Timeline for Interesting results in algebraic geometry accessible to 3rd year undergraduates
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| Aug 31, 2016 at 23:30 | comment | added | KConrad | @TheNumber23 stereographic projection is $\mathbf P^1(\mathbf C)$, and the projective plane is $\mathbf P^2(\mathbf R)$. The interpretation of asymptotes to real algebraic curves in $\mathbf R^2$ as tangent lines to missing points on the curve that you can find in $\mathbf P^2(\mathbf R)$ does not work if you extend the plane by just one point with stereographic projective: different asymptotes are typically tangent lines to different missing points that are revealed in $\mathbf P^2(\mathbf R)$. | |
| Aug 31, 2016 at 22:04 | comment | added | TheNumber23 | @KConrad In what sense is the projective plane a better extension of the plane than sterographic projection? In particular what reasons would any of these students understand? | |
| Nov 21, 2015 at 16:57 | history | edited | KConrad | CC BY-SA 3.0 |
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| Jul 12, 2010 at 20:55 | comment | added | David Corwin | @KConrad: These days, I think it's common to call Michael Artin's Algebra a classic. There also is some introductory material to algebraic geometry, so I assume he is talking about that. | |
| Apr 4, 2010 at 12:03 | comment | added | Dror Speiser | @Franz: Solving quadratic equations appears in Diophantus' Arithmetica. | |
| Apr 3, 2010 at 21:32 | history | edited | KConrad | CC BY-SA 2.5 |
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| Apr 2, 2010 at 21:56 | history | edited | KConrad | CC BY-SA 2.5 |
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| Apr 2, 2010 at 18:32 | history | edited | KConrad | CC BY-SA 2.5 |
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| Apr 2, 2010 at 15:31 | comment | added | Anonymous | KConrad's answer is great! | |
| Apr 2, 2010 at 12:35 | comment | added | Franz Lemmermeyer | I don't think the ancient Greeks solved quadratic equations; perhaps you mean the Babylonians? | |
| Apr 2, 2010 at 9:48 | vote | accept | ifk | ||
| Apr 2, 2010 at 9:48 | vote | accept | ifk | ||
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| Apr 2, 2010 at 9:47 | vote | accept | ifk | ||
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| Apr 2, 2010 at 6:35 | comment | added | KConrad | I don't think Emil Artin ever wrote a book called ALGEBRA, and I think Michael Artin's book ALGEBRA is too comparatively recent to be called a classic (but maybe that just makes me look old). Since you refer to geometric algebra ideas, could you mean Emil Artin's Geometric Algebra? No, I don't think topics in there would encourage someone to want to study algebraic geometry. Maybe you mean Michael Artin's book after all. | |
| Apr 2, 2010 at 6:24 | comment | added | The Mathemagician | LOTS of good suggestions here,KConrad.I can also suggest you look at Artin's classic ALGEBRA for more geometric algebra ideas for your students to mine. | |
| Apr 2, 2010 at 6:19 | history | edited | KConrad | CC BY-SA 2.5 |
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| Apr 2, 2010 at 6:06 | history | edited | KConrad | CC BY-SA 2.5 |
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| Apr 2, 2010 at 5:55 | history | answered | KConrad | CC BY-SA 2.5 |