Timeline for What does the generating function $x/(1 - e^{-x})$ count?
Current License: CC BY-SA 2.5
14 events
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| Apr 13, 2017 at 12:57 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Sep 29, 2015 at 15:02 | comment | added | roy smith | @Tom Copeland: Thank you for the link and the history! now i see the reference on p. 16 of the preliminary material in Hirzebruch's book. | |
| Sep 28, 2015 at 4:26 | comment | added | roy smith | i guess i am also pretty innocent of number theory, since i first encountered this series in Hirzebruch's discussion of the Todd class and its use in his Riemann Roch theorem. indeed the discussion in my notes on RRT (p.49) does not even mention Bernoulli: alpha.math.uga.edu/~roy/rrt.pdf | |
| Nov 28, 2014 at 23:39 | comment | added | abel | i am glad i teach bernoulli numbers and its generating function as an application of euler-mclaurin formulae in my calculus class. this is in the two weeks we get after ap exam. | |
| Jul 15, 2010 at 18:11 | comment | added | Victor Protsak | I would add that it's nearly impossible to learn the BCH formula (with the proof, of course) and $\mathit{not}$ to see Bernoulli numbers mentioned. There is another lesson here, possibly that one needs to read textbooks systematically rather than just pick up bits and pieces. | |
| Jun 3, 2010 at 19:16 | comment | added | Mark Meckes | I also know people who would definitely add numerical analysis and scientific computing to the list. But at this point I'm clearly getting silly and should probably be ignored. | |
| Jun 3, 2010 at 19:10 | comment | added | Mark Meckes | Of course there's a lot of room for interpretation in "real knowledge", not to mention "real analysis". Also, you seem to be thinking mainly of undergrads, whereas I was thinking of graduate school and beyond. I'd say you list the bare essentials, including one topic (NT) I sadly lack. I'd add (in no special order) differential geometry, Fourier analysis, algebraic topology (in case you only meant point-set), and differential equations. I think it'd be easy to find people who would also add logic, dynamical systems, algebraic geometry, classical mechanics, and category theory to the list. | |
| Jun 3, 2010 at 17:22 | comment | added | Pete L. Clark | @Mark: Well, I'm the only one in the room at the moment, but my suggestions are: real and complex analysis, algebra, number theory, topology, combinatorics and probability. And "real knowledge" sounds intimidating, but I did, for instance, take undergraduate courses -- or portions of courses -- on all the above topics. | |
| Jun 3, 2010 at 17:02 | comment | added | Mark Meckes | I'd certainly agree with your last suggestion (and in particular wish I knew more about number theory than I do). Next, take a roomful of mathematicians, get all their suggestions for fields that should be added to "elementary number theory" here. What would you guess is the probability that any one of the mathematicians in the room has any real knowledge of all the fields that have been named? | |
| Jan 3, 2010 at 4:29 | comment | added | Pete L. Clark | Well, certainly not only to number theory, anyway. | |
| Jan 3, 2010 at 4:19 | comment | added | Idoneal | Bernoulli numbers are fairly ubiquitous. They come up, for example, in very basic real analysis; namely in Euler-Maclaurin summation formula. So I am not sure if these numbers should be thought of as pertaining to number theory. | |
| Dec 18, 2009 at 2:52 | vote | accept | Theo Johnson-Freyd | ||
| Dec 18, 2009 at 2:50 | comment | added | Theo Johnson-Freyd | You win. I know a lot about Lie algebras, and I've never studied any number theory. I think I've seen the Bernoulli numbers once or twice, but never really encoded them. | |
| Dec 18, 2009 at 2:46 | history | answered | Pete L. Clark | CC BY-SA 2.5 |