Timeline for Self-taught undergrad math: ordering of topics?
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14 events
| when toggle format | what | by | license | comment | |
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| Feb 22, 2011 at 15:41 | comment | added | Unknown | ...continued. If you wish to continue up the ladder of math education, I still believe that you have to find ways to certify your present learning( a +ve addition to your grad school application)... | |
| Feb 22, 2011 at 15:40 | comment | added | Unknown | @Mathmoggy, I have had experiences of learning some subjects just on my own b4 I came to Uni. Experience tells me that having somebody guide you as a mentor(or at least a competitive friend) is one of the best ways to get yourself into commitment and to comply with your preplanned program. However,what ever method you use to learn math, you (and I) should ALWAYS experiment with 2 or more exercises for any new math concept you(and I) learn. Continued... | |
| Feb 22, 2011 at 12:59 | comment | added | Peter Arndt | If you want to teach yourself besides a day job, then following all strands in parallel might a bit much. If it motivates you more you can choose a single of the strands to start with, or follow an approach which is motivated more by content, as those proposed here (especially the number theory strand will lead you to all the things you mentioned above): math.stackexchange.com/questions/5018/… | |
| Feb 22, 2011 at 0:54 | vote | accept | mathmoggy | ||
| Feb 22, 2011 at 0:32 | answer | added | Javier Álvarez | timeline score: 7 | |
| Feb 21, 2011 at 22:52 | comment | added | mathmoggy | @solomon: I wish! I could open a whole discussion (but won't) on the complete dearth of online/distance ed math degrees... you'd think that a subject that exists in an almost-entirely abstract domain would be a great candidate for teaching methods that don't involve quitting the day job, but no... | |
| Feb 21, 2011 at 22:28 | comment | added | Unknown | I think you could cover more(in short period of time) if you can enrol in some good college or if you can audit these courses in a nearby institution. | |
| Feb 21, 2011 at 21:44 | comment | added | mathmoggy | Wow... thanks for all comments; I have no re-tagging rights, I had to pick something, and math ed was closest. Agree with cyclical nature or math learning, but a newb has to enter the cycle somewhere! :-) Thanks Yemon about advice not to have too rigid a structure. Thx for some high-level corrections to my very newbie tree... | |
| Feb 21, 2011 at 21:42 | comment | added | Michael Hardy | "analysis -> complex variables" makes exactly as much sense as "analysis -> calculus", for the same reasons. There are approaches to teaching complex variables that are informal in the same way in which first-year calculus is, and they can make sense to the same extent that a first-year calculus course can. | |
| Feb 21, 2011 at 21:12 | comment | added | Yemon Choi | By the way, I am not sure that this really warrants the tag "mathematics-education", which I always thought was more to do with pedagogy rather than requests about learning | |
| Feb 21, 2011 at 21:11 | comment | added | Yemon Choi | My personal view is the the four streams you have identified are, to some extent, artifacts of the way you are learning things, or being taught them, and the fact you have not seen very much of the vast body of mathematical knowledge that has been developed over many years. For a start, professional number theorists know a lot of abstract algebra and ideas from algebraic topology. So I would counsel against having a rigid plan, because you will find during your mathematical development that your views and diagnoses may change | |
| Feb 21, 2011 at 21:09 | comment | added | Thierry Zell | In (4), you forgot Multivariate calculus -> Probability -> Statistics. More seriously, the nice thing about math is that you don't get a tree, but a graph that does contain many cycles. So many orderings of topics will yield a feasible plan of study (though finding textbooks that match this order will be trickier). | |
| Feb 21, 2011 at 21:07 | comment | added | Owen Sizemore | Just to comment on 2). It depends on what you mean by topology. If you mean point-set topology (as is often the first seen) then it is much closer to analysis. While algebraic topology is of course closer to algebra. Also manifold theory (differentiable top) you should definitely have familiarity with multi variable calc and linear algebra | |
| Feb 21, 2011 at 20:57 | history | asked | mathmoggy | CC BY-SA 2.5 |