Okay,so I have been intending to learn a lot of things for some time,but every time I start one of these,I wonder:Will I need it now?What's the point if I forget it?
So I proceed to a new topic,and then,the exact same thing happens.I must now confess that I haven't learnt anything new for quite some time now.I have intended to do the following things,but I just leave them midway,and then I forget about them:
1)Finish the proof of quadratic reciprocity
3)Learning about fields,rings in solving diophantine equations.
2)More graph theory
5)Generating functions in solving recurrences
6)Special numbers(Stirling numbers of 1st and 2nd kind,Catalan numbers):I have done a very basic study of both,but they seem to be ubiquitous.
1)Do practice problems on trigonometry
3)Generalized binomial theorem for negative exponents(I have not bothered with it because I think Calculus is required if I want to get a deeper insight)
That's about what I can remember.I have the following queries:
1)In what order did you learn things?
2)When you concentrate on a subject(say quadratic reciprocity) but then have an unexplained desire to leave it in order to pursue something more interesting,what do you do?
3)In what order should I learn the above things?
I of course realize that there is no correct order of learning maths.That said,there are subjects that are worth studying first if one is interested in problem solving.