COMMENT ⊗   VALID 00006 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	.DEVICE XGP
C00003 00003	.COMMENT 3 tasks
C00004 00004	.COMMENT Math thy
C00005 00005	.COMMENT 3 tasks
C00006 00006	.COMMENT Facets
C00009 ENDMK
C⊗;
.DEVICE XGP
.COMMENT !XGPCOMMANDS←"/TMAR=50/PMAR=2100/BMAR=50";

.FONT 1 "BASB30"
.FONT 2 "BDR66"
.FONT 4  "BDI40"
.FONT 7  "BDR40"
.FONT 8 "BDR25"
.FONT 9 "GRFX35"
.TURN ON "↑α[]↓_π{"
.TURN ON "⊗" FOR "%"
.TABBREAK
.ODDLEFTBORDER ← EVENLEFTBORDER ← 1000
.PAGE FRAME 54 HIGH 91 WIDE
.AREA TEXT LINES 1 TO 53
.DOUBLE SPACE
.PREFACE 2
.NOFILL
.PREFACE 1
.!XGPLFTMAR←100
.MACRO B ⊂ BEGIN NOFILL SELECT 9 INDENT 0 GROUP PREFACE 0 MILLS TURN OFF "{↑↓}[]α" ⊃
.MACRO E ⊂ APART END ⊃
.NEXT PAGE
.INDENT 0
.SELECT 1
.COMMENT 3 tasks;
.GROUP SKIP 4
.ONCE CENTER SELECT 2
↓_DISCOVERY  AS_↓
.ONCE CENTER SELECT 2
↓_HEURISTIC  SEARCH_↓

.BEGIN SELECT 2 PREFACE 2 INDENT 20 SKIP 2

(1)  Starting knowledge
(2)  Legal operators
(3)  Heuristic strategies

.END
.SKIP TO COLUMN 1
.COMMENT Math thy;
.ONCE CENTER SELECT 2
↓_Mathematical Theory_↓

.BEGIN SELECT 2 PREFACE 0  TURN ON "→"

.GROUP SKIP 6


.ONCE CENTER
DEFINITIONS and THEOREMS



  Axioms and Postulates
	  Operators →FOUNDATION
	Undefined objects
.END
.SKIP TO COLUMN 1
.COMMENT 3 tasks;
.GROUP SKIP 4
.ONCE CENTER SELECT 2
↓_MATHEMATICAL DISCOVERY_↓
.ONCE CENTER SELECT 2
↓_as HEURISTIC SEARCH_↓

.BEGIN SELECT 2 PREFACE 2 INDENT 20 SKIP 2

(1)  Starting knowledge about math
(2)  Legal operators
(3)  Heuristic strategies

.END
.SKIP TO COLUMN 1
.COMMENT Facets;
.ONCE CENTER SELECT 2
↓_Facets of a Concept_↓

.BEGIN SELECT 2 PREFACE 0

Characterizations
	⊗7Name(s)⊗*  
	⊗7Definitions ⊗*  
	⊗7Algorithms ⊗* 
	⊗7Domain/range⊗*
	⊗7Intuitions: abstract representations⊗*

Ties to other concepts
	⊗7Specializations⊗*
	⊗7Generalizations⊗*
	⊗7Examples⊗*
	⊗7Operations one can do to this concept⊗*
	⊗7Conjectures/theorems involving this concept⊗*
	⊗7Analogies⊗*

Heuristics
	⊗7Worth: Why this concept is worth naming⊗*
	⊗7Interest: When an instance of it is (un)interesting⊗*
	⊗7Fillin: Hints for filling in parts of instances⊗*
	⊗7Suggest new activities for AM to consider⊗*
	⊗7Check: things to watch out for⊗*
.END
.SKIP TO COLUMN 1
.COMMENT Facets: COMPOSE;
.ONCE CENTER SELECT 2
↓_Facets of  "COMPOSE"_↓

.BEGIN SELECT 2 PREFACE 0

Characterizations
	⊗7Name(s): Compose ⊗*  
	⊗7Definitions: recursive, opaque, wffs⊗*  
	⊗7Algorithms: opaque, transparent, destructive ⊗* 
	⊗7Domain/range: Relations x Relations → Relations⊗*
	⊗7Intuitions: refiring arrows, time sequence⊗*

Ties to other concepts
	⊗7Specializations: Compose f with itself⊗*
	⊗7Generalizations: Relation⊗*
	⊗7Examples: (Intersect, Complement) → Set-difference⊗*
	⊗7Conjec: (AoB)oC ≡ Ao(BoC)⊗*
	⊗7Analogies: multiplying two matrices⊗*

Heuristics
	⊗7Worth: Primitive. Creates new active Concepts⊗*
	⊗7Interest: Domain=Range; both args are interesting⊗*
	⊗7Fillin: D/R are Domain(arg1) and Range(arg2)⊗*
	⊗7Sugg: Check AoB for properties which A or B have⊗*
	⊗7Check: Domain(arg2) should intersect Range(arg1)⊗*
.END
.SKIP TO COLUMN 1