How to develop the ability for mathematical thinking?

Question

Mathematics

The other day, at a computer science lesson, they gave a problem:
If you could fold a sheet of paper 0.01 cm thick 42 times, it would reach the moon.
I solved it using a loop. And the other dude's code was many times smaller and consisted of variable declarations and a formula. Then I realized that without mathematical thinking, without the lack of the ability to express the essence of the problem in the form of a mathematical model, programming is not the best solution. Question: how to learn to think abstractly, mathematically? I'm ready to bite into the theory, just tell me where to start?

Answer 1

Here is a question of knowledge. You either know it's a geometric progression or you don't. I'm sorry, but this is a school. No, you can undoubtedly pretend to be Gauss and derive the formula yourself, here it is generally not difficult, but I doubt very much that this is your case.
There is a huge amount of very cool literature. "Algorithms. Construction and Analysis" by Kormen and Leyzerson, "The Art of Programming" and "Concrete Mathematics" by Knuth. There is a khanacademy- a very cool section of mathematics, just from geometric progressions to differential equations, convolutions of functions and combinatorial sets. Is it just English. And yes, practice. Start, then, with Cormen, and with the implementation of all the exercises in some Python. And in parallel, Grannemann's pocket guide, so that the scripts come out not as a collection of interactive pauses, but with a user-friendly CLI. Well, for general development, it is useful to master the Begginers Guide section on wiki.archlinux.org .

Answer 2

The easiest way in my opinion is the olympiads.
It's so easy to take and give birth to a mat. thinking won't work. You need to solve tasks of the Olympiad type and watch how others solve. You can, of course, learn the theory by heart, but it will be gradually forgotten in the absence of practice (and solving tasks from problem books is a pure development of the skill of solving, here you need tasks that you need to think about). Therefore, for example, they took a task on graphs, took a book on graphs, and accordingly learn the material of the graphs themselves and the topics adjacent to them that are required to solve the problem.
Over time, the Olympiad puzzles become the same type.
PS Matan, physics and computer science contribute very well to matan. thinking.