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> n the case of real analysis, it is an issue of switching from "Can you apply known operations to produce the right answer?" to "Do you understand the structu

> n the case of real analysis, it is an issue of switching from "Can you apply known operations to produce the right answer?" to "Do you understand the structure of the reals well enough to prove it?". Is this really the case in general? My math degree curriculum started with 100% proof-driven classes almost immediately, long before most people got around to taking real analysis. It was my impression that that kind of approach was fairly ubiquitous.

btilly 10y ago
In the USA and Canada, it is standard for the professor to stand at the board and present proofs of everything, but students are not expected to understand them. If you can learn the formulas and apply the techniques that are in the homework sets, you can pass the class. I strongly question the value of having the professor recite proofs that the students do not really understand. However it is traditional to do that. The first course where students are expected to write their own proofs varies. My personal experience was that the transition happened in third year courses aimed at math majors. So I began writing proofs in abstract algebra and real analysis. But not in my third year differential equations course that was required for engineering and physics majors. When I was in grad school at Dartmouth, they introduced it earlier in a linear algebra course. I taught the last linear algebra course that did that, the next quarter they took proofs out of it.
- wutbrodo 10y ago
  Hm interesting. My undergrad degree at Berkeley was pretty much solely the professor running through proof after proof, and our homework was more proofs. It actually suited me just fine, it was one of the few curricula in my life that I found presented any challenge. My impression was that it worked fine for the majority of the other students as well, but I don't have tons of data on that or anything.
  - btilly 10y ago
    I'm not surprised that Berkeley is an outlier in this regard. Talk to people who went to other universities and I'm confident that you'll find my experience to be more common.
- deleted 10y ago
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btilly 10y ago

In the USA and Canada, it is standard for the professor to stand at the board and present proofs of everything, but students are not expected to understand them. If you can learn the formulas and apply the techniques that are in the homework sets, you can pass the class. I strongly question the value of having the professor recite proofs that the students do not really understand. However it is traditional to do that. The first course where students are expected to write their own proofs varies. My personal experience was that the transition happened in third year courses aimed at math majors. So I began writing proofs in abstract algebra and real analysis. But not in my third year differential equations course that was required for engineering and physics majors. When I was in grad school at Dartmouth, they introduced it earlier in a linear algebra course. I taught the last linear algebra course that did that, the next quarter they took proofs out of it.

wutbrodo 10y ago
Hm interesting. My undergrad degree at Berkeley was pretty much solely the professor running through proof after proof, and our homework was more proofs. It actually suited me just fine, it was one of the few curricula in my life that I found presented any challenge. My impression was that it worked fine for the majority of the other students as well, but I don't have tons of data on that or anything.
- btilly 10y ago
  I'm not surprised that Berkeley is an outlier in this regard. Talk to people who went to other universities and I'm confident that you'll find my experience to be more common.
deleted 10y ago
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