Timeline for Sophisticated treatments of topics in school mathematics
Current License: CC BY-SA 4.0
41 events
| when toggle format | what | by | license | comment | |
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| Feb 21, 2023 at 3:22 | history | edited | Timothy Chow | CC BY-SA 4.0 |
Added link to LaTeX version of James Dolan's posts
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| Aug 18, 2022 at 18:24 | history | edited | Timothy Chow | CC BY-SA 4.0 |
Added link to old USENET posts
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Dec 11, 2015 at 7:43 | review | Close votes | |||
| Dec 11, 2015 at 13:10 | |||||
| Dec 11, 2015 at 7:41 | comment | added | Daniel Moskovich | Federico: Thanks. I'm asking something much stronger of course, more like for examples where "sophisticated concepts give me a new way to look at school concepts". The examples given in the body of the quesion and the (great!) trigonometry answers are the kind of examples I sought- also there were some nice arithmetic answers. Also, from my POV calculus is quite borderline- as you hint, school calculus is a teaser for a more advanced subject. | |
| Dec 11, 2015 at 7:29 | comment | added | Federico Poloni | I don't understand what you are asking here. Do you mean "which result of advanced mathematics contains an elementary topic as a special case?" Then, almost all of analysis would refer to calculus, and almost all of geometry would refer to Euclidean geometry, since these are the easiest examples that fit in their framework. Otherwise, what is the kind of relation between an elementary and a non-elementary concept that you are looking for? | |
| Dec 11, 2015 at 2:14 | comment | added | Matt Samuel | In the seventeenth century, the product rule for derivatives was brilliant, research level work. Just saying. | |
| Dec 10, 2015 at 19:11 | answer | added | Mikhail Katz | timeline score: 14 | |
| Dec 9, 2015 at 2:45 | comment | added | Benjamin Dickman | Maybe an example is captured by the notion of "simplifying" as discussed in MO 126519? | |
| Dec 8, 2015 at 17:03 | answer | added | Timothy Chow | timeline score: 29 | |
| Dec 8, 2015 at 13:03 | answer | added | Todd Trimble | timeline score: 14 | |
| Dec 8, 2015 at 11:19 | comment | added | YCor | "school mathematics" sounds fine! | |
| Dec 8, 2015 at 8:06 | answer | added | Stella Biderman | timeline score: 2 | |
| Dec 8, 2015 at 5:38 | history | edited | Daniel Moskovich | CC BY-SA 3.0 |
K-12 changed to "school" in the title
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| Dec 8, 2015 at 5:37 | comment | added | Daniel Moskovich | YCor : Compromise suggestion- "school mathematics"? I've edited it to that- please feel free to edit again if you have a better suggestion. Note that it's a nontrivial point- there have been answers whose idea both of "elementary" and of "sophisticated" is different from what was meant in the question. | |
| Dec 8, 2015 at 0:48 | answer | added | truebaran | timeline score: 3 | |
| Dec 7, 2015 at 23:05 | answer | added | foliations | timeline score: 6 | |
| Dec 7, 2015 at 22:48 | answer | added | PhD | timeline score: 8 | |
| Dec 7, 2015 at 22:16 | answer | added | Julian Rosen | timeline score: 82 | |
| Dec 7, 2015 at 22:12 | comment | added | YCor | I edited K-12 to elementary in the title since K-12 is not universal, but US inner language. The OP claims that elementary is subjective which is possible, but anyway the title is supposed to give a vague information, and K12 is not vague information, but empty information to any user not acquainted with US gibberish. | |
| Dec 7, 2015 at 19:23 | comment | added | Daniel Moskovich | Sebastian Goette: archives.math.utk.edu/k12.html#topics K-12 means primary and secondary school. I don't know the precise curriculum in the US either, but I imagine it's roughly the same everywhere... Please feel free to read "K-12" as "from kindergarten until the end of high school". | |
| Dec 7, 2015 at 19:23 | answer | added | Sebastian Goette | timeline score: 15 | |
| Dec 7, 2015 at 19:20 | comment | added | Sebastian Goette | Could you exand on "USA K-12" please? Does this mean the last class in high school? What do you teach there? Please excuse my ignorance. | |
| Dec 7, 2015 at 16:38 | answer | added | Timothy Chow | timeline score: 5 | |
| Dec 7, 2015 at 16:34 | answer | added | Timothy Chow | timeline score: 15 | |
| Dec 7, 2015 at 14:37 | history | made wiki | Post Made Community Wiki by Ben Webster♦ | ||
| Dec 7, 2015 at 13:23 | comment | added | Steve Huntsman | 76888math106.wordpress.com/category/extra-credit | |
| Dec 7, 2015 at 11:25 | history | rollback | Daniel Moskovich |
Rollback to Revision 3 - Rollback: "Elementary" is subjective and I'm afraid it will lead to the wrong kind of examples. I'm not American, but I don't think K-12 is an obscure term. Thanks for the edit though.
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| Dec 7, 2015 at 11:16 | answer | added | Pietro Majer | timeline score: 2 | |
| Dec 7, 2015 at 10:24 | history | edited | YCor | CC BY-SA 3.0 |
changed K12 into elementary in title (K12 is an obscure term outside US)
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| Dec 7, 2015 at 10:02 | answer | added | Gerry Myerson | timeline score: 21 | |
| Dec 7, 2015 at 10:01 | answer | added | Qiaochu Yuan | timeline score: 73 | |
| Dec 7, 2015 at 9:49 | comment | added | Daniel Moskovich | @Qiaochu Fair enough. The primary objective of asking for references is to rule out trivial and degenerate examples (e.g. natural numbers are decategorifications of finite sets, and the Peano axioms are pretty recent, woohoo). But sure- if it's not degenerate and trivial then please feel free to post an example which doesn't have a good reference- the answer you posted is fantastic! | |
| Dec 7, 2015 at 9:45 | history | edited | Daniel Moskovich | CC BY-SA 3.0 |
link fixed
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| Dec 7, 2015 at 9:37 | comment | added | Qiaochu Yuan | I just feel like your examples are fine without the references, and that the references don't add much. Your first example is just making explicit the observation that $\mathbb{Z}_{100}$ is a nontrivial extension of $\mathbb{Z}_{10}$ by $\mathbb{Z}_{10}$. Anyone with a decent understanding of group cohomology and/or homological algebra could've made it. | |
| Dec 7, 2015 at 9:27 | answer | added | Qiaochu Yuan | timeline score: 86 | |
| Dec 7, 2015 at 9:25 | history | edited | Daniel Moskovich | CC BY-SA 3.0 |
edit added
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| Dec 7, 2015 at 9:22 | comment | added | Daniel Moskovich | Yes please. One example per answer. And yes- I'm primarily interested in cases the bar is high, such as in the two examples I gave- i.e. not trivial and obvious examples, research-level or close. There is a grey zone between these two extremes, but I'm more interested in things on the black end of that zone, and monotone less interested as it gets whiter. | |
| Dec 7, 2015 at 9:05 | comment | added | Qiaochu Yuan | Also, does "nontrivial enough to have appeared in research-level publications" mean you want us to actually give citations as in your examples? This seems like an extremely high bar to clear... | |
| Dec 7, 2015 at 8:59 | comment | added | Qiaochu Yuan | Do you want us to give separate examples in separate answers? | |
| Dec 7, 2015 at 8:54 | history | asked | Daniel Moskovich | CC BY-SA 3.0 |