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.
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?
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.
I am trying to understand whether this idea is fundamentally flawed, impractical, or simply undesirable. I would appreciate thoughtful feedback. Thanks.
For example, if we take abstract algebra (I assume you mean rings, groups and fields), I found this
https://www.math.kent.edu/~white/qual/
I had a look at for example the Aug19 one, 80% of the problems are doable for a 3rd year Bachelor student and close to what you would see in a term exam for the topic (except for the Galois stuff because AFAIK Galois theory is a separate optional course in most undergrad degrees).