1. MANAGING DATA MATHEMATICALLY

2. MANAGING DATA MATHEMATICALLY
DATA AS A
MATHEMATICAL OBJECT

3. MANAGING DATA MATHEMATICALLY
- THEORETICAL FOUNDATIONS
- PRACTICAL APPLICATIONS

4. PREVIEW THEORETICAL FOUNDATIONS EXTENTIONS TO SET THEORY
DATA AS A MATHEMATICAL OBJECT
TRANSACTIONS AS SET OPERATIONS

5. PREVIEW PRACTICAL APPLICATIONS ADAPT TRANSACTION TO DATA
ADAPT DATA TO TRANSACTION
LIVE DEMONSTRATION
ADAPTIVE DATA RESTRUCTURING
ON 1, 2, 4, 8, & 10 GB OF RAW DATA

6. ARPA - 1965 CONCOMP RESEARCH PROJECT DATA MANAGEABLE MATHEMATICALLY?
MATHEMATICALLY SOUND SYSTEMS
DATA MANAGEABLE MATHEMATICALLY?
MATHEMATICAL IDENTITY FOR DATA
MATHEMATICAL EXPRESSION FOR DATA BEHAVIOR

7. Identifying Characteristics of Data
Content
Represented Relationships
Structure
Form of Representation
Behavior
Response to Manipulation

11. Identifying Characteristics of Data
Content
Represented Relationships
Structure
Form of Representation
Behavior
Response to Manipulation

12. Two Remarks on Set Theory [Th. Skolem, Math. Scand. 5 (1957), 40-46]
2. The ordered n-tuples as sets
“ But in literature I have found no answer to the general question how to define the ordered n-tuple as a set.”
In conclusion: “I shall not pursue these considerations here, but only emphasize that it is still a problem how the ordered n-typle can be defined in the most suitable way.”
n-tuples behave badly, e.g.,
<a, b>  <a, c> = <a, a>

13. XST Definition of n-tuple
<a, b, c> = { a1, b2, c3}
<x, b, y> = { x1, b2, y3}
<a, b, c>  <x, b, y> = {b2}

19. Working Definitions Data A Representation of Relationships
Data Transaction Any Transformation of Data from One State to Another

20. Logical Data Physical Data Transaction Types
Representations friendly to humans
Used to specify enterprise transactions
Physical Data
Representations friendly to machines
Used to support execution of enterprise transactions
Transaction Types
Logical Data to Logical Data
Logical Data to Physical Data
Physical Data to Physical Data
Physical Data to Logical Data L P

21. Visual Summary E-DATA M-DATA Disjoint Environments Logical Enterprise
Specification
Brains
Execution
Bytes
M-DATA
Physical
Machine
Disjoint Environments

22. Mathematical View L2 L1 P1 P2 f a b F
Logical
Enterprise f L1 L2
Specification a b
Brains
Execution
Bytes P1 P2 F
Physical
Machine
XST: f (L1) = b ( F ( a ( L1) ) ) = L2

31. Information Access Strategies
Adapt Query to Data
Adapt Data to Query

39. Information Access Strategies
Adapt Query to Data
Adapt Data to Query