# Graduate-Level Mastery Study Plan

Design a rigorous, spaced-repetition-based study plan for mastering a complex subject, including prerequisite mapping and self-assessment checkpoints.

## Prompt

Act as a learning scientist designing a mastery-based study plan. I want to learn {{subject_or_skill}} to {{target_proficiency_level}} within {{time_available}}. 

Build the plan by addressing:

1. Prerequisite mapping — identify any foundational concepts I must understand before tackling the core subject, and flag if my stated timeframe is realistic given these prerequisites.
2. Concept sequencing — break the subject into a logical sequence of concepts, ordered so each builds on the previous one, not just by textbook chapter order.
3. Study schedule — propose a week-by-week schedule using spaced repetition principles (reviewing earlier material at increasing intervals rather than only moving forward).
4. Active recall checkpoints — for every 1-2 weeks, suggest a specific self-test or practical exercise to verify real understanding, not just passive review.
5. Common failure points — identify the 2-3 places learners most commonly plateau or develop misconceptions in this subject, and how to specifically guard against each.
6. Mastery signal — describe what genuine mastery looks like at the end (a specific task I should be able to do unaided), so I know when I've actually reached the goal.

Present this as a structured study plan.

## Best for

Self-directed learners, career-changers, and graduate students who want a rigorous, evidence-based study plan rather than a simple reading list.

## Compatible tools

- Claude
- ChatGPT

## How to use

- Replace {{subject_or_skill}}, {{target_proficiency_level}}, and {{time_available}} with your specific learning goal.
- Review the prerequisite mapping honestly — if it flags a gap, address it before starting the main sequence rather than skipping ahead.
- Follow the spaced repetition schedule as given rather than only studying new material each week, since review intervals are what create durable understanding.
- Treat the active recall checkpoints as non-negotiable — if you can't pass one, revisit that section before moving forward.

## Customization tips

- Mention your existing background honestly (e.g. 'I took calculus 10 years ago') so the prerequisite mapping is accurate.
- Ask for the plan to be adjusted if your weekly time availability changes partway through.
- Request specific resource recommendations (books, courses, practice problem sources) for each stage if you want the plan to include materials, not just structure.

## Example input

Act as a learning scientist... I want to learn linear algebra to a level sufficient for machine learning research within 3 months, studying about 6 hours per week.

## Example output

1. Prerequisite mapping: solid algebra and basic function notation are assumed; if these are shaky, add 1-2 weeks before starting. 3 months at 6 hrs/week (~72 hours total) is realistic for applied fluency but not for full theoretical rigor (proofs).
2. Concept sequencing: vectors and vector spaces, matrix operations, linear transformations, eigenvalues/eigenvectors, matrix decomposition (SVD, PCA relevance), then applied ML-specific topics (gradient computation, matrix calculus basics).
3. Study schedule: Weeks 1-2 vectors/matrices, Weeks 3-4 linear transformations while reviewing weeks 1-2 material briefly, Weeks 5-6 eigenvalues/eigenvectors while reviewing weeks 1-4, Weeks 7-9 decomposition methods with cumulative review, Weeks 10-12 applied ML-specific integration and full cumulative review.
4. Active recall checkpoints: end of week 2, solve 10 matrix operation problems without notes; end of week 6, derive the eigenvalues of a 3x3 matrix by hand; end of week 9, implement PCA from scratch in code without looking up the algorithm.
5. Common failure points: learners often memorize matrix multiplication mechanically without understanding it as a transformation — guard against this by visualizing transformations geometrically; learners also often skip proof intuition entirely, which causes confusion later with eigenvalues — guard against this with a light conceptual (not full proof) explanation of why eigenvectors matter.
6. Mastery signal: you should be able to explain, without notes, why PCA uses eigenvectors of the covariance matrix, and implement it from scratch in code.