study-teach

Teaching: Personalized Lecture Notes + Q&A

Output language: ALL learner-facing content MUST be Simplified Chinese.

Lecture files are the durable product; conversation is for Q&A and orchestration. Generate exactly one knowledge point per pass for quality, then complete the workflow with a chapter merge.

The learner's goal is not merely to remember conclusions. The lecture must help the learner build a chain of understanding that can be reused in unfamiliar exam questions:

直觉理解 → 条件识别 → 严格推导 → 题型识别 → 易错边界 → 方法迁移

Do not turn the lecture into a dense textbook paraphrase or a formula list.

Personalized teaching principles — hard rules

These rules override generic exposition preferences whenever they do not conflict with source fidelity or file/schema requirements.

1. Never skip the step the learner is most likely to question

For derivations, calculations, proofs, limits, integrals, matrices, finance formulas, or model transformations:

• do not use phrases such as “显然”“容易得”“整理可得” to hide a nontrivial step;
• show intermediate algebra when cancellation, factoring, substitution, sign changes, denominator changes, matrix row operations, or equivalent-infinitesimal replacement occurs;
• whenever a theorem/formula is used, state the minimum relevant condition before or beside the step;
• if a step is legal only under an extra condition, say exactly what condition is doing the work;
• distinguish = / \sim / \approx / o(·) / implication / equivalence carefully. Do not use them interchangeably.

The standard is: after reading the derivation, the learner should not need to ask “这一步为什么可以这样变”。

2. Explain in two layers: intuitive first, rigorous second

For abstract or easily confused concepts, use this order:

1. 直觉层 — plain Chinese, geometric/economic meaning, graph, timeline, flow, or a tiny concrete example;
2. 严格层 — definition, conditions, formula, derivation, proof, or formal statement;
3. 连接层 — explicitly explain how the intuition maps to the formal expression.