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Godzilla-3301
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I am a 14 year old who is very interested in Physics, especially astrophysics, but I don’t know exactly which math I should study in order to learn more in depth of the field. What is the best thing to learn?
Thanks, I will use this advice to heart.fresh_42 said:Physics is written in mathematics, a rather specific mathematical dialect to be exact. It is usually taught parallel to the standard courses in physics.
You could begin to learn calculus or linear algebra because these two are the fundamentals of basically everything else.
BUT ...
... there are some serious implications which must be considered:
So unless you're a genius, there are some severe obstacles to be considered. The best recommendation is very likely: Learn as much as you can along with your regular classes at school, especially in math, physics, and chemistry, maybe biology, too, and try to understand those subjects on a deeper level of understanding. Always ask why, read additional texts, e.g. Wikipedia pages, and do your homework.
- If you learn it wrong because you are alone and have no feedback from a teacher, it is very difficult to "unlearn" misconceptions.
- If you learn it right, e.g. because you regularly checked your knowledge here on PF, then you will probably get bored if it is time to learn it at a university. And being bored is a serious danger as it kills curiosity, the most important attitude of all.
- You could get frustrated because things are more difficult than you thought. And frustration is a sad thing. People tend to give up if being frustrated.
- Where do you learn the school stuff, which is in between your current knowledge and the beginning of a calculus textbook?
If you want to know where you are at, you can test your knowledge with the books on https://openstax.org/subjects or have a look at the high school problems in https://www.physicsforums.com/threads/solution-manuals-for-the-math-challenges.977057/. Those problems (all of them) give you an example of where you want to go. Keep in mind that you are not supposed to understand them, yet, so do not get frustrated. They are challenges, and even physicists or mathematicians cannot solve all of them from the spot.
Summary: Be good at school!
Speaking for experience:fresh_42 said:
- If you learn it right, e.g. because you regularly checked your knowledge here on PF, then you will probably get bored if it is time to learn it at a university. And being bored is a serious danger as it kills curiosity, the most important attitude of all.
Classical physics is the branch of physics that studies the behavior of macroscopic objects, while Quantum physics deals with the behavior of subatomic particles and their interactions.
The most important math concepts for Classical Physics are calculus, linear algebra, and differential equations. These are used to describe the motion and forces acting on macroscopic objects.
Quantum Physics requires a strong foundation in calculus, linear algebra, and differential equations, as well as more advanced concepts such as complex numbers, probability theory, and group theory.
No, a strong understanding of math is essential for studying Quantum Physics. Without a solid foundation in math, it will be difficult to grasp the complex concepts and equations used in this field.
While it is not impossible, it is highly recommended to have a good understanding of Classical Physics before diving into Quantum Physics. Many of the concepts and principles in Quantum Physics build upon those in Classical Physics.