(Legally, if possible).
This is where a massive repository of solved problems becomes indispensable. It acts not just as an answer key, but as a repository of techniques.
Consider the concept of a normal subgroup . A lecture defines it as: N ◁ G if gNg⁻¹ ⊆ N for all g in G. It sounds like gibberish until you solve 20 variations of "Prove this subgroup is normal" or "Find a counterexample where it isn't."
You do not need to solve all 3,000 problems linearly. That would take 1,000 hours. Instead, use the
~3000
Most textbooks give you 20–30 problems per chapter, with answers only for odd numbers. If you get stuck on problem #17, you might stare at the page for an hour or simply give up.
Having a PDF that spans these categories allows students to diagnose their own weaknesses. If you can compute but cannot prove, you know exactly where to focus.