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Mon Oct 8 10:20:04 PDT 2012

# 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 ]

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# Alternative Web Friendly Math Notations

[ mrwmath.htm ] ( Math ASCII Notation ).

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# 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 ]

# 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.