This page has a lot of pointers to ready made mathematical systems. If you are new here focus on the links to files with names that start "intro"( see Introduction below). For more (simpler) samples see: [ Search in index ]
As a test I have transcribed 30 years of hand written and typed notes. These are in files with names that start with 'logic' or 'math'.
Another test was to document MATHS using MATHS. The files with names that start 'notn' and 'types' contain this information.
For a "Vision statement" see the MATHS Manifesto: [ 10.manifesto.html ]
[ intro_characters.html ] , . . . [ intro_documentation.html ] , . . . [ intro_dynamics.html ] , . . . [ intro_ebnf.html ] , . . . [ intro_function.html ] , . . . [ intro_grammar.html ] , . . . [ intro_logic.html ] and [ logic_history.html ] , . . . [ intro_records.html ] , . . . [ intro_relation.html ] , . . . [ intro_sets.html ] , . . . [ intro_standard.html ] , . . . [ intro_strings.html ] , . . . [ intro_structure.html ]
How Mathematics differs from pure logic [ math_10_Intro.html ]
Also see [ Mathematics ] below.
[ Logic ] [ intro_logic.html ]
(introductions to MATHS):
[ intro_characters.html ]
[ intro_documentation.html ]
[ intro_ebnf.html ]
[ notn_10_Lexicon.html ]
(overview): of notation
[ math.syntax.html ]
[ notn_00_README.html ]
(names and expressions in MATHS): in MATHS
[ notn_11_Names.html ]
[ notn_12_Expressions.html ]
(intro):
[ intro_documentation.html ]
(syntax of MATHS):
[ notn_13_Docn_Syntax.html ]
(semantics of MATHS):
[ notn_14_Docn_Semantics.html ]
[ notn_15_Naming_Documentn.html ]
(structure):
[ notn_2_Structure.html ]
(UML model):
[ maths.mdl ]
(conveniences):
[ notn_3_Conveniences.html ]
(reuse):
(extension):
[ notn_4_Re_Use_.html ]
(formatting):
[ notn_5_Form.html ]
(tables):
[ notn_9_Tables.html ]
(algebras):
[ notn_6_Algebra.html ]
[ notn_7_OO_vs_Algebra.html ]
(reasoning):
[ notn_8_Evidence.html ]
A description of the notation: A lexicon [ notn_10_Lexicon.html ]
More details: [ notn_11_Names.html ] [ notn_12_Expressions.html ] [ notn_13_Docn_Syntax.html ] [ intro_ebnf.html ] [ notn_14_Docn_Semantics.html ] [ intro_grammar.html ] [ notn_15_Naming_Documentn.html ]
Specific Notations: [ intro_documentation.html ] [ notn_2_Structure.html ] [ notn_3_Conveniences.html ] [ notn_4_Re_Use_.html ] [ notn_5_Form.html ] [ notn_8_Evidence.html ]
Mathematical and Logical Rules: [ intro_standard.html ] [ notn_11_Names.html ] [ notn_12_Expressions.html ] [ intro_dynamics.html ] [ intro_function.html ] [ intro_logic.html ] [ intro_sets.html ] [ intro_relation.html ] [ intro_strings.html ] [ intro_structure.html ] [ notn_6_Algebra.html ] [ notn_7_OO_vs_Algebra.html ]
. . . . . . . . . ( end of section The Notation Used to Generate these Notes) <<Contents | End>>
. . . . . . . . . ( end of section MATHS) <<Contents | End>>
. . . . . . . . . ( end of section Theories that may be useful rather than traditional) <<Contents | End>>
. . . . . . . . . ( end of section Traditional Discrete Mathematics) <<Contents | End>>
. . . . . . . . . ( end of section Algebras with two operators) <<Contents | End>>
. . . . . . . . . ( end of section Algebras) <<Contents | End>>
. . . . . . . . . ( end of section Theories) <<Contents | End>>
. . . . . . . . . ( end of section Probability, Multisets, Bags, Fuzzyiness, Spectra) <<Contents | End>>
. . . . . . . . . ( end of section Topology) <<Contents | End>>
. . . . . . . . . ( end of section Logic) <<Contents | End>>
Also see [ fuzzy sets ] [ bags ]
. . . . . . . . . ( end of section Sets) <<Contents | End>>
[ logic_41_HomogenRelations.html ]
. . . . . . . . . ( end of section Relations) <<Contents | End>>
. . . . . . . . . ( end of section Functions) <<Contents | End>>
[ types.html ]
. . . . . . . . . ( end of section Types) <<Contents | End>>
. . . . . . . . . ( end of section Principles) <<Contents | End>>
. . . . . . . . . ( end of section More Advanced topics in Logic) <<Contents | End>>
. . . . . . . . . ( end of section Logic and Discrete Math On the Internet) <<Contents | End>>
Proofs follow a natural deduction style that start with assumptions ("Let") and continue to a consequence ("Close Let") and then discard the assumptions and deduce a conclusion. Look here [ Block Structure in logic_25_Proofs ] for more on the structure and rules.
The notation also allows you to create a new network of variables and constraints. A "Net" has a number of variables (including none) and a number of properties (including none) that connect variables. You can give them a name and then reuse them. The schema, formal system, or an elementary piece of documentation starts with "Net" and finishes "End of Net". For more, see [ notn_13_Docn_Syntax.html ] for these ways of defining and reusing pieces of logic and algebra in your documents. A quick example: a circle might be described by Net{radius:Positive Real, center:Point, area:=π*radius^2, ...}.
For a complete listing of pages in this part of my site by topic see [ home.html ]
For a more rigorous description of the standard notations see