Timeline for Place of Analytic geometry in modern undergraduate curriculum
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 30, 2017 at 6:47 | comment | added | Peter Heinig | The first systematic treatment of analytic geometry over countable extension of $\mathbb{Q}$, which I think are "worth studying for a modern math major", in particular in the age of electronic computers, is sometimes credited to Hilbert's 1899 'Grundlagen der Geometrie'. | |
| Aug 30, 2017 at 6:47 | comment | added | Peter Heinig | It seems not irrelevant to mention the (in undergraduate education at least) very underappreciated fact that a whole new world opens up if one does "analytic geometry" over countable field extensions of $\mathbb{Q}$ such as $\mathbb{Q}(\{\sqrt{a}\colon a\in\mathbb{Z}, a>0\})$, or over $\mathbb{Q}(\{\sqrt{a^2+b^2}\colon a,b\in\mathbb{Z},a,b>0\})$. Then, new algorithmic questions of constructibility arise. | |
| Aug 30, 2017 at 5:51 | history | edited | Martin Sleziak | CC BY-SA 3.0 |
removed deprecated (geometry) tag - see the tag info: http://mathoverflow.net/tags/geometry/info; if there are some other geometry-related tags which are suitable, please use some of them instead
|
| Mar 28, 2011 at 17:26 | comment | added | Mariano Suárez-Álvarez | @Pete, well, more generally, we should start a campaign to vanish the word Introduction from titles! | |
| Mar 28, 2011 at 17:17 | comment | added | Pete L. Clark | @K: right. I still get a little embarrassed when I go to a cafe and place my copy of Jacobson's Basic Algebra II on the table... | |
| Mar 28, 2011 at 16:39 | comment | added | KConrad | It's just like the word "algebra", which is used today with very different meanings at the high school level and more advanced level. | |
| Mar 28, 2011 at 15:52 | comment | added | Pete L. Clark | @unknowngoogle: When research mathematicians say "analytic geometry", I expect them to be talking about complex (or rigid-, or Berkovich-, or...) analytic spaces, yes. But I wouldn't say the same about college freshmen. | |
| Mar 28, 2011 at 15:13 | comment | added | Qfwfq | [BTW, I think the term "analytic geometry" used to denote geometry-done-with-coordinates is an old fashioned one, as nowadays the term "analytic geometry" tends to refer to the geometry of complex (i.e. holomorphic) manifolds and complex spaces...] | |
| Mar 28, 2011 at 11:22 | answer | added | Bananeen | timeline score: 1 | |
| Mar 28, 2011 at 9:22 | answer | added | Pete L. Clark | timeline score: 7 | |
| Mar 28, 2011 at 9:04 | comment | added | Pete L. Clark | Using Harvard's Math 55 as an example of what the typical American freshman math major is learning is sort of like using Buckingham Palace as an example of where the typical London resident is living. It's the reality for some people, but certainly not the majority. | |
| Mar 28, 2011 at 8:48 | answer | added | KConrad | timeline score: 11 | |
| Mar 28, 2011 at 8:31 | answer | added | Charles Matthews | timeline score: 5 | |
| Mar 28, 2011 at 8:26 | comment | added | KConrad | Aaron, he wasn't saying math majors only study real analysis and linear algebra, but that this is the focus of the freshman year standard course for the well-prepared math students. That's true at Harvard, MIT, Princeton, and other places. Complex analysis, algebraic topology, etc. usually come later. | |
| Mar 28, 2011 at 7:46 | history | edited | Dmitry | CC BY-SA 2.5 |
added 9 characters in body
|
| Mar 28, 2011 at 7:35 | comment | added | Aaron Mazel-Gee | Math majors in the US don't just study algebra and real analysis! There's complex analysis, differential/Riemannian geometry, number theory, perhaps some point-set and/or algebraic topology... I think the main point of the statement (about "concrete representation") is that you could study linear algebra completely abstractly, but in fact one can very often illustrate/reformulate its statements as facts about linear maps on $\mathbb{R}^n$. But the methods and ideas in analytic geometry really do belong more properly to calculus. | |
| Mar 28, 2011 at 7:20 | history | asked | Dmitry | CC BY-SA 2.5 |