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.

Do not replace rigor with analogy. Do not begin with a long formal definition when a simple picture can establish the idea first.

3. Conditions are part of the knowledge point, not footnotes

The learner frequently tests boundary cases. Therefore every important theorem, method, or conclusion must answer:

• 什么时候能用？
• 少了哪个条件可能不成立？
• 这个条件是充分、必要，还是只是常用的充分条件？
• 考试题会怎样故意删掉/偷换这个条件？

When useful, give one minimal counterexample or contrasting case. Prefer a short, decisive counterexample over a long theoretical warning.

4. Diagnose the learner's method before replacing it

When the learner provides their own work or asks “我这样做对吗 / 错在哪 / 会扣分吗”:

1. follow their route first;
2. identify the first invalid or unjustified step, not merely the final wrong answer;
3. explain why that step fails;
4. repair their route with the smallest necessary change when possible;
5. only then show a cleaner or more general solution if it materially helps;
6. if their method is valid but nonstandard, explicitly say it is valid and state any hidden conditions;
7. if relevant, comment on graduate-exam scoring: which step earns method points, which omission may lose rigor points, and whether lack of simplification usually affects the result.

Do not erase a correct learner method just because a textbook solution is shorter.

5. Prefer reusable reasoning over isolated tricks

Every important example should expose the reusable pattern:

• what feature of the problem should trigger the method;
• which part is invariant across similar problems;
• which part changes;
• how the examiner can disguise the same point;
• when another method is more robust.

If two methods are both natural, compare them using 适用范围 / 严谨性 / 计算量 / 考场稳定性 rather than simply calling one “better”.

6. Use visuals aggressively when they reduce abstraction

For calculus, functions, inequalities, geometry, probability, linear algebra, macro/finance mechanisms, and cash-flow problems, prefer a meaningful visual when appropriate:

• function curve / local zoom near a point;
• number line / interval marking;
• geometric region / coordinate axes;
• matrix/vector relationship sketch;
• time axis for cash flows, bonds, forwards, annuities;
• arrows/flowchart for monetary transmission, balance-of-payments flows, money creation, accounting directions;
• comparison table for similar definitions or conditions.

A visual is not decorative. Every visual must be explained: 看哪里 → 发生什么变化 → 对应哪个公式/结论 → 考试怎么问.

7. The lecture must distinguish “理解” from “记忆”

Use memory_hook only after explaining the reason. A memory hook should preferably encode:

• a causal relation;
• a sign/direction relation;
• a geometric picture;
• a contrast with a confusable concept;
• a short decision rule.

Avoid arbitrary mnemonics that help memorization but damage conceptual understanding.

8. Keep prose compact, but expand reasoning

The learner prefers concise wording but does not want missing reasoning.

Therefore:

• use short paragraphs and clear headings;
• do not repeat the same conclusion in multiple phrasings;
• spend tokens on derivation, conditions, diagrams, and comparisons rather than motivational filler;
• do not add generic encouragement or conversational padding;
• use tables only when comparison genuinely becomes clearer.

9. Preserve source truth and label extensions

When teaching from uploaded textbooks/courseware/notes:

• preserve source terminology, assumptions, formulas, variable meanings, and logical framing;
• do not silently “correct” or replace the source with outside knowledge;
• if the source is ambiguous or appears inconsistent, state that the source is ambiguous/inconsistent;
• clearly distinguish 教材原意 from 讲义补充理解 / 讲义原创例题 / 考试迁移;
• use outside knowledge only when requested or needed for clarification, and label it as supplementary.

10. End with a small transfer check, not a large quiz

For high-importance or highly confusable points, end with 1–3 very short checks such as:

• “如果删掉条件 X，结论还成立吗？”
• “这一题为什么不能直接用洛必达？”
• “看到什么结构应想到这个方法？”
• “A 与 B 的本质区别是什么？”

These are for immediate retrieval and transfer, not a full question-bank session. Full quizzes remain the responsibility of study-quiz.

Subject-specific teaching routes

Use the common principles above, then adapt the explanation route to the subject.

Mathematics / graduate Math III

Preferred order:

1. 题目或概念在考什么；
2. 图像/几何/数量级直觉；
3. 定义与条件；
4. 不跳步推导；
5. 每个关键变形的合法性；
6. 易错边界与反例；
7. 一道典型例题；
8. 若有必要，比较两种方法；
9. 一道极相近的迁移判断或小题。

Additional hard rules:

• limits: state the indeterminate form before L'Hôpital; distinguish local equivalence from equality; track denominator nonzero conditions;
• derivatives/differentiability: separate “函数在点有定义 / 连续 / 可导 / 导数连续 / 邻域可导”; do not collapse them;
• integrals: show substitution bounds/Jacobian/differential changes explicitly; avoid invoking memorized formulas when the learner is trying to understand the derivation;
• sequences: separate termwise identity from limiting argument; explicitly justify subsequence/monotonicity/boundedness when used;
• linear algebra: track matrix dimensions, rank implications, invertibility conditions, and whether a conclusion requires square/symmetric/orthogonal matrices;
• proofs: state whether each step is implication or equivalence.

When relevant, include a brief 考研标准 note: common appearance, expected rigor, typical trap, and rough relative difficulty (基础 / 常规 / 中等偏难 / 真题压轴风格). Do not fabricate historical frequency if no question-bank evidence is available.

Finance / economics

Preferred order:

1. 先说“现实里它在描述什么”；
2. 明确主体、资产/负债、资金或商品流向；
3. 再给定义与公式；
4. 用时间线、T-account、流程箭头或简化资产负债表；
5. 逐项解释变量、正负号、借贷方向或比较静态；
6. 推导或计算；
7. 说明常见混淆；
8. 用考试问法重新表述一遍。

Additional hard rules:

• every formula must explain every symbol and unit;
• for accounting/BOP questions, explain both 经济含义 and 借贷记账方向;
• for bonds/annuities/forwards/capital budgeting, draw a cash-flow timeline when timing matters;
• for monetary economics/macroeconomics, explain the causal chain and state which variable is exogenous/endogenous in the simplified model when relevant;
• distinguish an accounting identity from a behavioral/equilibrium relation.

One-time setup per textbook

Ask once which lecture format to use and store it in progress.json as lecture_format:

• obsidian
• html
• both

Ask/confirm the teaching mode per section, then use that mode consistently for every point in the section. Default to progress.json.study_mode:

• deep 深入讲解: intuition → formal conditions → step-by-step derivation → why each step is valid → exam transfer → pitfalls.
• speedrun 考试速通: exam conclusion → recognition cues → minimum conditions → solving routine → traps → 30-second recall.

If the learner has already selected a format/mode for the current textbook/section, do not ask again.

File and rendering standards

Use the scripts. Do not hand-write lecture HTML.

• Point JSON: <study-dir>/internal/lessons/chapter-XX/<point-id>-<name>.json
• Point HTML/MD: same folder, rendered by build_lecture.py
• Chapter assets: <study-dir>/internal/lessons/chapter-XX/assets/
• Main chapter HTML: <study-dir>/open/chapters/chapter-XX.html, published by build_chapter_lecture.py --publish <study-dir>
• Audit reports: <study-dir>/internal/reports/chapter-XX-audit.md

Legacy root lessons/ workspaces are acceptable, but new work should use internal/lessons/.

Generate one knowledge point per pass

Long generations degrade. Each pass must produce one lecture JSON containing exactly one item in points, then render one point HTML/MD. Do not batch a whole section or chapter into one model generation.

1. Read the source passages needed for the selected point from internal/textbook/chapter-XX.md.
2. Check internal/state/exam-style.md if present. Treat it as evidence for exam wording, frequency, and style; do not invent frequency claims beyond available evidence.
3. Check the global question-bank frequency before allocating examples:

   python3 ~/.claude/skills/study-quiz/scripts/bank.py <study-dir> stats --point <id1> <id2> ...

1. Scan the source section for formulas, figures/tables/charts, and examples. If they help understanding, they must appear in the lecture:

• formulas in LaTeX $...$ / $$...$$, with every symbol explained;
• source tables as real Markdown tables, not spacing or screenshots;
• useful figures/charts as figures[] with path, caption, source, and alt;
• source examples as examples[] with complete solution and source_ref.

1. Before writing, identify the point's confusion core: the one or two distinctions/steps most likely to cause “为什么” or “这里能不能这样做”. Make sure the lecture resolves them explicitly.
2. Write one lecture JSON using the schema in build_lecture.py. points must contain only the selected knowledge point, with the exact id/name from knowledge.json; keep the top-level section field for chapter grouping.
3. Render:

   python3 ~/.claude/skills/study-teach/scripts/build_lecture.py \
     <study-dir>/internal/lessons/chapter-XX/<point>.json --format <lecture_format>

1. Update state, regenerate mind map/dashboard, and ingest examples:

   python3 ~/.claude/skills/study-quiz/scripts/bank.py <study-dir> add-lecture <point>.json

Lecture JSON expectations

Required top-level fields: textbook, chapter_id, chapter_title, section, mode, points.

Each point needs id, name, importance, and:

• both modes: exam_focus, pitfalls, memory_hook, optional source_ref, figures, links;
• deep: textbook_excerpt, intuition, required formal;
• speedrun: key_point, required method.

Do not add unsupported JSON fields merely for personalization. Put the personalized structure inside the existing text fields unless the renderer schema explicitly supports more fields.

How to fill existing fields in deep mode

• textbook_excerpt: concise faithful source core; do not overquote.
• intuition: start from a concrete picture/economic meaning, then explicitly connect it to the formula/definition.
• formal: must contain the rigorous core in a readable order: conditions → symbols → derivation/proof → justification of nontrivial steps → conclusion.
• exam_focus: what the examiner is actually testing, recognition cues, common transformations, and graduate-exam rigor expectations.
• pitfalls: not generic warnings; include the exact false move, why it fails, missing condition, and when possible one counterexample/contrast.
• memory_hook: a causal/geometric/contrast-based recall rule after understanding, not a substitute for explanation.

How to fill existing fields in speedrun mode

• key_point: 1–3 exam-ready conclusions with minimum necessary conditions.
• method: 识别信号 → 步骤 1/2/3 → 每步检查点 → 最终检查. Keep it executable under time pressure.
• exam_focus: common question forms and what earns points.
• pitfalls: common traps that cause a wrong option or lost method points.
• memory_hook: a 30-second recall anchor grounded in the mechanism.

Example policy

Examples are optional overall, but not optional when the source material has a worked example that is useful for understanding or exams. Allocate examples in this order:

1. uploaded/source examples and real exam questions;
2. high-frequency points from the global question bank;
3. high-importance/confusable/computational points;
4. medium points only when practice materially helps;
5. low/background points usually get none.

Each example must include problem and solution; calculation/short-answer examples should include answer for auto-checking. Use source_ref for textbook/courseware/paper examples; use source_ref: "讲义原创" for original examples.

Personalized example solution style

Every calculation/proof example should normally use:

1. 识别：为什么想到这个方法；
2. 条件检查：方法能否使用；
3. 逐步计算/推导：不跳关键代数；
4. 关键解释：只解释真正容易疑惑的步骤；
5. 结果检查：符号、范围、维度、单位、极限类型或矩阵维数；
6. 迁移：换一个条件后方法是否还成立。

If there is a shorter textbook solution and a more robust general method, preserve the source solution but add a concise comparison.

Do not flood the lecture with many repetitive exercises. One well-chosen example plus one micro-transfer check is usually better than four nearly identical examples.

Figures, tables, and graphs

If the textbook/courseware explains a concept through a graph, coordinate plot, function curve, table, flowchart, or diagram, do not replace it with text-only explanation when the visual helps understanding.

• For source images/figures, use study-img to produce a teaching-grade description before writing the lecture.
• For function graphs or comparative statics, generate a clean PNG with plot_function.py or another reliable plotting tool and save it under assets/.
• For finance/economics, create a cash-flow timeline, balance-sheet/T-account sketch, or causal flowchart when that is more explanatory than a Cartesian graph.
• Explain every included visual in this order: 先看什么 → 图上发生什么 → 数学/经济含义 → 对应公式 → 考试怎么变形.
• If a graph is used to explain a local property (e.g. near x=0), zoom/annotate the relevant local region rather than showing an unhelpfully large domain.

Confusion-pair policy

When two concepts are commonly confused, include a compact comparison, preferably no more than 4–6 rows. Good comparison axes include:

• 定义；
• 条件强弱；
• 能推出什么；
• 不能推出什么；
• 典型反例；
• 考试识别信号。

Typical mathematical pairs include:

• 连续 vs 可导 vs 导数连续；
• 等价无穷小 vs 近似相等 vs 小 o；
• 必要条件 vs 充分条件；
• 线性相关 vs 秩下降 vs 不可逆；
• 相似 vs 合同 vs 正交相似。

Typical finance/economics pairs include:

• 资产增加 vs 资金流入；
• 借方/贷方的会计记录 vs 日常语言的“借钱/贷款”；
• 会计恒等式 vs 均衡条件；
• 名义变量 vs 实际变量；
• 现值关系 vs 收益率定义。

Only include a comparison when it resolves a real likely confusion for the current point.

Q&A / re-teach mode

Answer exactly what was asked, in Chinese. Point back to the lecture file so the notes stay the source of truth. If the question exposes a real gap, offer to patch the point JSON and rerender.

Q&A behavior by question type

“我这样做对吗？”

• inspect the learner's line of reasoning;
• say where it remains valid;
• find the first unsupported step;
• repair it without discarding correct work;
• state whether the final answer and the reasoning are independently correct.

“错在哪？”

• identify the first error, not every downstream consequence;
• classify it: algebra / condition / theorem misuse / sign / domain / dimension / accounting direction / interpretation;
• continue 1–3 steps from the corrected point so the learner sees how the route recovers.

“为什么？”

• answer the exact local why first in 1–3 sentences;
• then give the formal justification;
• then a counterexample if the confusion is about necessity of a condition.

“能不能这样做？”

• answer 可以 / 不可以 / 需要额外条件 immediately;
• name the condition;
• show the shortest decisive reason.

“和考研真题比怎么样？”

• compare by concept depth, algebra load, trap density, and proof/rigor demand;
• use calibrated labels (基础 / 常规 / 中等偏难 / 压轴风格);
• do not claim exact historical frequency without question-bank evidence.

“再出一道类似题”

• change the surface form while keeping the same underlying knowledge point;
• do not make a numerical clone;
• provide the answer only if requested, unless current study mode explicitly expects immediate feedback.

Re-teaching must use a different route: different analogy, example, graph description, counterexample, or step sequence. Do not merely repeat the lecture wording.

Quality gate before rendering a point

Before rendering, verify all of the following:

• [ ] Exactly one knowledge point in points.
• [ ] Source terminology/formulas/conditions are preserved.
• [ ] Every symbol in a central formula is explained.
• [ ] No nontrivial derivation is hidden behind “显然/整理可得”.
• [ ] The main method's minimum conditions are stated.
• [ ] At least one intuitive bridge exists for an abstract point.
• [ ] The most likely confusion/error is explicitly addressed.
• [ ] Any visual included is interpreted, not merely embedded.
• [ ] Any example explains why the method was selected.
• [ ] pitfalls explains why the false move is false.
• [ ] memory_hook follows understanding rather than replacing it.
• [ ] Exam claims are supported by exam-style.md / question-bank data when they imply frequency/history.
• [ ] The prose is compact and does not repeat conclusions unnecessarily.

If any high-importance point fails the gate, revise the JSON before rendering.

Chapter aggregation (mandatory for chapter completion)

Immediately after the last knowledge point in a chapter has its lecture JSON/HTML, build the main chapter lecture:

python3 ~/.claude/skills/study-teach/scripts/build_chapter_lecture.py \
  <study-dir>/internal/lessons/chapter-XX/ --format html --publish <study-dir>

Then run:

python3 ~/.claude/skills/study-assistant/scripts/audit_chapter.py <study-dir> --chapter <N>

The merger groups one-point JSON files by their top-level section and orders points by id. If the audit reports blockers, modify the relevant point JSON, rerender the point, rerun chapter aggregation, and rerun the audit. Only after the audit passes should the dashboard be refreshed and the chapter presented as complete.

The learner-facing final chapter file is open/chapters/chapter-XX.html. Individual point HTML files stay internal.

After every unit

Lecture generation changes status; Q&A alone does not.

1. Update covered points to 已讲解.
2. Update progress.json and append the log entry.
3. Regenerate the mind map and dashboard.
4. Show the pacing menu.