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Mon May 5 10:45:03 PDT 2008

Contents

    Index to the MATHS site

      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. The next idea was to give symbolic names to mathematical and logical systems and to link these together. 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 brouse the topics by subject at:

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

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

      Changes in 2008

      Latest -- [ math_92_Metric_Spaces.html ] [ math_5_Object_Theory.html ] [ logic_10_PC_LPC.html ] [ intro_records.html ] (optional and multiple parts) [ intro_objects.html ] [ intro_copywrite.html ] [ notn_14_Docn_Semantics.html ] [ notn_13_Docn_Syntax.html ] [ logic_25_Proofs.html ] [ intro_function.html ] [ math_95_Function_Spaces.html ] [ math_45_Three_Operators.html ] (Trying to understand Quantum Theory....) -- Oldest

      Changes in 2007

       Latest -- [ logic_10_PC_LPC.html ] (linking MATHS to Term Logic and Aristotlean Logic) [ math_21_Order.html ] [ logic_20_Proofs100.html ] [ math_81_Probabillity.html ] (Bayesian Probability matches abductive reasoning), [ intro_objects.html ] (exploring adding OO dynamics to Nets), [ logic_30_Sets.html ] [ logic_2_Proofs.html ] [ intro_ebnf.html ] [ math_21_Order.html ] [ logic_20_Proofs100.html ] -- Oldest

      Changes in 2006

       Latest -- [ notn_13_Docn_Syntax.html ] [ intro_characters.html ] [ math.lexicon.html ] [ math.syntax.html ] (changing notation to separate formula from bullet points/paragraphs), [ logic_27_Tableaux.html ] (Semantic tableax), [ logic_2_Proofs.html ] is now refactored into [ logic_20_Proofs100.html ] and [ logic_25_Proofs.html ] -- Oldest

      Changes in 2005

       [ logic_2_Proofs.html ] (added more on semantic tableaux)

      Changes in 2004


      (2004): Latest -- [ logic_30_Sets.html ] [ logic_8_Natural_Language.html ] [ notn_14_Docn_Semantics.html ] [ notn_12_Expressions.html ] [ notn_16_Classification.html ] [ notn_13_Docn_Syntax.html ] [ notn_3_Conveniences.html ] [ notn_2_Structure.html ] [ notn_11_Names.html ] [ math_77_Enumerations.html ] [ math_25_Categories.html ] -- Oldest

      Changes in 2003
      (2003): -- Latest [ intro_standard.html ] [ math_73_Process_algebra.html ] [ math_82_MultiSets_and_Bags.html ] [ math_83_Fuzzy_Sets.html ] [ 00_overview.html ] [ math_84_Spectra.html ] [ notn_9_Tables.html ] [ logic_9_Modalities.html ] [ logic_41_HomogenRelations.html ] -- Oldest

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

    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 = Net{radius:Positive Real, center:Point}.

    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