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I have recently finished my higher maths in Scotland which is equivalent to A-Level maths in the uk or APs in the USA (I think).

I want to concentrate fully on geometry and trigonometry so I don't think I want to do a maths degree, but I would like to concentrate solely on these subjects.

Can anyone recommend any courses online that I can use to further my knowledge?

dagda1
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  • Please don't ask this type of questions here.While reviewing posts for quality we have different types or criterion for which posts are closed as off-topic for this site.One such criterion is -"Primarily opinion based-Author is asking for personal advice on career path etc. "..your question will soon be closed under that criterion. – Soham Jul 13 '16 at 07:14
  • ho very helpful. really thank you' for being unfriendly and pedantic. I'm stunned – dagda1 Jul 13 '16 at 07:16
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    @tatan: As far as I can see this is not really a "career" question, but a question about how to progress with mathematics as a hobby outside formal education. It's not clear to me that this is covered by the not-welcome-here consensus. In particular, the consensus is based on the fact that people who're actually students will get better help by asking advisors and faculty at their institution, but in this case there's no institution to punt to. – hmakholm left over Monica Jul 13 '16 at 07:21
  • @HenningMakholm NO problem...if you think my comments are inappropriate,I am deleting them... – Soham Jul 13 '16 at 07:22
  • @tatan: I think your comments are wrong. That doesn't necessarily make them "inappropriate" -- but in general even where a question is off-topic (but still honestly asked) it is better to phrase the comment not as "go away!" but as "unfortunately you can't get a good answer to that here because ..." – hmakholm left over Monica Jul 13 '16 at 07:26
  • Modern algebra is strictly related to linear algebra, so you should start to study it first. Alternatively, I suggest you to read this book : in here there is no linear algebra at all. – Crostul Jul 13 '16 at 07:27

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You may be able to find material that "concentrate fully on geometry and trigonometry", but I don't think it's a good idea to limit your focus so absolutely. Everything in mathematics is connected ... okay, that is too strong, but many things in mathematics are connected, and if your goal is understanding, then you shouldn't spurn other areas that might give valuable insight into your areas of interest.

To start with, your trigonometry will be crippled without some complex analysis. And for geometry in general, linear algebra is indispensable. If you want to study the symmetries of geometric figures, that leads to group theory. Geometry generalizes to algebraic geometry, for when straight lines and circles begin to get boring (plenty of higher algebra enters then), and differential geometry, for geometry on curved surfaces (which depends on calculus and a whole slew of additional linear algebra). And of course we can't forget the utility of calculus for solving optimization problems and determining areas and volumes.

As a hobbyist, of course, nobody says you need to attack all that at once. And it is fine, to begin with, to follow your interest that leads in a particular direction now; just don't make it harder for yourself by deciding too firmly that this is the only direction you want to go in ever.

Still, be careful about thinking that the nice cut-and-dried headings that mathematics is presented under at the secondary education level necessarily reflect a deeper division in mathematics. Among your two choices "geometry" is certainly an area of study, but "trigonometry" is not really a coherent whole beyond the high-school curriculum. Generalizations and applications of high-school trigonometry abound, of course, but they don't fit into a crisply delineated area of "advanced trigonometry" that it makes sense to study on its own.

hmakholm left over Monica
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