问HN：人们如何验证在数学或计算机科学方面的深入自学？
我最近决定更好地理解现代密码学和零知识证明。尽管我在大学时修过数学课程，但那已经是多年前的事了，因此我开始自学一本本科抽象代数教材，每晚阅读并解决问题。
我取得了一些进展，但发现没有明确的外部标准来保持动力是很困难的。我一直希望能有一个标准化、严谨的抽象代数考试，我可以提前注册。这样可以激励我持续学习，并提供一个客观的理解水平衡量，就像提前几个月报名参加马拉松一样。
据我所知，这类考试在正式的学位项目之外基本上是不存在的。这让我产生了一个疑问：为什么不呢？是否有必要设计一小套书面考试，涵盖线性代数、抽象代数或算法等主题，旨在评估理解的深度，而不是速度或记忆？
我听说并调查过一些常见的答案，比如GRE科目考试、MOOC、认证以及“只需动手做”，但这些都没有让我觉得符合我的需求。我可能遗漏了什么。
我想了解这个想法是否根本上存在缺陷、不切实际，或者仅仅是不受欢迎。我会很感激能收到有建设性的反馈。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.