Course Intermediate

Modeling and Representation

By the end of this course

Counts how many distinct systems a representation collapses onto the same symbol
Distinguishes the executions a behavioral representation covers from those it does not
Counts separately the constraint dropped and the decision invented on the way from a conceptual model to a physical schema

Start course

Structural Diagrams

The information elements a notation family carries, the ambiguity the relationship type and multiplicity symbols take on in class notation, and the partitions the component and deployment notations distinguish.

01 Notation Family and Loss A representation is a projection of a system that discards information: a structural representation that writes 20 of the 31 facts of a five-association maintenance workshop collapses 2048 distinct systems onto a single diagram, and the 11 discarded fields cannot be recovered from the representation.
02 Class Diagrams The share of the ambiguity that relationship-type and multiplicity symbols take: 20 symbols leave 2048 systems, 25 leave 64, 31 leave 1; a binary field's symbol takes exactly one bit, while a three-valued field's symbol takes 1.58.
03 Component and Deployment Diagrams The same six classes fall into 203 distinct runtime partitions: a five-symbol component representation reduces 540 class distributions to 20, never states the internal-association load, and fixes the remote-link count only once deployment is written.

Behavioral Diagrams

Counting what the use case, sequence, activity, and state machine notations carry, what they omit on purpose, and where they under-accept or over-accept.

01 Use Case Diagrams Counting separately what the actor, scenario, and system-boundary notation carries and what it drops: seven internal steps omitted on purpose, two links dropped by accident, and 512 systems collapsing into the same diagram.
02 Sequence Diagrams Measuring the trace coverage of a diagram that shows message exchange along a time axis: 0.0417 for one of 24 traces, 0.1667 for four, 1.0 with alternative and loop fragments — and 24 cases of over-approximation if the loop bound is left unwritten.
03 Activity Diagrams Counting, with topological sort, how many total orderings the diagram accepts when it shows a workflow through prerequisites: ten tasks, thirteen prerequisites, 168 total orderings, a six-layer critical path, and where adding one prerequisite sends the 168.
04 State Machine Diagrams Counting the under-approximation and over-approximation of the state, transition, and guard-condition notation separately: a four-state machine rejects two real sequences, and adding two transitions brings the rejected count to zero while raising over-approximation from 2 to 26.

Data Modeling

What the entity-relationship model states, the constraints dropped in the shift between three abstraction levels, and the decisions a physical schema invents that the model never states.

01 The Entity–Relationship Model The conceptual model of a maintenance shop states 26 facts: 5 entities, 12 attributes, 4 relationships, 5 constraints. When cardinality is written but participation is not, 1,048,576 systems collapse onto the same notation.
02 Conceptual, Logical, and Physical Model When the same 26 facts are converted into a relational structure, the table count rises from 5 to 7, 13 fields appear that are never named in the model, and 2 of the 5 constraints drop; the structural reason for the two that drop is shown by exhaustive count.
03 From Model to Schema For seven tables and twenty-five fields, 100 field decisions and 14 table decisions are given: a total of 114, 4.4 times the 26 facts the conceptual model states. Every decision the model does not state is a decision someone makes that does not appear in the model.