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The point is that mathematics and its methods are not learned by simply reading. Sometimes when I have faced a particularly difficult mathematical theory, I have said, well calmly simply read the main results and constructions and nothing else. Unfortunately, that is a failure, virtually always.
You can only learn mathematics by exercising them. I think many people who train in mathematics continuously (I do), will say something like this:
- You need to identify your level, do not worry, do not want to show that you know more than you know, choose your level or one slightly lower, it will only take you 18 or 24 months to leave that level behind (unless you already have one Doctorate in hard sciences or bachelor's degree in mathematics).
- Once you have identified your level, you need to make a list of theories or methods relevant to that level (people try to look for something applied to their work, it may serve the beginning but if you focus exclusively on content rather than methods, Will stagnate).
- Now you will need a list of 4 or 5 books on these theories, I would say that depending on your ability to concentrate read 2 or 3 at the same time and if you can any more, then better. And you need to do a lot of exercises, not exercises to do, but the ones that really are like "changing levels in a video game". You need to solve problems, when you have one resolved ask yourself if you could solve a more complicated variant, every time you do that you will advance, it is the only thing that works. But it is a very demanding mental gymnastics.
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Here I leave the rules explained by an assistant of Joseph-Louis de Lagrange, possibly the best mathematician of the eighteenth century on the technique of that mathematician:
- When Lagrange was not able to overcome a difficulty, he put aside and took a second moment (we talked about that the best mathematician in the world was sometimes unable to solve a problem of his time to the first, so With more reason any of us).
- Lagrange never left a book that had started if I had assimilated it completely (I personally do not do it with books but with chapters if I pass from 50% then I force myself to finish it if the beginning I see difficult to climb to something else).
- Lagrange always tried to understand the reason why the authors of a book had followed one way and not another (solving a same problem by different methods is fantastic, because you learn to realize the conditions of when you make a better method).
- Lagrange, whenever possible, sought to obtain his own method or theory on essential points in the problems he solved or the matters he worked on.
- Lagrange never finished a day of work without being written what would be the next task to be solved, thanks to which he surpassed what he called "natural human sloth."
Thank you for your time, you always have to try nothing is difficult. 😊☺
Interesting, thanks.
May I make a suggestion - I curate the @math-trail community account - to include at least one #mathematics tag or these posts may be hard to find for maths enthusiasts.
One other thing I try to do with students is to get them to design their own questions - trying to enter the mind of an examiner. It rarely works, as most are so used to just answering stuff.
!-=o0o=-!
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Thanks friend, I'll follow them.
Hi @jonathanxvi, in my country we learn maths by memorizing the formulas and just practice and practice the problems. nice article
thanks friend :D
Probably you could start a series of posts sharing methods of understanding various topics in maths. Since every country has different kind of syllabus, could be interesting. But just a thought : )
Great post! Something I'd like to highlight, along with the practical advice you have outlined, is the importance of persistence! Try, try, and try again (and again!) - you may be on the brink of breaking through into the realm of understanding, so don't give up; it will all 'click' eventually, it just takes time.
Approaching the problem from a different perspective can be helpful, as well as talking to colleagues (contrary to widespread belief, maths is a social endeavour, too).
One final tip, adding to your advice, is to try and prove the result yourself, first, before looking at the proof given in the book - even if you are studying a new topic, this will do wonders for your intuition. Prove everything!
Cheers, D.
thanks for the comment :D
Really nice article, followed! I think it is important for who studying math even for a master student. I think you may change a tag to mathematics. Resteemed!