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Mon Oct 8 10:20:04 PDT 2012

Contents


    Index to the MATHS site

      Plans and PBIs

      [ todo.html ]

      Recent Changes

      [ blog.html ]

      Start Here

      MATHS is an attempt to free mathematical notation from the tyrany of blackboards and dead trees. I'm searching for a way to record ideas quickly, cheaply, simply, on simple devices, and then calculate with them. MATHS shows my current best practice. It is a work in progress... sometimes in regress.

      A key discovery in this search was the power of hypertext links. They let you connect a symbol to its meaning. They can connect a theorem to its proof, or a premise to its statement. The next idea was to give symbolic names to mathematical and logical systems and to link these together. So a short name for a piece of mathematics can be linked to a full description of it.

      As a result any set of assumptions and notation can be linked into another document. I hoped that this would be useful. It lets you reuse earlier ideas. A side effect has been the generation of many pages that document existing mathematics and logical systems.

      I'd like them to be used.

      How to use this site

      For a quick glance at a cheatsheet of abbreviations see [ intro_standard.html ] which lists some of the ways of making formulas.

      Here are some suggestions for using this site: [ How to use the maths site in home ]

      You can seach the site for any defined term, theorem, formula, declaration, etc etc:

    1. search::= See http://cse.csusb.edu/dick/maths/lookup.php

      Or you can brouse the topics by subject at:

    2. listing::= See http://cse.csusb.edu/dick/maths/home.html

      You can submit suggestions of material to be added:

    3. suggestions::= See http://cse.csusb.edu/dick/maths/hole.html and your work, if accepted will be published and creditted to you. Regular contributors will be invited to become editors, in time.

      Why

      The following explains why this site exists: [ 10_manifesto.mth ] (source) [ 10_manifesto.html ] (HTML) and [ rjb9Xb.discrete.html ]

    . . . . . . . . . ( end of section Index to the MATHS site) <<Contents | End>>

    Alternative Web Friendly Math Notations

      [ mrwmath.htm ] ( Math ASCII Notation ).

    . . . . . . . . . ( end of section Alternative Web Friendly Math Notations) <<Contents | End>>

    More on MATHS

      Samples

      [ http://cse.csusb.edu/dick/samples/ ]

      Papers

      [ rjb93a.xbnf.html ] [ rjb96x.xbnf.html ] [ rjb9Xa.lift.html ] [ rjb95a.semantics.html ] [ rjb95x.semantics.html ] [ rjb9x.Relations.vs.Programs.html ] [ rjb9x.Timed.Relations.html ] [ rjb96b.mth2tex.html ]

      Monograph

      [ http://cse.csusb.edu/dick/monograph/ ]

    . . . . . . . . . ( end of section More on MATHS) <<Contents | End>>

    Quick Listing of Pages by File

    [ 00_overview.html ] [ 10_manifesto.html ] [ 10.manifesto.html ] [ blog.html ] [ comment.html ] [ css.html ] [ dictionary.html ] [ faq.html ] [ getmth.html ] [ holefaq.html ] [ hole.html ] [ home.html ] [ index.html ]

    [ intro_characters.html ] [ intro_copyright.html ] [ intro_copywrite.html ] [ intro_documentation.html ] [ intro_dynamics.html ] [ intro_ebnf.html ] [ intro_function.html ] [ intro_grammar.html ] [ intro_logic.html ] [ intro_note.html ] [ intro_objects.html ] [ intro_README.html ] [ intro_records.html ] [ intro_relation.html ] [ intro_sets.html ] [ intro_standard.html ] [ intro_strings.html ] [ intro_structure.html ] [ intro_structures.html ]

    [ lexicon.html ]

    [ logic_0_Intro.html ] [ logic_10_PC_LPC.html ] [ logic_11_Equality_etc.html ] [ logic_20_Proofs100.html ] [ logic_25_Proofs.html ] [ logic_27_Tableaux.html ] [ logic_2_Proofs.html ] [ logic_30_Sets.html ] [ logic_31_Families_of_Sets.html ] [ logic_32_Set_Theory.html ] [ logic_40_Relations.html ] [ logic_41_HomogenRelations.html ] [ logic_42_Properties_of_Relation.html ] [ logic_44_n-aryrelations.html ] [ logic_5_Maps.html ] [ logic_6_Numbers..Strings.html ] [ logic_7_Semantics.html ] [ logic_8_Natural_Language.html ] [ logic_9_Modalities.html ] [ logic_history.html ]

    [ math_10_Intro.html ] [ math_11_STANDARD.html ] [ math_12_Structure.html ] [ math_13_Data_Bases.html ] [ math_14_Dynamics.html ] [ math_15_Unary_Algebra.html ] [ math_21_Order.html ] [ math_22_graphs.html ] [ math_22_Graphs.notable.html ] [ math_23_Flow_Diagrams.html ] [ math_23.html ] [ math_24_Domains.html ] [ math_25_Categories.html ] [ math_31_One_Associative_Op.html ] [ math_32_Semigroups.html ] [ math_33_Monoids.html ] [ math_34_Groups.html ] [ math_41_Two_Operators.html ] [ math_42_Numbers.html ] [ math_43_Algebras.html ] [ math_44_Formal_Calculus.html ] [ math_45_Three_Operators.html ] [ math_49_Dimensioned_numbers.html ] [ math_5_Object_Theory.html ] [ math_61_String_Theories.html ] [ math_62_Strings.html ] [ math_63_Languages.html ] [ math_64_Meta_Macros.html ] [ math_65_Meta_Linguistics.html ] [ math_66_SuperStrings.html ] [ math_71_Auto...Systems.html ] [ math_72_Systems_Algebra.html ] [ math_73_Process_algebra.html ] [ math_74_Games.html ] [ math_75_Programs.html ] [ math_76_Concurency.html ] [ math_77_Enumerations.html ] [ math_81_Probabillity.html ] [ math_82_MultiSets_and_Bags.html ] [ math_83_Fuzzy_Sets.html ] [ math_83_Spectra.html ] [ math_84_Spectra.html ] [ math_85_Statistics.html ] [ math_91_Topology.html ] [ math_92_Metric_Spaces.html ] [ math_93_Graphics.html ] [ math_94_Calculus.html ] [ math_95_Function_Spaces.html ] [ math.lexicon.html ] [ math.syntax.html ]

    [ notn_00_README.html ] [ notn_10_Lexicon.html ] [ notn_11_Names.html ] [ notn_12_Expressions.html ] [ notn_13_Docn_Syntax.html ] [ notn_14_Docn_Semantics.html ] [ notn_15_Naming_Documentn.html ] [ notn_16_Classification.html ] [ notn_2_Structure.html ] [ notn_3_Conveniences.html ] [ notn_4_Re_Use_.html ] [ notn_5_Form.html ] [ notn_6_Algebra.html ] [ notn_7_OO_vs_Algebra.html ] [ notn_8_Evidence.html ] [ notn_9_Tables.html ] [ notn_dlex.d.html ]

    [ standard.header.sh ] [ standard.include.sh ] [ standard.include.html ] [ standard.include.mth ] [ standard.include.txt ] [ standard.style.css ]

    [ todo.html ]

    [ types.html ]

    [ welcome.html ]

    Notes on MATHS Notation

    Special characters are defined in [ intro_characters.html ] that also outlines the syntax of expressions and a document.

    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 ]

    Notes on the Underlying Logic of MATHS

    The notation used here is a formal language with syntax and a semantics described using traditional formal logic [ logic_0_Intro.html ] plus sets, functions, relations, and other mathematical extensions.

    For a more rigorous description of the standard notations see

  1. STANDARD::= See http://www.csci.csusb.edu/dick/maths/math_11_STANDARD.html

    Glossary

  2. above::reason="I'm too lazy to work out which of the above statements I need here", often the last 3 or 4 statements. The previous and previous but one statments are shown as (-1) and (-2).
  3. given::reason="I've been told that...", used to describe a problem.
  4. given::variable="I'll be given a value or object like this...", used to describe a problem.
  5. goal::theorem="The result I'm trying to prove right now".
  6. goal::variable="The value or object I'm trying to find or construct".
  7. let::reason="For the sake of argument let...", introduces a temporary hypothesis that survives until the end of the surrounding "Let...Close.Let" block or Case.
  8. hyp::reason="I assumed this in my last Let/Case/Po/...".
  9. QED::conclusion="Quite Easily Done" or "Quod Erat Demonstrandum", indicates that you have proved what you wanted to prove.
  10. QEF::conclusion="Quite Easily Faked", -- indicate that you have proved that the object you constructed fitted the goal you were given.
  11. RAA::conclusion="Reducto Ad Absurdum". This allows you to discard the last assumption (let) that you introduced.

End