Ask HN: 各位如何验证在数学或计算机科学领域的深度自学成果？
1 分•作者: _willhf•6 个月前
最近，我决定深入了解现代密码学和零知识证明。虽然我在大学里学过数学课程，但那已经是很多年前的事了，所以我开始自学本科的抽象代数教材，每天晚上阅读并解决问题。<p>我取得了一些进展，但发现如果没有明确的外部标准，很难保持学习的动力。我一直希望有一个标准化的、严谨的抽象代数考试，可以提前报名参加。就像提前几个月报名参加马拉松一样，这能激励我持续学习，并提供一个客观的理解衡量标准。<p>据我所知，这种考试在正规学位课程之外基本上是不存在的。这引发了我的一个疑问：为什么会这样？如果有一小组笔试科目考试，例如线性代数、抽象代数或算法，旨在评估理解的深度而不是速度或记忆，这是否有价值？<p>我听说过并研究过常见的答案，例如 GRE 专业考试、MOOC、认证和“直接构建东西”，但这些都感觉不太像我想要的。我可能遗漏了什么。<p>我正在努力理解这个想法是否从根本上存在缺陷、不切实际，或者仅仅是不受欢迎。我很感谢您的深思熟虑的反馈。谢谢。
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I recently decided I wanted to better understand modern cryptography and zero-knowledge proofs. Although I took mathematics courses in college, that was years ago, so I began working through an undergraduate abstract algebra textbook on my own, reading and solving problems most evenings.<p>I made progress, but found it difficult to stay motivated without a clear external benchmark. I kept wishing there were a standardized, rigorous abstract algebra examination I could register for in advance. Something that would motivate sustained study and provide an objective measure of understanding, much like signing up for a marathon months ahead of time.<p>As far as I can tell, exams like this largely do not exist outside formal degree programs. That raised a question for me: why not? Would there be value in a small set of written subject matter exams, for example linear algebra, abstract algebra, or algorithms, designed to assess depth of understanding rather than speed or memorization?<p>I have heard and investigated the common answers, such as GRE subject tests, MOOCs, certifications, and "just build things," but none of those felt quite like what I was looking for. I may be missing something.<p>I am trying to understand whether this idea is fundamentally flawed, impractical, or simply undesirable. I would appreciate thoughtful feedback. Thanks.