Timeline for Interesting applications (in pure mathematics) of first-year calculus
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Aug 11, 2010 at 11:50 | comment | added | Jose Brox | Can you give some references for derivatives of polynomials over general rings? (The stranger, the better). Thanks! | |
| Aug 10, 2010 at 21:11 | comment | added | KConrad | To avoid any misunderstanding, I am not suggesting the formal defn. of derivative should come first in teaching, since of course the real derivative in calculus provides extra geometric intuition. | |
| Aug 10, 2010 at 21:09 | comment | added | KConrad | Two comments. First, I don't agree that it is "much easier" to use the limit defn. of the real derivative to prove differentiation rules than it is to use induction for proving the same rules on polynomials over any (comm.) ring. Second, it is not legitimate to argue that the formal derivative was introduced only after calculus was developed. The formal derivative on real polynomials came first! See J. Grabiner, "The Changing Concept of Change: the Derivative from Fermat to Weierstrass," Math. Magazine 56 (1983), 195-206. On JSTOR this is at jstor.org/stable/2689807 | |
| Aug 10, 2010 at 19:21 | history | answered | David Corwin | CC BY-SA 2.5 |