Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add hwl668/Scientific-learning-skills- --skill deepening-learninggit clone --depth 1 https://github.com/hwl668/Scientific-learning-skills-Wrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/hwl668/scientific-learning-skills-/deepening-learning)<a href="https://agentmods.dev/skills/hwl668/scientific-learning-skills-/deepening-learning"><img src="https://agentmods.dev/badge/skills/hwl668/scientific-learning-skills-/deepening-learning/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/hwl668/scientific-learning-skills-/deepening-learning"><img src="https://agentmods.dev/badge/skills/hwl668/scientific-learning-skills-/deepening-learning.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00076 | $0.01265 |
| Opus 5 | $0.00038 | $0.00633 |
| Sonnet 5 | $0.00015 | $0.00253 |
| Haiku 4.5 | $0.00008 | $0.00127 |
Grade A, and why
deepening-learning scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 12d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
What it actually says
目标
在已有基础上，从多个维度深化对一个知识点的理解，建立更丰富的认知结构。
适用场景
- 已经理解基本概念，能做常规题目
- 想知道"这个知识还能怎么看"
- 想知道这个知识和其它知识的关联
- 想知道这个知识在实际中怎么用
- 想看到这个知识的证明/推导
Memory 系统
类型：分析记忆（不参与间隔复习）。
存储位置：memory/deepening-learning/
存储内容：
- 有效的深化角度组合：哪些维度组合（如"多视角+反例+跨知识"）在哪些知识点上效果好
- 高频关联知识：哪些跨知识连接被用户反复追问（说明连接价值高）
读/写规则：
- 写入：每次深化结束后，记录使用的维度组合和用户反馈。
- 读取：下次遇到同类知识点的深化请求时，参考已记录的高效维度组合。
- 管理：说"清除 deepening-learning 记忆"删除。
输入判断
确认学习者已经掌握了基础。快速验证：
- 能用一句话说清楚这个概念吗？
- 能做一道基本题吗？
如果基础还没牢固，先用 fuzzy-understanding 或 zero-base-learning。
执行流程
根据具体情况选择 2-4 个深化维度，不需要全做：
选择维度 → 深入展开 → 跨知识连接 → 高维验证
七大深化维度
1. 多视角解释
同一个概念的不同解释方式。例如：
- 导数 = 切线斜率（几何视角）
- 导数 = 变化率（物理视角）
- 导数 = 线性近似（近似视角）
- 导数 = 函数局部线性化的算子（算子视角）
2. 跨知识联系
把当前知识和其它知识连接起来。例如：
- 矩阵的秩、方程组的自由变量个数、线性变换的核空间维数，这三者在说同一件事。
3. 证明或推导
展示关键定理的证明思路。不是全文背诵，而是抓住核心技巧。
4. 反例意识
给出满足部分条件但不满足全部条件的反例，说明为什么定理的条件缺一不可。
5. 变式迁移
改变问题条件，观察方法是否仍然适用。不适用时需要怎么调整。
6. 实际应用
这个概念在物理/工程/计算机中的实际应用场景。
7. 高阶题训练
1-2 道综合题，需要同时调用多个知识点。
输出格式
## 基础确认
[快速验证理解]
## 深化维度
### [维度名称]
[展开内容]
## 综合训练
[一道需要综合理解的题]
## 延伸阅读方向
[下一步可以学什么]
常见误区
| 常见错误 | 为什么错 | 正确理解 |
|---|---|---|
| "深化 = 学更难的内容" | 把"深"等同于"高"——用实分析"深化"微积分是用更高阶知识替代深化 | 深化是同一概念的多视角、反例、跨知识联系，不是升维 |
| "多罗列几个视角就是深化" | 堆视角不建立联系 = 信息堆叠，没有结构 | 选 2-4 个互补视角，明确说明它们如何互相支撑 |
| "深化不需要验证" | 以为"懂了"就行 | 深化后必须用变式题验证——能解决改了条件的问题才是真深化 |
反例：什么时候不要这样做
- 学习者基础不牢 → 先修复基础
- 不是讲更难的内容（如微积分还没学清楚就去讲实分析）
- 不是堆更多公式和定理
- 不要讲和当前知识没有联系的高阶内容
- 不要假设学习者有研究者级别的数学成熟度
测试样例
输入：我学完了一元微积分，导数和积分都会算。但我觉得我对"微积分基本定理"的理解还很表面——我知道它是说微分和积分互为逆运算，但就这？
期望输出方向：
- 基础确认：让学习者用自己话说一遍 FTC
- 多视角解释：从"累积量"和"变化率"的关系重新理解 FTC
- 证明思路：用黎曼和的视角展示为什么微分是积分的逆
- 跨知识联系：FTC 和泰勒定理的关系（积分余项）
- 反例：连续性是必要条件——给出一个可积但不可在某点微分的例子
- 综合训练：一道需要先用 FTC 再换元的题
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 12d ago First seen · 128 lines · 76 tokens per session scan A c438c80d6508
deepening-learning is a skill published in the GitHub repository hwl668/Scientific-learning-skills- (13 stars, last pushed 1mo ago), licensed MIT. It adds 76 tokens to every session and 1,265 once invoked, about $0.0004 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-30.
Other skills, from other repositories
deeptutor-cli
Configure, manage, and use DeepTutor through its CLI, including capabilities, knowledge bases, partners, memory, sessions, notebooks, providers, skills, and the server or Web app.
exam-study-guide
A study-guide builder for a completed exam chapter that has not yet passed its required checks. It creates a structured teaching checklist and, in full mode, a self-contained HTML and printable PDF guide with readable formulas, visible images, explanations, examples, and answers.
exam-ingest
A workspace setup tool for exam preparation. It reads PDFs, Word documents, presentations, spreadsheets, images, text files, and Markdown, then creates chapter notes, a question bank, and tracked preparation data.
exam-cram
An exam-preparation guide for studying shortly before a test. It turns course materials into chapter notes and a question bank, then manages teaching, practice, grading, mistake review, and progress tracking.
exam-tutor
A teaching workflow for learning one chapter from a study wiki at a time, using everyday comparisons and step-by-step explanations of formulas and important questions. TDD is not involved here; the material concerns guided study and exam preparation.
exam-audit
A read-only health check for an exam-preparation workspace, meaning the folder that stores study materials, questions, notes, plans, and progress. It reports missing, inconsistent, or incomplete parts without changing them.