Order of learning maths and problem solving

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:

Number theory:

1)Finish the proof of quadratic reciprocity

2)Continued fractions

3)Learning about fields,rings in solving diophantine equations.

Combinatorics:

1)Probability

2)More graph theory

3)Order theory

4)Marriage lemma

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.

Algebra:

1)Do practice problems on trigonometry

2)Basic Calculus

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)

4)Conics

Geometry:

1)Transformations

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?

N.B:

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.

#ProblemSolving #SelfImprovement

Note by Rahul Saha
6 years, 4 months ago

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Comments

Great list!

Once you learn about these topics, please help us out by adding to the wiki pages. Marriage lemma could use some explanation, so that the applications page would be more easily understood. Similarly for my generating functions - linear recurrences page, which could use many more examples / approaches.

Calvin Lin Staff - 6 years, 4 months ago

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That's exactly where the problem is.Every time I try to learn the Marriage lemma in a more in-depth way,my mind tells me that the lemma is related to graph theory.So I begin to learn graph theory in a more in-depth way,and then I remember that I didn't complete the proof of Van Ore's theorem.So I go to Van Ore's theorem,and then midway through the proof,I find some other problem and then move on to some other thing.This is just an example.

I am getting frustrated with this.How do I manage this?In what order should I learn things?How do I maintain my concentration on a particular math subject?

Rahul Saha - 6 years, 4 months ago
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