Problem understanding math sorry for my english but I am a foreigner. I'm writing to ask you for help with a problem I have with mathematics. I'm going to go to university physics but I have serious problems as regards mathematics and want to do everything to overcome them. I consider mathematics as something incredible and yet I've never been able to understand how it must: give an example at least up to the limits I could do it properly all the exercises that were assigned but now I can not understand anything. I think I've always wrong to study mathematics, I was studying as something mechanical: Learn the rule, apply the rule.
This is my situation: I want to ask in what way should I study in order to understand it in depth and detailed mathematics. What should I do and how should I act, I am willing to make every effort to repair this my problem.
Thank you for all the help that you will give me and for all your answers. And again sorry for my English.
 A: "Mathematics is not a spectator sport" , said someone famous.
In my opinion to fully understand it you must do it, and you must do it a lot.
here is my approach to learning new topics.
1) read a theorem then spend 5-15 minutes thinking about what it means. try to understand it in the context of the chapter or section.
2) think of some examples that are true that fit the theorem, the bigger the list that you can make the better. try to think of different types of examples, not just the same one with small variants.
3)do the problems assigned relating to the theorem. most importantly, do not not move on to the next problem until you completely understand why the solution is correct, and what it has to do about the theorem.
the more time, effort, and thought you put into each topic, the better you understand it.
Once you have done the first 3 steps, try and explain the concept to someone else. If you can explain it to someone else and teach them how to do it, your understanding becomes solidified and stays with you much longer.
These are the basic strategies I use to learn math every day. Good luck!
A: One suggestion, to "get your feet wet" so to speak and to break away from the mode of approaching mathematics as merely the rote application of rules one has memorized: 

See Thinking Mathematically, 2nd edition, by J. Mason, L.Burton, and K. Stacey. 

The link is to Amazon.com, where you can preview the book. It has been a very well-received book, it is well written, and it addresses what I think you will find both helpful and enjoyable. There are many examples included in the book, as well as exercises to apply what you're learning. 

Note that the first chapter is entitled: Everyone can start!


For additional resources:


*

*One classic that addresses problem-solving in general is George Polya's How to Solve IT.

*For a great introduction into how to approach, understand, and write proofs, see Daniel J. Velleman's book How to Prove It: A Structured Approach. 
Both of the above links take you to to Amazon.com where you can "preview" the books (e.g., the table of contents, introductions, etc.).
