How does mathematics work? What sections are required to study for physics?

Question

Mathematics

I am a 10th grade student. I recently fell in love with math and physics, but I don't understand how math works, how algebra works and what we study, and how physicists use it (I'm not simple arithmetic or "F=ma"). I asked these questions to my math teacher, but I didn't get the right answer. Guru of mathematics and physics please help. I think that there are books or something that will help me in understanding such a wonderful field as mathematics. Thanks in advance.

Answer 1

Mathematics works in a fictional world in which there are a number of axioms and definitions. Therefore, it is an ideally exact science.
It works by the method of theorems and proofs, which look like various mathematical equalities or visualization with graphs.
Physics works differently - there are laws of nature, they are slowly discovered and refined. She works experimentally. Many calculations in physics can come close in accuracy to mathematics, but there is always a certain limit beyond which it is not clear how to count.
But if, thanks to certain calculations, according to the scientific method of cognition, it is possible to set up an experiment and unambiguously reproduce the result, they are taken as sufficient for practical use.

Answer 2

Look matprofi from the very first topic. There, the list of sections is universal, but in an accessible form without strict evidence. There is even a field theory. Just study the sections, then understand how they apply, and then understand how they work.

Answer 3

you need to ask physicists and not school teachers.
depends on what areas of physics you are going to study
At least tensor calculus, vector algebra and group theory

Answer 4

R. Courant, G. Robbins. What is mathematics?
A. Poincare. About science.
Both books can be found on the MTsNMO website.