Are there some fundamentals or elements for thinking mathematically?
Thanks for replying. Once I read in Quora that some of most important theories in maths are: Set theory, number theory and functionsLots and lots of practice and hanging around other people who think mathematically is how I got to be good at it.
I don't think there are any short cuts. But there can be some organizing principles for approaching different classes of textbook type problems.
A solid foundation for solving lots of textbook type problems in physics, chemistry, and math eventually provides a big toolbox for other kinds of problems that occur in other contexts. But building up the toolbox takes years of practice and homework in courses with lots of textbook type problems.
Always ask "why" and don't be satisfied by an answer which didn't convince you. Because the professor said or because it is written in the book are no valid answers.Are there some fundamentals or elements for thinking mathematically?
One fundamental from information theory that helps me think mathematically and solve difficult problems can be called step-wise refinement in the context of the modular hypothesis, now theory. Given a large intractable problem, breakdown or refine the problem into simple steps that you can solve. Faced with a difficult landscape, consider simple shapes that combine to define or map the actual terrain.Are there some fundamentals or elements for thinking mathematically?