What is the best way to prepare for core maths subjects in university?

[pivoxa15]

I will be doing my final, third year of undergrad next year and will be doing intro subjects to the main areas of pure maths like algebra, analysis, topology. The problem is I have not done well in second year maths and don't feel I understand the material. However, I really like to do well in these core subjects next year. What should I do to prepare for them?

Should I mostly concentrate on:
1) Starting next year's material early
2) Review 1st and 2nd year maths hence do them again
3) Do high school maths competition problems (I always did poorly in those) hence increase my general mathematical thinking and problem solving ability in the hope of being able to pick up mathematical concepts in my subjects quicker.

3) would be the most fun but how useful would it be? If 1) than it would involve reviewing 2nd year material as well since they are needed in order to learn the 3rd year stuff. Although 2) would mean doing them more thoroughly.

 

[symbolipoint]

Best pick is most likely your #2; to study second year material and learn it better. This idea, in general, has helped me, although my major field was not Mathematics. If you are weak at pre-requisites, then you are not likely to succeed in the courses which use those pre-requisites.

 

[0rthodontist]

I would concentrate on 1. There's nothing like seeing material for a second time to give you a boost.

 

[quasar987]

I vote for #2.

A "master" in some discipline is not characterised by the amount of things he knows, but by the extend at which he masters the basics. That is the key imjo.

Also, don't review the material from the same source as you learned it the first time. Get other books. It will give you another perspective.

 

[Office_Shredder]

If you study the material you're expected to know, then by default if you run into something you don't get because you don't have enough background knowledge, you'll have to learn the background knowledge.

Just some food for thought

 

[pivoxa15]

Come to think of it, 2) does seem to be the best. Although a bit of 3) would be good as well I think, at least it will be fun. I am thinking of starting everyday with one of those problems and then study some proper uni material.

The great Terry Tao would probably have recommended 2) as well when he said in an interview which can be seen in full here http://www.ms.unimelb.edu.au/~paradox/archive/issues/p06-3.pdf

"If I learned something in class that I only partly understood, I wasn’t satisfied until I was able to work the whole thing out; it would bother me that the explanation wasn’t clicking together like it should. So I’d often spend a lot of time on very simple things until I could understand them backwards and forwards, which really helps when one then moves on to more advanced parts of the subject."