Learning Graph for Inverting the Impossible
Open Learning Graph Viewer Fullscreen
This section contains the learning graph for Inverting the Impossible: Systematic Thinking for Innovation Radiation — a course on Matrix Morphology developed by David Quimby.
A learning graph is a graph of concepts used in this course. Each concept is represented by a node in a network graph. Concepts are connected by directed edges that indicate what concepts each node depends on before that concept can be understood by the student.
A learning graph is the foundational data structure for intelligent textbooks that can recommend learning paths. A learning graph is like a roadmap of concepts to help students arrive at their learning goals.
At the left of the learning graph are prerequisite or foundational concepts. They have no outbound edges — only inbound edges for other concepts that depend on them. At the far right we have the most advanced concepts in the course. To master these concepts you must understand all the concepts that they point to.
Course Description
We use the Course Description as the source document for the concepts included in this course. The course description uses the 2001 Bloom taxonomy to order learning objectives.
List of Concepts
We use generative AI to convert the course description into a Concept List. Each concept is in the form of a short Title Case label with most labels under 32 characters long. This course contains 200 concepts organized across 12 thematic categories.
Concept Dependency List
We use generative AI to create a Directed Acyclic Graph (DAG). DAGs do not have cycles where concepts depend on themselves. We provide the DAG in two formats. One is a CSV file and the other format is a JSON file that uses the vis-network JavaScript library format. The vis-network format uses nodes, edges, and metadata elements with edges containing from and to properties. This makes it easy to view and edit the learning graph using an editor built with the vis-network tools.
This graph contains 200 nodes and 348 edges.
Analysis and Documentation
Course Description Quality Assessment
This report rates the overall quality of the course description for the purpose of generating a learning graph.
- Course description fields and content depth analysis
- Validates course description has sufficient depth for generating 200 concepts
- Identifies content gaps and strengths
- Bloom's Taxonomy level coverage
View the Course Description Quality Assessment — Score: 100/100 🟢
Learning Graph Quality Validation
This report gives you an overall assessment of the quality of the learning graph. It uses graph algorithms to look for specific quality patterns in the graph.
- Graph structure validation — all concepts are connected
- DAG validation (no cycles detected)
- Foundational concepts: 26 entry points
- Indegree distribution analysis
- Longest dependency chains (max: 14)
- Connectivity: 100% of nodes connected to the main cluster
View the Learning Graph Quality Validation
Concept Taxonomy
In order to see patterns in the learning graph, it is useful to assign colors to each concept based on the concept type. We use generative AI to create about a dozen categories for our concepts and then place each concept into a single primary classifier.
This course uses 12 taxonomy categories ranging from Foundations and Context (SteelBlue) to Learning and Assessment (DeepPink), with no category exceeding 13% of all concepts.
Taxonomy Distribution
This report shows how many concepts fit into each category of the taxonomy. No category exceeds 30% of all concepts.