Timeline for Is Galois theory necessary (in a basic graduate algebra course)?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 2, 2010 at 7:51 | comment | added | Charles Matthews | @Andrew L: Certainly. But the trouble in such discussions (apart from the fact that such a course is probably also remedial for students who, perhaps for no fault of their own, have not learned much as an undergraduate of core 20th century mathematics) is that if people saying "noncommutative geometry" engage in debate with people saying "quintics are not solved by radicals", where does the pedagogic truth lie? Mathematical fashion does vary. But matrices aren't going to start to commute, and not all modules are free, and Riemann surfaces (per Victor) are still a testbed of what we understand. | |
| Aug 2, 2010 at 7:43 | history | edited | Charles Matthews | CC BY-SA 2.5 |
typo
|
| Aug 2, 2010 at 1:53 | comment | added | Victor Protsak | The usual statements of Galois theory for fields may not seem relevant for algebraic topology, but its methods are akin to the fundamental group-covering spaces line of development in AT (with monodromy group providing a direct connection). | |
| Aug 1, 2010 at 22:48 | comment | added | The Mathemagician | Part of the problem here is the enormous growth of the importance of algebra in other areas of mathematics since the 1950's. I doubt half the areas of mathematics that have either been created or undergone serious development since then-such as noncommutative geometry and modern deformation theory-could even be EXPRESSED without a mastery of a huge-and very nonspecific-chunk of the machinery of abstract algebra.So the question of what mathematicans need to know about algebra these days before beginning thesis research is a difficult one indeed. | |
| Aug 1, 2010 at 21:35 | history | answered | Charles Matthews | CC BY-SA 2.5 |