Timeline for The role of the mean value theorem (MVT) in first-year calculus
Current License: CC BY-SA 2.5
8 events
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| Jul 13, 2010 at 15:12 | history | edited | Deane Yang | CC BY-SA 2.5 |
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| Jul 12, 2010 at 15:20 | comment | added | Deane Yang | Franklin, I see from your CV that you grew up in a country that probably has much better math education than in the US (I'm serious). On top of that, you participated in math olympiad competitions, so my guess is that you went to one of the better schools in your country. So I now believe your assertions regarding secondary schools you are familiar with, but I can assure you that at most only a handful of American schools teach math like this. | |
| Jul 12, 2010 at 15:09 | comment | added | Deane Yang | 1) Could you tell me the rigorous definition of $x$ degrees, for each real number $x$, that is taught in the secondary schools you know? 2) I'm also curious about how the number $e$ is defined in the secondary schools you know. (In my experience the vast majority of students understand $e$ very poorly both before and after they take calculus) | |
| Jul 12, 2010 at 4:53 | history | made wiki | Post Made Community Wiki by S. Carnahan♦ | ||
| Jul 11, 2010 at 18:56 | comment | added | O.R. | Well, even $e$ and $log$ are defined in secondary school (again time and place dependent). The ultimate reason for the treatment is again about examples about the power of the formalism of the real numbers. If $e$ and $log$ are the ones that are used is one, because they are objects that play a more central role in calculus than angles (which would only appear in applications [notice that you don't need angles to talk about $sin$ and $cos$]) and for the sake of examples one chooses some (the most appropriate), not all of the possible ones. I repeat the angles is not a very good example. | |
| Jul 11, 2010 at 17:53 | comment | added | Deane Yang | We all learn about degrees in secondary school, but I disagree that we learned how to define it rigorously. What we learned, at best, was a rigorous definition of a rational multiple of 360 degrees. | |
| Jul 11, 2010 at 17:36 | comment | added | O.R. | I agree with the above, but the degrees and radians is not a very good example, students are supposed to be using them long before taking calculus. Depending on the country and time, that is something you learn around primary school, rigorously. | |
| Jul 11, 2010 at 17:17 | history | answered | Deane Yang | CC BY-SA 2.5 |