Timeline for Teaching and students
Current License: CC BY-SA 2.5
11 events
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| Jun 28, 2022 at 4:06 | comment | added | Martin Sleziak | The link math.uga.edu/~pete/expositions.html no longer works - the page has been moved here: alpha.math.uga.edu/~pete/expositions2012.html. Still, if you're interested in the Real Analysis II mentioned in the post, probably it is better to look at the Wayback Machine snapshot from the time when this answer was posted. | |
| Jun 22, 2022 at 8:14 | history | edited | CommunityBot |
replaced http://www.math.uga.edu/~pete with http://alpha.math.uga.edu/~pete
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| Jan 25, 2010 at 8:14 | comment | added | Andrew Stacey | I like almost all of this answer except the insinuation that it is better to teach advanced topics than lower-level ones. Absolutely not! The lower-level ones are where you can hook the students and show them that mathematics is something far beyond the dull stuff they learnt in school. By the time you get to the advanced courses, it's too late - the ones that might have been mathematicians but never realised it have gone on to be something else. Because the material itself is something you almost don't have to think about any more, you can concentrate so much more on how to communicate it. | |
| Jan 22, 2010 at 17:53 | comment | added | Harry Gindi | Nevermind. I was talking about something entirely unrelated having not read your entire post, and the sarcasm was poking fun at Bourbaki. | |
| Jan 22, 2010 at 14:04 | comment | added | Pete L. Clark | @Harry: I do not follow your comment -- there is no homeomorphism between Q with the p-adic topology and Q with the p'-adic topology that respects the group structure. And, once again, please do not make comments with a sarcastic tone or which could be reasonably construed as being nasty. | |
| Jan 22, 2010 at 6:47 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
copyediting
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| Jan 21, 2010 at 19:16 | comment | added | Pete L. Clark | Homeomorphic? Sure. (I'm not sure how much easier that is to prove than the question itself, since there also nonterminating but repeating expansions.) After I wrote this message, I came up with the following amusingly ridiculous map that I think is a homeomorphism: regarding the positive rationals as the free abelian group generated by the primes, just consider the map which interchanges p and p'! Anyway, this is not really the point: I wouldn't come back and tell my class about this, because we have more important things to discuss, and they are capable of exploring this on their own. | |
| Jan 21, 2010 at 18:24 | comment | added | Qiaochu Yuan | Aren't the rationals equipped with the p-adic topology always homeomorphic to the subset of the Cantor set whose decimal expansions terminate? (That would be my guess, anyway.) | |
| Jan 21, 2010 at 3:34 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
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| Jan 21, 2010 at 3:22 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
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| Jan 21, 2010 at 3:15 | history | answered | Pete L. Clark | CC BY-SA 2.5 |