Timeline for There must be a good introductory numerical analysis course out there!
Current License: CC BY-SA 3.0
22 events
| when toggle format | what | by | license | comment | |
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| Mar 1, 2016 at 20:22 | answer | added | Ryan Budney | timeline score: 3 | |
| Jan 29, 2016 at 22:19 | answer | added | Lauren Jatana Vathje | timeline score: 4 | |
| Oct 22, 2015 at 20:48 | answer | added | Anita Faul | timeline score: 4 | |
| Jun 14, 2011 at 2:45 | answer | added | Orr Shalit | timeline score: 5 | |
| May 24, 2011 at 16:50 | vote | accept | Nilima Nigam | ||
| May 24, 2011 at 6:49 | answer | added | Ryan Budney | timeline score: 11 | |
| May 20, 2011 at 16:35 | vote | accept | Nilima Nigam | ||
| May 24, 2011 at 16:50 | |||||
| S May 20, 2011 at 16:35 | vote | accept | Nilima Nigam | ||
| May 20, 2011 at 16:35 | |||||
| May 20, 2011 at 16:35 | vote | accept | Nilima Nigam | ||
| S May 20, 2011 at 16:35 | |||||
| May 19, 2011 at 19:20 | answer | added | MRB | timeline score: 8 | |
| May 19, 2011 at 14:35 | history | edited | Nilima Nigam | CC BY-SA 3.0 |
rephrased 'rationale for...obscure' in response to Serre's comment.
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| May 19, 2011 at 14:34 | comment | added | Nilima Nigam | Dear Denis, I should edit my question to read: 'any rationale for .... is obscured in the course'. For instance, root-finding does not seem explicitly used in the algorithms for interpolation. Newton's interpolatory polynomials could be used to derive differencing formulae, but instead the latter are typically introduced via Taylor series. One could introduce the ODE methods directly after numerical integration and interpolation, postponing quadrature until discussions of measures of error and reconstruction. | |
| May 19, 2011 at 8:18 | answer | added | Michael Kissner | timeline score: 12 | |
| May 19, 2011 at 7:43 | history | edited | Pete L. Clark | CC BY-SA 3.0 |
deleted 38 characters in body
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| May 19, 2011 at 6:53 | comment | added | Denis Serre | Did you have a look to M.Schatzman's book ? By teh way, I disaggree with your statement that "any rationale ... is obscure". At least, root-finding,interpolation by polynomials, quadrature, numerical differentiation must be taught in this order because each topic uses the previous ones. | |
| May 19, 2011 at 4:37 | comment | added | Brian Borchers | One problem in teaching such courses is that neither group (engineering students or mathematics majors) is likely to have an adequate background in computer science. This makes it extremely difficult if not impossible to talk about computational complexity in such a course. It also makes it hard to do much practical work on problems of real world size and scope. | |
| May 19, 2011 at 3:45 | comment | added | Nilima Nigam | Zen, I'd aver that some deep ideas are well within the reach of these students. For example, most of them have seen Fourier series in their PDE courses, and are thus familiar with notions of projection and convergence. Orthogonality is also familiar as a concept. A numerical analysis course would be a neat place to introduce the importance of these notions in the construction of algorithms. There are indeed fundamentally better algorithms out there, some of which we should be introducing earlier. Why wait before describing the FFT? | |
| May 19, 2011 at 3:08 | comment | added | Zen Harper | Is it the case that all the "truly deep and interesting aspects" of numerical analysis are too complicated, or long, to explain in an ordinary course? e.g. how do meteorologists/computational physicists/etc. solve huge systems of equations? Is it really just using the same algorithms that we see in the books, but with expensive supercomputers, or are there fundamentally better techniques which are too difficult to cover? | |
| May 19, 2011 at 2:53 | answer | added | Igor Rivin | timeline score: 3 | |
| May 19, 2011 at 2:50 | comment | added | Nilima Nigam | Thanks- the notes by Iserles are indeed lovely, and are aimed at the students preparing for the Cambridge Tripos. | |
| May 19, 2011 at 2:44 | comment | added | Yemon Choi | I am not really qualified to judge, but do any of the notes at damtp.cam.ac.uk/user/na/na.html do some of what you hope for? | |
| May 19, 2011 at 2:39 | history | asked | Nilima Nigam | CC BY-SA 3.0 |