Course Distiller

Course Material Distillation Skill

Core Philosophy

考试是考试，不是用来搞学术研究的。

This skill is built on Linus-style pragmatism:

• Enough > Perfect: 75分的实用 > 100分的理论
• ROI-Driven: 40分的MDP > 12分的Logic, 先拿大头
• Anti-Academic: 去他妈的形式主义，够用就行
• 6-Day Constraint: 如果6天看不完，就不是好材料

What we optimize for:

• Can the student score 90+ in 6 days?

What we DON'T optimize for:

• Complete coverage of all topics
• Academic rigor and proofs
• "Understanding deeply" (unless it helps score)

When to Use This Skill

Trigger this skill when:

• User uploads multiple course files (lecture notes, slides, past exams, textbook chapters)
• User asks to "summarize for exam", "create study guide", "prepare in X days"
• Files contain academic/educational content that needs condensing for exam prep

Don't use when:

• User wants to "deeply understand" a topic (not exam-focused)
• Only 1 file uploaded (no cross-analysis needed)
• User is writing a thesis/paper (wrong context)

Process Overview

Input: Multiple course files
  ↓
Phase 1: Diagnose (What's wrong with these materials?)
  ↓
Phase 2: Cross-Analyze (Where are gaps? What's tested most?)
  ↓
Phase 3: Distill (Cut to core, rank by ROI)
  ↓
Phase 4: Reconstruct (Build exam-ready guide)
  ↓
Output: 6天能看完、能拿分的作战手册

Phase 1: Diagnosis

Step 1.1: Classify Files

For each uploaded file, determine:

File: [filename]
- Type: [lecture notes | slides | past exam | textbook | cheat sheet]
- Topics: [list major topics covered]
- Length: [page count or word count]
- Density: [High detail | Medium | Just questions]
- Exam relevance: [Directly tested | Background only | Unclear]

Step 1.2: Identify Common Problems

Flag these issues:

❌ 缺少活人感觉 (Too academic):

• Formal language like "验证方法", "概念对比表"
• No "why", only "what"
• Reads like a textbook, not a study guide

❌ 信息过载 (Information overload):

• Same concept repeated 6 times in different files
• Too many examples (more than needed to "get it")
• Feature-complete but not exam-complete

❌ 有点散 (Lacks structure):

• No learning path (what to study first?)
• No priority (which topics are worth more points?)
• Topics isolated (no connections)

❌ 形式大于内容 (Form over function):

• Excessive formatting (tables, emojis, headers)
• Layered structure (速记层, 仿真层, 白板层) that doesn't serve exam goals
• Long code blocks that won't be tested

Phase 2: Cross-File Analysis

Step 2.1: Build Knowledge Coverage Matrix

Create a table showing which topics appear in which sources:

| Topic | Lecture | Textbook | Exam 2024 | Exam 2023 | Exam 2022 |
|-------|---------|----------|-----------|-----------|-----------|
| A* Search | ✅ 20 pages | ✅ Ch 3 | ✅ 15 pts | ✅ 12 pts | ✅ 18 pts |
| Policy Iter | ❌ Missing | ✅ Brief | ✅ 5 pts | ✅ 8 pts | ❌ No |
| Responsible AI | ❌ No | ❌ No | ✅ 10 pts | ❌ No | ❌ No |

Flag these patterns:

🚨 Red Flag: Exam tests but no lecture/textbook coverage

• Example: "Responsible AI" worth 10 points but not taught
• Action: Must include from exam context or external source

⚠️ Yellow Flag: Only 1 source covers it

• Example: "Policy Iteration" only in textbook
• Action: Extract and simplify, student might miss it

✅ Green: Multiple sources, consistent definitions

• Example: "A* Search" everywhere
• Action: Condense, delete redundancy

Step 2.2: Calculate Topic ROI

For each topic, compute:

ROI = (Total Exam Points × Frequency) / (Study Difficulty × Time)

Where:
- Total Exam Points: Sum across all past exams
- Frequency: How many exams test it (%)
- Study Difficulty: 1 (easy) to 5 (hard)
- Time: Estimated hours to master

Example:

MDP Value Iteration:
- Points: 15 + 18 + 12 = 45 points
- Frequency: 3/3 exams = 100%
- Difficulty: 3/5 (medium, just apply formula)
- Time: 2 hours

ROI = (45 × 1.0) / (3 × 2) = 7.5

Q-learning:
- Points: 12 + 15 + 10 = 37 points  
- Frequency: 3/3 = 100%
- Difficulty: 3/5
- Time: 2.5 hours

ROI = (37 × 1.0) / (3 × 2.5) = 4.9

Logic (Resolution):
- Points: 8 + 0 + 12 = 20 points
- Frequency: 2/3 = 67%
- Difficulty: 2/5 (easy pattern matching)
- Time: 1.5 hours

ROI = (20 × 0.67) / (2 × 1.5) = 4.5

Sort topics by ROI descending → This becomes study priority

Step 2.3: Check Consistency

For topics appearing in multiple sources, verify definitions align:

Concept: "Admissible Heuristic"

Lecture: h(n) ≤ h*(n)
Textbook: "Never overestimates cost to goal"
Exam 2023: "Non-overestimating heuristic"

Status: ✅ Consistent (just different wording)
---
Concept: "Discount Factor γ"

Lecture: "Patience parameter"
Textbook: "Weight for future rewards"  
Exam: [No definition, used in problems]

Status: ⚠️ Inconsistent terminology
Action: Use exam context to pick clearest term

If contradictions found → Exam definition wins (that's what grader expects)

Phase 3: Distillation (The Ruthless Cut)

Step 3.1: Build 作战地图 (Battle Map)

Create a 5-minute global overview:

## 作战地图

**这门课在讲什么？**
[1-2 sentence big picture]

**考试结构：**
- Topic A: X points (主战场 / 送分题 / 看运气)
- Topic B: Y points
- Topic C: Z points

**学习顺序：**
Day 1-2: [Highest ROI topics]
Day 3: [Medium ROI]
Day 4: [Lower ROI but still tested]
Day 5: Mock exam
Day 6: Trap review

Step 3.2: Extract ONLY Core Concepts

For each topic, identify the minimum viable knowledge:

1. The Big Idea (1 sentence - why does this exist?)
2. Key Formula (1 equation - what to apply)
3. Memory Anchor (1 analogy - how to remember)

Example:

### MDP (Markov Decision Process)

**Why learn this?**
World is random, can't plan a fixed path, only a strategy

**Key Formula:**
V*(s) = max_a [R(s,a) + γ Σ T(s,a,s') V*(s')]

**Memory Anchor:**
Like planning a road trip where weather is uncertain:
- Can't say "I'll take route A", only "If sunny, take A; if rainy, take B"
- γ is how much you care about tomorrow vs today

Step 3.3: Delete Ruthlessly

Apply these cuts:

❌ Delete:

• Formulas that appear 6 times → Keep 1 best version
• Proofs (unless exam explicitly asks)
• Long code blocks (unless exam is coding-heavy)
• Examples beyond 2nd one (1-2 examples enough to "get it")
• Sections like "Historical background", "Alternative approaches"

❌ Simplify:

• Multi-page explanations → 1 paragraph
• Complex tables → Simple bullet points (unless table helps calculation)
• Academic terminology → Plain language

✅ Keep:

• Hand-calculation steps (if exam has calculation problems)
• Common traps (from past exams)
• Edge cases that are frequently tested

Ruthless Test:

"If I delete this, will the student score lower?"

• No → DELETE
• Yes → KEEP

Step 3.4: Rank and Prioritize

Reorganize content by ROI (not by course structure):

Priority P0 (40+ points): MDP, RL
Priority P1 (20-35 points): Search, CSP  
Priority P2 (10-20 points): Game Theory, Logic
Priority P3 (<10 points): Fringe topics

Time allocation:

• P0: 50% of study time
• P1: 30%
• P2: 15%
• P3: 5% or skip if time-constrained

Phase 4: Reconstruction

Step 4.1: Establish Learning Path

Based on ROI and topic dependencies:

## 6-Day Study Plan

**Day 1-2** (主战场 - 40 points):
- MDP: Value Iteration, Bellman equation
- RL: Q-learning, SARSA
- Self-test: Can you hand-calculate Value Iteration in 5 minutes?

**Day 3** (送分题 - 35 points):
- Search: A* algorithm, admissible/consistent
- CSP: Arc Consistency (AC-3), Backtracking
- Self-test: Can you trace A* on graph in 3 minutes?

**Day 4** (看运气 - 25 points):
- Game Theory: Minimax, Alpha-Beta pruning
- Logic: Resolution, CNF conversion
- Concept review: Policy Iteration, MC vs TD

**Day 5**: 
- Mock exam under time pressure
- Identify weak spots

**Day 6**:
- Review trap list
- Quick formula refresh
- Sleep well

Step 4.2: Add Memory Anchors

For each concept, create concrete analogies (not abstract labels):

✅ Good Anchor:

Q-learning = 理想主义者
→ Like learning to drive: Instructor teaches perfect technique, 
  but you actually make mistakes while practicing
→ Learns "optimal policy" but follows "exploratory policy"

❌ Bad Anchor:

Q-learning = "乐观逼"  ← What does this mean?

Extreme case anchors:

Discount factor γ:
- γ = 0: Agent is short-sighted, only cares about immediate reward
  (像只看眼前的傻子)
- γ = 1: Agent is far-sighted, values future as much as now
  (像长远规划的智者)
- γ > 1: INVALID, future rewards worth more than present? Nonsense.

Step 4.3: Tabularize Calculations

Convert text-based calculation steps to tables:

Before:

Step 1: pop(A) with f=90. Expand B, C. 
PQ now has C (f=7) and B (f=101).
Step 2: pop(C) with f=7. Expand D.
PQ now has D (f=96) and B (f=101).
...

After:

| Step | Pop | f(n)=g+h | Expand | New PQ | Note |
|------|-----|----------|--------|--------|------|
| 1 | A | 90 | B, C | C(7), B(101) | Pick min f |
| 2 | C | 7 | D | D(96), B(101) | C is goal? No |
| 3 | D | 96 | E, F | E(95), B(101), F(102) | Pick E |

Why tables?

• 考场上一目了然
• 不容易算错
• Grader容易给分

Step 4.4: Anti-Academic Language Check

Replace academic phrases with plain language:

Tone:

• ❌ "本章节将探讨强化学习的理论框架"
• ✅ "强化学习就是：环境规则未知，只能边试边学"

Output Format

Final Deliverable Structure

# [Course Name] 考场作战手册

## ⚡ 开门见山（30秒版）

这门课考什么：[1 sentence]
怎么拿高分：[3 bullet points]

---

## 🗺️ 作战地图 (5分钟看全局)

**考试结构：**
[分值分布、题型]

**学习顺序：**
[6天计划]

**自测标准：**
- [ ] 能白板默写核心公式吗？
- [ ] 手算题5分钟能完成吗？

---

## 📚 核心模块 (按ROI排序)

### 模块1: [最高ROI] - XX分

#### 为什么学这个？
[1句话 - 这玩意儿解决什么问题]

#### 核心概念（记住这3个就够）
1. **概念A** - 记忆锚点：[具体类比]
2. **概念B** - 记忆锚点：[极端情况]
3. **概念C** - 记忆锚点：[反例]

#### 考场手算（5分钟搞定）
[表格化步骤]

**公式：**
[关键公式 1-2个]

**计算流程：**
| Step | Do What | Example | Note |
|------|---------|---------|------|
| ... | ... | ... | ... |

#### 陷阱库（别踩这些坑）
- ❌ 常见错误1：[对应题号 2024 Q1]
- ❌ 常见错误2：[对应题号 2023 Q2]

#### 概念速查（选择题专用）
- Policy Iteration vs Value Iteration
- MC vs TD learning
- [其他概念题]

---

### 模块2: [次高ROI] - YY分
[重复上述结构]

---

## 🎯 考场清单（考前15分钟过一遍）

**公式速查：**
- MDP: V*(s) = ...
- Q-learning: Q(s,a) += ...
- [其他核心公式]

**常见陷阱：**
1. admissible不等于consistent！
2. Q-learning用max，SARSA用actual
3. [其他易错点]

**时间分配：**
- P0题型（40分）：50分钟
- P1题型（35分）：40分钟  
- P2题型（25分）：30分钟

---

## 📌 Appendix: 概念杂烩（选择题速查）

[Policy Iteration, MC vs TD, Responsible AI等快速查阅]

Quality Checklist

Before delivering, verify:

✅ Pragmatism Check

• 6天能看完吗？ (字数 < 5000 words for typical course)
• 删掉了所有"学术味"吗？ (no 验证方法, 推导过程等)
• 按ROI排序了吗？ (不是按课程顺序)
• 有明确的"够用就行"界限吗？ (不追求100%覆盖)

✅ Cross-File Analysis

• 覆盖度矩阵建了吗？ (知道哪些topic在哪些文件)
• Gap标记了吗？ (考试考但lecture没教的)
• 一致性检查了吗？ (不同文件定义矛盾的)

✅ Exam Focus

• 对应真题题号了吗？ (每个知识点标注考频)
• 手算步骤表格化了吗？ (不是纯文字描述)
• 有自测标准吗？ (怎么验证自己掌握了)

✅ Memory Aids

• 每个核心概念有锚点吗？ (类比、极端情况、反例)
• 锚点具体吗？ (不是抽象标签)
• 有"why"吗？ (不只是"what")

Anti-Patterns (绝不要做的事)

❌ Academic Completeness Trap

Don't: "Let me cover every single topic from the textbook to be thorough"

Do: "Let me identify the 20% of topics that give 80% of the points"

Why: 考试不是博士答辩，没人care你懂不懂所有细节

❌ Feature Creep

Don't: Add 速记层, 试卷仿真层, 白板复现层, 遗漏补充篇...

Do: One version, one source of truth

Why: Layers只是形式主义，考试只需要一个能用的版本

❌ 平等主义谬误

Don't: Treat all topics equally ("每个都很重要")

Do: Brutal ROI prioritization

Why: MDP值40分，Logic值12分，时间分配不能1:1

❌ 学术语言病

Don't: "本节将阐述Bellman方程的理论基础及其在马尔可夫决策过程中的应用"

Do: "Bellman方程：怎么算最优策略"

Why: 考场上没时间读废话

Example: Before/After

Before (Academic approach)

## Admissible Heuristics

### Definition
A heuristic h(n) is admissible if and only if:
h(n) ≤ h*(n) ∀n

where h*(n) represents the true optimal cost from node n to goal.

### Verification Methodology
To verify admissibility:
1. Enumerate all nodes in state space
2. For each node n, compute h(n)
3. Compute h*(n) via exhaustive search
4. Validate inequality h(n) ≤ h*(n)

### Theoretical Implications
Admissibility is a sufficient condition for A* optimality when 
combined with tree search. For graph search, consistency 
(monotonicity) is required...

[3 more paragraphs]

After (Pragmatic approach)

## Admissible（乐观估计）

**为什么？**
如果你瞎估距离太大，A*可能剪掉最优路径

**公式：**
h(n) ≤ 实际距离

**记忆锚点：**
像个乐观的人，永远说"还有3公里"，实际可能5公里
→ 只要不高估，A*保证找到最优解

**考场怎么判断？** (2024 Q1, 2023 Q1)
1. 看每个节点的h值
2. 问：到终点可能更近吗？
3. 可能更近 → 不admissible ❌

**陷阱：**
❌ Admissible ≠ Consistent!
- Admissible只要不高估
- Consistent要求前后不矛盾

Difference:

• Before: 500 words, academic tone, theoretical focus
• After: 100 words, plain language, exam focus
• Both cover same concept, but After is 5x faster to read and remember

Final Reminder

When using this skill, always ask:

"如果学生只有6天，这份材料能让TA考90+吗？"

If answer is no → Keep cutting until yes.

The enemy is not incomplete coverage. The enemy is wasting time on low-ROI content.

Enough > Perfect. 实用 > 学术. 干就完了.