Timeline for Assessing effectiveness of (epsilon, delta) definitions
Current License: CC BY-SA 3.0
7 events
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| Mar 5, 2014 at 14:04 | comment | added | Mikhail Katz | @PaulSiegel, Dawkins wrote "both at the calculus and analysis level of instructions". In the title of his section 2.3 he is merely including calculus as part of analysis and using analysis as a general term. Most of the studies he cites have to do with calculus teaching. Kleinfeld's title mentions "calculus" and Bishop is similarly talking about calculus teaching. | |
| Mar 4, 2014 at 21:04 | comment | added | Paul Siegel | @katz: Hold on, now I'm confused. The first sentence in the text of your question referred to "definitions in real analysis", and your quote from Dawkins begins with "Student difficulties with real analysis definitions." Additionally, Jake Shreffler's answer refers to "introductory analysis" classes. The question about what precise definitions should be taught in a freshman calculus class is a very different one (whose best answer is probably "none"), so if that is what you are asking you should make it clearer in your question. | |
| Mar 4, 2014 at 19:49 | comment | added | Mikhail Katz | @PaulSiegel, I don't think anybody would argue that analysis can (or should) be taught without $\epsilon,\delta$ definitions. Rather, we are talking about freshman calculus. Just as you don't construct the real line in freshman calculus, it would be inappropriate to construct the hyperreals. Rather, you define infinitesimals via violation of the Archimedean property, and show students how to work with them rigorously. In my first hand experience, they relate to this much more positively than being dressed to perform multiple-quantifier epsilontic stunts on pretense of being taught calculus | |
| Feb 28, 2014 at 12:55 | comment | added | Paul Siegel | I think it is very smart to explain how the $\epsilon$, $\delta$ definition captures Newton's and Leibniz's informal notion of an infinitessimal, but I think that actually trying to teach real analysis students about hyperreals is a very bad idea. Your choices are either to try to define things properly using non-principal ultrafilters or whatever, in which case $\delta$'s and $\epsilon$'s will look like a walk in the park; or wave your hands at the definition, which defeats the whole purpose of a real analysis class. | |
| Feb 27, 2014 at 14:37 | comment | added | Mikhail Katz | Interesting reply. Feel free to elaborate on Sato. | |
| Feb 27, 2014 at 14:13 | review | First posts | |||
| Feb 27, 2014 at 14:14 | |||||
| Feb 27, 2014 at 13:55 | history | answered | Jake Shreffler | CC BY-SA 3.0 |