nostr:nprofile1qy2hwumn8ghj7un9d3shjtnyd968gmewwp6kyqpqp3qx0ddf4ruhfrrrgvhlhffnzv3u8j0aqurgt4glqutmkpnut8cqm7w55u nostr:nprofile1qy2hwumn8ghj7un9d3shjtnyd968gmewwp6kyqpqez3yya8tpgge7lk4jq2zxz0cj3d2mcg...
@nprofile1q... Making heights of trees irrelevant will be futile all the while mathematicians insist on only doing induction on measures even when there is an obvious notion of induction. I have had students had in work where they did induction on the length of a list and then do inversion from a length to deduce structure about the list.
The other problem is that lecture two of SoPL proves determinacy with an inefficient (but paedagogical) method. The students when asked to prove determinacy for the final supervision copy this method as if they have learned nothing since lecture two.
There is a nice (past SoPL Tripos) question that I used to set where the obvious proof is false as the IH is too weak. The students fail to spot this when I go through the proof very methodically. The solution note is also sloppy/informal about this; this motivates a good discussion on proof as a communication method between two parties and what each can assume about the other. A solution note is sloppy because it is from expert to expert. A Tripos question answer is from student to expert where the expert cannot assume informality rather than ignorance on the part of the student.
A serious primer on induction, and how to craft induction proofs including how to craft the motive would be an excellent addition to the Tripos.
@nprofile1q... @nprofile1q...
The other problem is that lecture two of SoPL proves determinacy with an inefficient (but paedagogical) method. The students when asked to prove determinacy for the final supervision copy this method as if they have learned nothing since lecture two.
There is a nice (past SoPL Tripos) question that I used to set where the obvious proof is false as the IH is too weak. The students fail to spot this when I go through the proof very methodically. The solution note is also sloppy/informal about this; this motivates a good discussion on proof as a communication method between two parties and what each can assume about the other. A solution note is sloppy because it is from expert to expert. A Tripos question answer is from student to expert where the expert cannot assume informality rather than ignorance on the part of the student.
A serious primer on induction, and how to craft induction proofs including how to craft the motive would be an excellent addition to the Tripos.
@nprofile1q... @nprofile1q...
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