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I disagree with the notion that if you question your solution then your solution isn’t correct. A beginner could easily fool herself onto thinking she has corr

by jeff76 8y ago

I disagree with the notion that if you question your solution then your solution isn’t correct. A beginner could easily fool herself onto thinking she has correct understanding, but actually her proof is buggy. Without feedback, she wouldn’t know.

svat 8y ago
I agree. Among other things, I'm pointing out the opposite risk: a beginner may come up with a correct solution to the exercise, check from the book's provided solutions that her solution is correct, and move on to the next section, fooling herself into thinking that she has sufficient understanding (hey, she solved the exercise correctly!), not realizing that “not needing to look at the solutions” and “coming up with (or finding from other sources) lots more exercises” is part of the task of understanding. BTW, I didn't mention this earlier, but for verifying solutions to exercises which ask to prove something, I've never found it useful to see a solution that is simply a proof. The only way to get more confidence that you've proved something correctly is to find someone adversarial (e.g. a friend with similar or greater mathematical maturity) and try to prove it to them while they keep say “why” or “I'm not convinced”. (A proof is a social process; you cannot get feedback on your proof from a static, non-interactive source like a book.) One's proof may be superficially similar to what's in the book and yet not be a proof, while it can be very different and still be fine. What provided proofs can help with is getting you unstuck when you've been unsuccessful at proving something. So they help with frustration and motivation, as I mentioned earlier (feedback not so much).
- jeff76 8y ago
  When you’re doing basic proofs, showing solutions are often simple enough for unconfused verification. There are often standard ways to go about proofs, solutions could provide those standard solutions with sufficient detail written out.
  - sigjuice 8y ago
    I haven't read this particular book, but if the text includes several examples of detailed proofs, I might be okay with not having access to solutions.

by jeff76 8y ago

svat 8y ago

I agree. Among other things, I'm pointing out the opposite risk: a beginner may come up with a correct solution to the exercise, check from the book's provided solutions that her solution is correct, and move on to the next section, fooling herself into thinking that she has sufficient understanding (hey, she solved the exercise correctly!), not realizing that “not needing to look at the solutions” and “coming up with (or finding from other sources) lots more exercises” is part of the task of understanding. BTW, I didn't mention this earlier, but for verifying solutions to exercises which ask to prove something, I've never found it useful to see a solution that is simply a proof. The only way to get more confidence that you've proved something correctly is to find someone adversarial (e.g. a friend with similar or greater mathematical maturity) and try to prove it to them while they keep say “why” or “I'm not convinced”. (A proof is a social process; you cannot get feedback on your proof from a static, non-interactive source like a book.) One's proof may be superficially similar to what's in the book and yet not be a proof, while it can be very different and still be fine. What provided proofs can help with is getting you unstuck when you've been unsuccessful at proving something. So they help with frustration and motivation, as I mentioned earlier (feedback not so much).

jeff76 8y ago
When you’re doing basic proofs, showing solutions are often simple enough for unconfused verification. There are often standard ways to go about proofs, solutions could provide those standard solutions with sufficient detail written out.
- sigjuice 8y ago
  I haven't read this particular book, but if the text includes several examples of detailed proofs, I might be okay with not having access to solutions.