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FFT Benchmarking Learning Graph

Overview

This directory contains a complete learning graph for the FFT Benchmarking course, generated using the Learning Graph Generator v0.03. The graph represents 200 interconnected concepts organized into a pedagogically sound structure.

Graph Statistics

  • Total Concepts: 200
  • Foundational Concepts: 10 (no prerequisites)
  • Total Dependencies: 348 directed edges
  • Taxonomy Categories: 12
  • Maximum Chain Length: 15 concepts
  • Connected Components: 1 (all concepts connected)

Generated Files

Core Outputs

  1. concept-list.md - List of 200 concept labels
  2. Organized by taxonomy category
  3. Title Case format (max 32 characters)

  4. Covers mathematical foundations through practical implementation

  5. learning-graph.csv - Dependency graph in CSV format

  6. Columns: ConceptID, ConceptLabel, Dependencies, TaxonomyID
  7. Dependencies use pipe-delimited format (e.g., "1|4|5")
  8. Valid DAG structure (no cycles)

  9. Ready for import into spreadsheet tools

  10. learning-graph.json - JSON format for visualization tools

  11. Nodes: 200 concepts with ID, label, and taxonomy
  12. Edges: 348 directed edges representing prerequisites
  13. Metadata: Course title, description, taxonomy definitions
  14. Compatible with vis.js and other graph visualization libraries

Analysis & Documentation

  1. course-description-assessment.md - Course content depth analysis
  2. Quality score: 98/100
  3. Validates course has sufficient depth for 200 concepts

  4. Identifies content strengths and suggestions

  5. quality-metrics.md - Graph structure validation

  6. DAG validation (no cycles detected)
  7. Foundational concepts: 10 entry points
  8. Indegree distribution analysis

  9. Longest dependency chain: 15 levels

  10. concept-taxonomy.md - Category organization

  11. 12 balanced categories (6% - 12% each)
  12. All categories under 30% threshold
  13. Pedagogical flow recommendations

  14. Clear 4-letter abbreviations

  15. taxonomy-distribution.md - Statistical breakdown

  16. Detailed concept listing by category
  17. Visual distribution table
  18. Balance verification

Taxonomy Categories

Code Name Concepts %
MATH Mathematical Foundations 16 8.0%
SIGP Signal Processing 16 8.0%
FOUR Fourier Theory 16 8.0%
FFTA FFT Algorithm 24 12.0%
HARD Hardware Platforms 16 8.0%
DSPI DSP Instructions 16 8.0%
PROG Programming 16 8.0%
LIBS FFT Libraries 12 6.0%
BNCH Benchmarking 18 9.0%
PERF Performance Optimization 14 7.0%
PIPE Signal Pipeline 12 6.0%
VAPP Visualization & Applications 24 12.0%

Quality Metrics Summary

  • DAG Structure: Valid - no cycles
  • Balanced Distribution: All categories < 30%
  • Foundational Base: 10 entry-point concepts
  • Average Dependencies: 1.83 per concept
  • Clear Progression: Max chain length of 15 levels
  • High Connectivity: Single connected component

Foundational Concepts

These 10 concepts have no prerequisites and serve as entry points:

  1. Complex Numbers
  2. Sine Wave
  3. Jean Baptiste Fourier
  4. Microcontroller
  5. Fixed Point Arithmetic
  6. C Language
  7. Assembly Language
  8. Python Language
  9. Benchmarking
  10. Data Visualization

Longest Learning Path

The longest dependency chain in the graph (15 concepts):

  1. Sine Wave → Cosine Wave → Periodic Functions → Harmonics
  2. → Fourier Series → Continuous Fourier Transform
  3. → Discrete Fourier Transform → DFT Definition → DFT Complexity
  4. → FFT Algorithm → FFT History → Cooley Tukey Algorithm
  5. → Radix-2 FFT → Radix-4 FFT → Split Radix FFT

Usage

For Course Development

  1. Use learning-graph.csv to plan weekly modules
  2. Follow dependency chains to order lessons
  3. Start with foundational concepts (zero dependencies)
  4. Build assessments based on taxonomy categories

For Visualization

Load learning-graph.json into visualization tools:

  • vis.js network diagram
  • D3.js force-directed graph
  • Graphviz DOT format
  • Neo4j graph database

Python Utilities

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# Validate graph structure
python analyze-graph.py learning-graph.csv quality-metrics.md

# Generate taxonomy distribution report
python taxonomy-distribution.py learning-graph.csv taxonomy-distribution.md taxonomy-names.json

# Convert CSV to JSON
python csv-to-json.py learning-graph.csv learning-graph.json color-config.json metadata.json

Pedagogical Recommendations

10-Week Course Structure

  • Weeks 1-2: MATH and SIGP foundations (32 concepts)
  • Weeks 3-4: FOUR and FFTA algorithm concepts (40 concepts)
  • Weeks 5-6: HARD and DSPI hardware (32 concepts)
  • Week 7: PROG programming and LIBS libraries (28 concepts)
  • Week 8: BNCH benchmarking methodology (18 concepts)
  • Week 9: PERF optimization and PIPE signal pipeline (26 concepts)
  • Week 10: VAPP applications and capstone project (24 concepts)

Learning Paths

  • Mathematics-First Path: MATH → FOUR → SIGP → FFTA → BNCH
  • Hardware-First Path: HARD → DSPI → PROG → LIBS → BNCH
  • Practical-First Path: LIBS → BNCH → PERF → VAPP

Next Steps

  1. Review and refine concept list and dependencies
  2. Create interactive visualization
  3. Develop detailed lesson plans per concept
  4. Design assessments aligned with Bloom's taxonomy
  5. Build capstone project integrating concepts
  6. Create MkDocs pages for each concept

References

  • Learning Graph Generator: https://github.com/dmccreary/learning-graphs
  • Graph Visualization: vis.js, D3.js, Cytoscape.js
  • Bloom's Taxonomy: Remember → Understand → Apply → Analyze → Evaluate → Create

License

Same as parent repository: Creative Commons ShareAlike Attribution Noncommercial