Systematic Foundations Tutorial

Use this skill when creating or rewriting a computer science fundamentals lesson for a beginner who needs a continuous mental model rather than a collection of summaries or interview notes. It applies to data structures, algorithms, computer organization, operating systems, networks, databases, concurrency, and related foundations.

Required teaching arc

Organize each lesson in this order:

1. Problem — begin with a concrete task or failure and explain why the naive approach is insufficient.
2. Prerequisites and model — state the concepts the reader needs, then show the objects, layers, states, or memory representation involved.
3. Invariant or governing rule — identify what must remain true, what contract a layer provides, or what law explains the behavior.
4. Main process — explain the normal path in time order, including participants, state changes, and outputs.
5. Implementation — present details, code, protocol fields, or hardware mechanisms only after the model is established.
6. Trade-offs and boundaries — compare alternatives by assumptions, complexity, latency, capacity, locality, isolation, reliability, or failure behavior.
7. Practice — end with a worked example, misconceptions, observable evidence, understanding checks, and exercises.

Heading discipline

Use second-level headings for complete learning stages, not isolated vocabulary terms. Merge headings that answer the same question. Keep concepts, implementation, applications, diagnostics, and interview prompts in separate major groups. A reader should be able to read from the first heading to the last without jumping between unrelated modes.

Explanation rules

• Introduce every unfamiliar abbreviation or English term with its full name, Chinese meaning, and role on first use.
• Explain the invariant, contract, or governing rule before implementation details.
• Use one running example through the lesson and show state changes with a small diagram or table.
• State whether a claim is worst-case, average-case, amortized, approximate, platform-dependent, or output-sensitive, and name the assumption.
• Keep lists for genuinely parallel facts. Convert sequences of causal claims into connected prose.
• Distinguish an abstract interface or layer from one concrete implementation.
• Explain why a mechanism exists before listing its components or parameters.
• Keep summaries short and point back to the explanation instead of repeating it.

Module-level organization

For an overview page, establish the learning dependency graph first. Group topics by the problem or operation they address, explain prerequisites, show a progression from simple models to composed systems, and provide a decision tree for selecting the next topic. Do not merely reproduce directory order.

Verification

Before finishing, check that headings form a coherent progression, prerequisites are stated, each lesson has a model diagram or equivalent concrete representation, examples match the stated invariant, edge cases are explicit, internal links resolve, and Markdown tests pass. Do not claim a lesson is rewritten merely because a glossary, summary, or introduction was added; the body must explain the mechanism in continuous prose.