Timeline for Balancing Rigour and Application When Teaching Generating Functions to Computer Science Students
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Sep 11 at 18:32 | comment | added | fedja | @Adam You are right. That's why I asked my first question above ;-) | |
| Sep 11 at 13:20 | comment | added | Adam | @fedja Aren't there tons of examples? e.g. most objects that are counted with labels. Now, for these you can usually pass to exponential generating functions and get a positive radius of convergence, but still. | |
| Sep 11 at 10:44 | history | became hot network question | |||
| Sep 11 at 10:13 | vote | accept | LeafGlowPath | ||
| Sep 11 at 9:58 | comment | added | fedja | Then just define them for the purposes of the course as power series with positive radius of convergence, enjoy all benefits of the theory of analytic functions in a disk, derive all formulas under this assumption, and just tell the students that "for some counting problems, the general method will result in a divergent series, in which case one will have to treat it in abstract algebraic rather than complex analytic way, but most computations will be pretty much the same" and stop there. There is nothing non-rigorous in that. You'll just restrict the applicability of the idea a bit. | |
| Sep 11 at 8:51 | answer | added | KCd | timeline score: 4 | |
| Sep 11 at 5:16 | comment | added | LeafGlowPath | Not really. But it's sort of standard thing in generating function textbooks to start by rigorously define them as formal power series. It feels a bit too hand-waving to drop them. | |
| Sep 11 at 4:10 | comment | added | fedja | Hmmm.... Do you really have many interesting applications where the radius of convergence is $0$? | |
| Sep 11 at 2:42 | history | asked | LeafGlowPath | CC BY-SA 4.0 |