A practical reading method
Build a Theorem Dependency Trail While Reading
Write the theorem’s claim and hypotheses in your own words, keeping the page and section number. List each cited definition, lemma, or prior theorem beside the exact proof step where it is used. Mark the first unsupported step as a question rather than filling it with an assumed result.
Use this when a mathematical text cites several earlier results and the proof becomes hard to reconstruct after a break. A dependency trail reveals the load-bearing ideas. It gives you a short route back into the proof instead of a second full reading.
Use case
When this method helps
Use this when a mathematical text cites several earlier results and the proof becomes hard to reconstruct after a break.
A dependency trail reveals the load-bearing ideas. It gives you a short route back into the proof instead of a second full reading.
Method
Build the note
1. Write the theorem’s claim and hypotheses in your own words, keeping the page and section number.
2. List each cited definition, lemma, or prior theorem beside the exact proof step where it is used.
3. Mark the first unsupported step as a question rather than filling it with an assumed result.
Example
See the boundary in practice
If compactness enters only when extracting a convergent subsequence, link that lemma to that step instead of tagging the whole proof ‘compactness.’
Quality check
Before you trust the note
Cover the proof and follow your dependency trail. It should reconstruct the logic without pretending to replace the details.