the U.S. National Science Foundation. [3]

  4. Formal system - Wikipedia

    en.wikipedia.org/wiki/Formal_system

    Formal language, which is a set of well-formed formulas, which are strings of symbols from an alphabet, formed by a formal grammar (consisting of production rules or formation rules). Deductive system, deductive apparatus, or proof system, which has rules of inference that take axioms and infers theorems, both of which are part of the formal ...

  5. Order of operations - Wikipedia

    en.wikipedia.org/wiki/Order_of_operations

    In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operations.

  6. Formal grammar - Wikipedia

    en.wikipedia.org/wiki/Formal_grammar

    A formal grammar describes which strings from an alphabet of a formal language are valid according to the language's syntax. A grammar does not describe the meaning of the strings or what can be done with them in whatever context—only their form. A formal grammar is defined as a set of production rules for such strings in a formal language.

  7. Chomsky hierarchy - Wikipedia

    en.wikipedia.org/wiki/Chomsky_hierarchy

    The rule is allowed if does not appear on the right side of any rule. The languages described by these grammars are exactly all languages that can be recognized by a linear bounded automaton (a nondeterministic Turing machine whose tape is bounded by a constant times the length of the input.)

  8. Well-formed formula - Wikipedia

    en.wikipedia.org/wiki/Well-formed_formula

    Using this grammar, the sequence of symbols (((p → q) ∧ (r → s)) ∨ (¬q ∧ ¬s)) is a formula, because it is grammatically correct. The sequence of symbols ((p → q)→(qq))p)) is not a formula, because it does not conform to the grammar. A complex formula may be difficult to read, owing to, for example, the proliferation of parentheses.

  9. Operator grammar - Wikipedia

    en.wikipedia.org/wiki/Operator_Grammar

    Operator grammar proposes that each human language is a self-organizing system in which both the syntactic and semantic properties of a word are established purely in relation to other words. Thus, no external system ( metalanguage ) is required to define the rules of a language.

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