Timeline for If I take Modern Analysis next year, will I be prepared to teach multivariable/vector calculus?
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19 events
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| Feb 26, 2023 at 22:47 | comment | added | KCd | Since you're asking how knowing more advanced analysis will help you teaching a calculus course, the answers on the page matheducators.stackexchange.com/questions/15237/… might interest you. | |
| Feb 25, 2023 at 4:41 | comment | added | James S. Cook | An efficient method to see how to teach multivariate calculus is to watch others do just that. I've learned much from videos on You Tube from various folks, I think Edward Frenkel's videos from multivariate calculus on Lagrange multipliers were very nice. Of course, keep in mind the target audience for the video your watching. Fwiw I have complete lecture series of Calculus III and Advanced Calculus (with a differential forms/ calculus on normed linear spaces... and more) posted on my You Tube channel. Lot's of folks have lots posted these days. | |
| Feb 24, 2023 at 19:53 | answer | added | obscurans | timeline score: 5 | |
| Feb 24, 2023 at 15:16 | comment | added | blakedylanmusic | @JochenGlueck yes, usually that’s how the 600 level sequences go, a few of the topics are picked out of a big list of topics based on the instructor’s discretion. So it makes sense that covering all of this would be impossible. | |
| Feb 24, 2023 at 11:01 | comment | added | Dave L Renfro | @Jochen Glueck: Now that you mention it, this does seem to be way, way too broad of a list of topics for a single course. Moreover, given the size of the graduate program there, it's even more likely (in my view) that this is, as you say, simply a smorgasbord list of topics in analysis (likely not exhaustive either) among which one could be selected, according to the interests of the instructor and expected students. | |
| Feb 24, 2023 at 10:46 | comment | added | Jochen Glueck | I can't know for sure of course, but it seems likely that the course description is just some boilerplate list of suggestions, and the individual instructor decides what actually ends up in the course. Each of the topics in the list would be sufficient to fill half a year on its own just for an introduction. I also agree with other comments that the topics on the list are very diverse (but if you happen to really meet someone who works both with ordered vector spaces and Lie groups, please send me their name - I would be very interested to check out their work). | |
| Feb 24, 2023 at 3:22 | answer | added | Timothy Chow | timeline score: 16 | |
| Feb 23, 2023 at 23:13 | answer | added | guest troll | timeline score: 3 | |
| Feb 23, 2023 at 20:36 | history | became hot network question | |||
| Feb 23, 2023 at 20:34 | comment | added | Dave L Renfro | If you have the opportunity to tutor people for the course, then this is excellent additional preparation, maybe more than trying to master C. H. Edwards (let alone more advanced stuff). Indeed, if you're able to do a lot of tutoring, you probably only need to work though something like Vector Calculus by Marsden/Tromba (any edition), saving something like C. H. Edwards for when you're actually teaching the course (not necessarily to help with teaching the course, but for your own elucidation of the material you're teaching). | |
| Feb 23, 2023 at 20:12 | vote | accept | blakedylanmusic | ||
| Feb 23, 2023 at 20:10 | comment | added | blakedylanmusic | @DaveLRenfro Thank you, I’ll be sure to read the C.H. Edwards! I wonder also if finding opportunities to tutor people taking that course would help me get a refresher and get practice teaching it. It’s certainly helped me get a refresher on other topics when I tutored for them too. | |
| Feb 23, 2023 at 18:15 | comment | added | Dave L Renfro | (returning two hours later) Of the books I listed, probably the most helpful for your later teaching is C. H. Edwards or Fleming, as the others are in my opinion more theoretically oriented than is optimally helpful for your needs. Of these two, I'd go with C. H. Edwards, since Fleming gets into Leb. integration and is less computationally oriented than C. H. Edwards. Incidentally, you'll want to be sufficiently "computationally oriented" so that you don't fall for the paradox I describe in this 20 May 2001 sci.math post. | |
| Feb 23, 2023 at 16:05 | comment | added | Dave L Renfro | OR Advanced Calculus: A Differential Forms Approach by H. M. Edwards (1994) OR Functions of Several Variables by Wendell Fleming (1977) OR Advanced Calculus by Loomis/Sternberg (1968/1990) OR Advanced Calculus by Nickerson/Spencer/Steenrod (1959/2011) OR others at what I'd call an "honors advanced calculus" level. | |
| Feb 23, 2023 at 16:05 | comment | added | Dave L Renfro | I realize that you're probably constrained in what you can take, but my feeling is that things like nonlinear analysis (@Steven Gubkin: probably means "nonlinear functional analysis"), ordered vector spaces, etc. will not help much for subject matter (not a good fit for what you actually need to know) or mathematical maturity (huge overkill to the point of diminishing returns). Best would be some kind of stiff 2-semester advanced calculus course such as would use Advanced Calculus of Several Variables by C. H. Edwards (1973/1994) (continued) | |
| Feb 23, 2023 at 15:11 | comment | added | blakedylanmusic | @StevenGubkin This will cover an entire school year so it makes sense that there are a lot of topics. That being said, usually for these 600 level courses the topics that are actually taught are up to the teacher (from what I’ve heard). | |
| Feb 23, 2023 at 14:39 | comment | added | Steven Gubkin | I am not sure what they mean by "nonlinear analysis". Harmonic Analysis will deal with things like the Fourier Transform which could be single-variable, multivariable, or done on topological groups. Analytic functions of one complex variable require understanding multivariable calculus of 2 real variables. Not sure about ordered vector spaces. Analysis on Lie groups will require a lot of multivariable calculus on differentiable manifolds. Operator theory is essentially infinite dimensional linear algebra. Seems like a lot of different topics in one course! | |
| Feb 23, 2023 at 11:10 | answer | added | Steven Gubkin | timeline score: 18 | |
| Feb 23, 2023 at 9:23 | history | asked | blakedylanmusic | CC BY-SA 4.0 |