That's definitely not how I read a math text, anyway!
That's now how anyone should read a math text, in my opinion. What I needed was someone to tell me I could look at later chapters at a high level to just grasp what they were about and what we were building up toward, instead of going, "No, Mildred, you're getting ahead! We must go line by line or it's not rigorous."
...Yes, if you're writing a proof. There is a difference between a rigorous proof and a rigorous pedagogy. The needs are different.
(My math and physics profs seemed to think that if they walked you through proofs line by line that was the same thing as teaching you, and you would then be able to 1) grasp the concepts, 2) apply the concepts to concrete problems without further effort. Maybe that works for the cahns of the world, but the Mildreds need "This pointless-looking lemma is building up to Galois theory, which is covered three chapters from now, and the point of Galois theory is blah blah," before learning the proof for each pointless-seeming lemma in isolation.)
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Re: Grad school
Date: 2023-01-10 11:55 pm (UTC)That's now how anyone should read a math text, in my opinion. What I needed was someone to tell me I could look at later chapters at a high level to just grasp what they were about and what we were building up toward, instead of going, "No, Mildred, you're getting ahead! We must go line by line or it's not rigorous."
...Yes, if you're writing a proof. There is a difference between a rigorous proof and a rigorous pedagogy. The needs are different.
(My math and physics profs seemed to think that if they walked you through proofs line by line that was the same thing as teaching you, and you would then be able to 1) grasp the concepts, 2) apply the concepts to concrete problems without further effort. Maybe that works for the
actually I think we got a fairly okay progression
More evidence you went to school in Sweden!