. How to use the MATHS site MATHS is a simple way of recording mathematical and logical systems on a computer. I can generate web pages from it. This site is a kind of hypertext encyclopedia of logic and mathematics. Some I've found to be useful and others are used in the texts and research in computer science and software engineering. Use it as a reference or as the basis for your own work. If you do quote from this site include a link or reference to the source and let me know by Email. If I know you are linking to part of the site I can leave the link in place for you. 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: .See http://www/dick/samples/index.html#Search .Open MATHS .Open Background . History I developed this notation to be a usable way of documenting and reasoning about complex discrete systems. It is designed to workable on any ASCII based system and to be translated into different forms for display and browsing. It is a formal language with room for informality. It is designed to allow reusable and distributed formal (and informal) documentation. As a result it is a hypertext system. 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: .See http://www/dick/monograph/10.manifesto.html . Introduction .See http://www.csci.csusb.edu/dick/maths/intro_README.html , . . . .See http://www.csci.csusb.edu/dick/maths/intro_note.html , . . . .See http://www.csci.csusb.edu/dick/maths/intro_copyright.html , and the following introductory topics: .See http://www.csci.csusb.edu/dick/maths/intro_characters.html , . . . .See http://www.csci.csusb.edu/dick/maths/intro_documentation.html , . . . .See http://www.csci.csusb.edu/dick/maths/intro_dynamics.html , . . . .See http://www.csci.csusb.edu/dick/maths/intro_ebnf.html , . . . .See http://www.csci.csusb.edu/dick/maths/intro_function.html , . . . .See http://www.csci.csusb.edu/dick/maths/intro_grammar.html , . . . .See http://www.csci.csusb.edu/dick/maths/intro_logic.html and .See http://www.csci.csusb.edu/dick/maths/logic_history.html , . . . .See http://www.csci.csusb.edu/dick/maths/intro_records.html , . . . .See http://www.csci.csusb.edu/dick/maths/intro_relation.html , . . . .See http://www.csci.csusb.edu/dick/maths/intro_sets.html , . . . .See http://www.csci.csusb.edu/dick/maths/intro_standard.html , . . . .See http://www.csci.csusb.edu/dick/maths/intro_strings.html , . . . .See http://www.csci.csusb.edu/dick/maths/intro_structure.html How Mathematics differs from pure logic .See http://www.csci.csusb.edu/dick/maths/math_10_Intro.html Also see .See Mathematics below. . STANDARD The Standard set of assumptions and notations .See http://www.csci.csusb.edu/dick/maths/intro_standard.html and .See http://www.csci.csusb.edu/dick/maths/math_11_STANDARD.html .See Logic .See http://www.csci.csusb.edu/dick/maths/intro_logic.html .Open The Notation Used to Generate these Notes . Syntax In essence a document is divided into a hierarchical outline with sections, subsections, paragraphs and lines. Sections have headlines that can act as identifiers. Paragraphs are eith informal comments, definitions, assumptions or proved results. The system is designed to make the searching and translation of the documents as easy as possible. (introductions to MATHS): .See http://www.csci.csusb.edu/dick/maths/intro_characters.html .See http://www/dick/maths/intro_documentation.html .See http://www.csci.csusb.edu/dick/maths/intro_ebnf.html .See http://www.csci.csusb.edu/dick/maths/notn_10_Lexicon.html (overview): of notation .See http://www.csci.csusb.edu/dick/samples/math.syntax.html .See http://www.csci.csusb.edu/dick/maths/notn_00_README.html (names and expressions in MATHS): in MATHS .See http://www.csci.csusb.edu/dick/maths/notn_11_Names.html .See http://www.csci.csusb.edu/dick/maths/notn_12_Expressions.html (intro): .See http://www.csci.csusb.edu/dick/maths/intro_documentation.html (syntax of MATHS): .See http://www.csci.csusb.edu/dick/maths/notn_13_Docn_Syntax.html (semantics of MATHS): .See http://www.csci.csusb.edu/dick/maths/notn_14_Docn_Semantics.html .See http://www.csci.csusb.edu/dick/maths/notn_15_Naming_Documentn.html (structure): .See http://www.csci.csusb.edu/dick/maths/notn_2_Structure.html (UML model): .See http://www.csci.csusb.edu/dick/maths/maths.mdl (conveniences): .See http://www.csci.csusb.edu/dick/maths/notn_3_Conveniences.html (reuse): (extension): .See http://www.csci.csusb.edu/dick/maths/notn_4_Re_Use_.html (formatting): .See http://www.csci.csusb.edu/dick/maths/notn_5_Form.html (tables): .See http://www.csci.csusb.edu/dick/maths/notn_9_Tables.html (algebras): .See http://www.csci.csusb.edu/dick/maths/notn_6_Algebra.html .See http://www.csci.csusb.edu/dick/maths/notn_7_OO_vs_Algebra.html (reasoning): .See http://www.csci.csusb.edu/dick/maths/notn_8_Evidence.html . Notation Introduction to the notation: .See http://www.csci.csusb.edu/dick/maths/intro_characters.html .See http://www/dick/maths/intro_documentation.html A description of the notation: A lexicon .See http://www/dick/maths/notn_10_Lexicon.html More details: .See http://www/dick/maths/notn_11_Names.html .See http://www/dick/maths/notn_12_Expressions.html .See http://www/dick/maths/notn_13_Docn_Syntax.html .See http://www.csci.csusb.edu/dick/maths/intro_ebnf.html .See http://www/dick/maths/notn_14_Docn_Semantics.html .See http://www.csci.csusb.edu/dick/maths/intro_grammar.html .See http://www/dick/maths/notn_15_Naming_Documentn.html Specific Notations: .See http://www/dick/maths/intro_documentation.html .See http://www/dick/maths/notn_2_Structure.html .See http://www/dick/maths/notn_3_Conveniences.html .See http://www/dick/maths/notn_4_Re_Use_.html .See http://www/dick/maths/notn_5_Form.html .See http://www/dick/maths/notn_8_Evidence.html Mathematical and Logical Rules: .See http://www.csci.csusb.edu/dick/maths/intro_standard.html .See http://www/dick/maths/notn_11_Names.html .See http://www/dick/maths/notn_12_Expressions.html .See http://www.csci.csusb.edu/dick/maths/intro_dynamics.html .See http://www.csci.csusb.edu/dick/maths/intro_function.html .See http://www.csci.csusb.edu/dick/maths/intro_logic.html .See http://www.csci.csusb.edu/dick/maths/intro_sets.html .See http://www.csci.csusb.edu/dick/maths/intro_relation.html .See http://www.csci.csusb.edu/dick/maths/intro_strings.html .See http://www.csci.csusb.edu/dick/maths/intro_structure.html .See http://www/dick/maths/notn_6_Algebra.html .See http://www/dick/maths/notn_7_OO_vs_Algebra.html .Close The Notation Used to Generate these Notes .Close MATHS .Open Mathematics .Open Theories that may be useful rather than traditional . Using Numbers to represent physical dimensions (dimensions): .See http://www.csci.csusb.edu/dick/maths/math_49_Dimensioned_numbers.html . A mathematical theory of record structures and data bases (data structure): .See http://www.csci.csusb.edu/dick/maths/intro_structure.html .See http://www.csci.csusb.edu/dick/maths/math_12_Structure.html (data bases): .See http://www.csci.csusb.edu/dick/maths/math_13_Data_Bases.html . Models of dynamic systems .See http://www.csci.csusb.edu/dick/maths/intro_dynamics.html (dynamical logic): .See http://www.csci.csusb.edu/dick/maths/math_14_Dynamics.html (dynamic systems): .See http://www/dick/maths/math_71_Auto...Systems.html .See http://www/dick/maths/math_76_Concurency.html (unary algebra): .See http://www.csci.csusb.edu/dick/maths/math_15_Unary_Algebra.html (enumerations): .See http://www.csci.csusb.edu/dick/maths/math_77_Enumerations.html .Close Theories that may be useful rather than traditional .Open Traditional Discrete Mathematics . Posets A model of collections of things that can often be put in order. (order): (posets): .See http://www.csci.csusb.edu/dick/maths/math_21_Order.html (cpos): .See http://www.csci.csusb.edu/dick/maths/math_24_Domains.html . Graphs, Flow diagrams, Categories (digraphs): .See http://www.csci.csusb.edu/dick/maths/math_22_graphs.html (flow diagrams): .See http://www.csci.csusb.edu/dick/maths/math_23_Flow_Diagrams.html (category theory): .See http://www.csci.csusb.edu/dick/maths/math_25_Categories.html .Close Traditional Discrete Mathematics .Open Algebras . Notational Abuses .See http://www.csci.csusb.edu/dick/maths/notn_6_Algebra.html . Algebras with one operator Common ideas: .See http://www.csci.csusb.edu/dick/maths/math_31_One_Associative_Op.html . Semigroups/Monoids/Groups (semigroups): .See http://www.csci.csusb.edu/dick/maths/math_32_Semigroups.html (monoids): .See http://www.csci.csusb.edu/dick/maths/math_33_Monoids.html (groups): .See http://www.csci.csusb.edu/dick/maths/math_34_Groups.html .Open Algebras with two operators . Rings (Rings): .See http://www.csci.csusb.edu/dick/maths/math_41_Two_Operators.html . Numbers (number theory): .See http://www.csci.csusb.edu/dick/maths/math_42_Numbers.html . General .See http://www.csci.csusb.edu/dick/maths/math_43_Algebras.html .Close Algebras with two operators . Algebras with More than two operators (calculus): .See http://www.csci.csusb.edu/dick/maths/math_44_Formal_Calculus.html (high school algebra): .See http://www.csci.csusb.edu/dick/maths/math_45_Three_Operators.html .Close Algebras .Open Theories . A theory of Objects (genesys): .See http://www.csci.csusb.edu/dick/maths/math_5_Object_Theory.html . Strings, Grammars, Languages, MetaLanguages, Superstrings .See http://www.csci.csusb.edu/dick/maths/intro_strings.html .See http://www.csci.csusb.edu/dick/maths/intro_grammar.html (strings in theory): .See http://www.csci.csusb.edu/dick/maths/math_61_String_Theories.html (strings): .See http://www.csci.csusb.edu/dick/maths/math_62_Strings.html (grammar theory): .See http://www.csci.csusb.edu/dick/maths/math_63_Languages.html (metalinguistics): .See http://www.csci.csusb.edu/dick/maths/math_64_Meta_Macros.html .See http://www.csci.csusb.edu/dick/maths/math_65_Meta_Linguistics.html (superstrings): .See http://www.csci.csusb.edu/dick/maths/math_66_SuperStrings.html . Systems, Automata, Games, Programs (automata): (systems theory): .See http://www.csci.csusb.edu/dick/maths/math_71_Auto...Systems.html (system algebra): .See http://www.csci.csusb.edu/dick/maths/math_72_Systems_Algebra.html (process algebra): .See http://www.csci.csusb.edu/dick/maths/math_73_Process_algebra.html (games): .See http://www.csci.csusb.edu/dick/maths/math_74_Games.html (programs): .See http://www.csci.csusb.edu/dick/maths/math_75_Programs.html (concurrent systems): .See http://www.csci.csusb.edu/dick/maths/math_76_Concurency.html .Close Theories .Open Probability, Multisets, Bags, Fuzzyiness, Spectra (probability): .See http://www.csci.csusb.edu/dick/maths/math_81_Probabillity.html (bags): .See http://www.csci.csusb.edu/dick/maths/math_82_MultiSets_and_Bags.html (fuzzy sets): .See http://www.csci.csusb.edu/dick/maths/math_83_Fuzzy_Sets.html (spectra): .See http://www.csci.csusb.edu/dick/maths/math_84_Spectra.html .Close Probability, Multisets, Bags, Fuzzyiness, Spectra .Open Topology . The theories of space (set theoretic topology): .See http://www.csci.csusb.edu/dick/maths/math_91_Topology.html (metric spaces): .See http://www.csci.csusb.edu/dick/maths/math_92_Metric_Spaces.html . Special Spaces - Graphic, Metric, etc .See http://www.csci.csusb.edu/dick/maths/math_93_Graphics.html (ndimensional calculus): .See http://www.csci.csusb.edu/dick/maths/math_94_Calculus.html (function spaces): .See http://www.csci.csusb.edu/dick/maths/math_95_Function_Spaces.html .Close Topology .Close .Open Principles .Open Logic (logic101): .See http://www.csci.csusb.edu/dick/maths/intro_logic.html .See http://www.csci.csusb.edu/dick/maths/logic_0_Intro.html (predicates): .See http://www.csci.csusb.edu/dick/maths/logic_10_PC_LPC.html (equality): .See http://www.csci.csusb.edu/dick/maths/logic_11_Equality_etc.html (proofs): .See http://www.csci.csusb.edu/dick/maths/logic_2_Proofs.html .See http://www.csci.csusb.edu/dick/maths/logic_20_Proofs100.html .See http://www.csci.csusb.edu/dick/maths/logic_25_Proofs.html .See http://www.csci.csusb.edu/dick/maths/logic_27_Tableaux.html (modes): .See http://www.csci.csusb.edu/dick/maths/logic_9_Modalities.html .Close Logic .Open Sets .See http://www.csci.csusb.edu/dick/maths/intro_sets.html (sets): .See http://www.csci.csusb.edu/dick/maths/logic_30_Sets.html (families of sets): .See http://www.csci.csusb.edu/dick/maths/logic_31_Families_of_Sets.html (set theory): .See http://www.csci.csusb.edu/dick/maths/logic_32_Set_Theory.html Also see .See fuzzy sets .See bags .Close Sets .Open Relations .See http://www.csci.csusb.edu/dick/maths/intro_relation.html .See http://www.csci.csusb.edu/dick/maths/logic_40_Relations.html .See http://www.csci.csusb.edu/dick/maths/logic_41_HomogenRelations.html .See http://www.csci.csusb.edu/dick/maths/logic_42_Properties_of_Relation.html .See http://www.csci.csusb.edu/dick/maths/logic_44_n-aryrelations.html .Close Relations .Open Functions .See http://www.csci.csusb.edu/dick/maths/intro_function.html .See http://www.csci.csusb.edu/dick/maths/logic_5_Maps.html .Close Functions .Open Types .See http://www.csci.csusb.edu/dick/maths/intro_records.html .See http://www.csci.csusb.edu/dick/maths/types.html .See http://www.csci.csusb.edu/dick/maths/math_77_Enumerations.html .Close Types .Close Principles .Open More Advanced topics in Logic .See http://www.csci.csusb.edu/dick/maths/intro_standard.html .See http://www.csci.csusb.edu/dick/maths/math_11_STANDARD.html .See http://www.csci.csusb.edu/dick/maths/intro_strings.html .See http://www.csci.csusb.edu/dick/maths/logic_6_Numbers..Strings.html .See http://www.csci.csusb.edu/dick/maths/logic_7_Semantics.html .See http://www.csci.csusb.edu/dick/maths/logic_8_Natural_Language.html .Close More Advanced topics in Logic .Close .Open Logic and Discrete Math On the Internet . Local Math Page .See http://www.math.csusb.edu/cgi-bin/cgiwrap/notes/contents.cgi . Description Logics .See http://www.ida.liu.se/labs/iislab/people/patla/DL/index.html .Close Logic and Discrete Math On the Internet .Close