Which level of math should I at least reach?

[YoungPhysicist]

I am a junior high school student who somehow loves visiting physics forums like these, I found myself completely able to understand the concept everyone is talking about but not every polynomials/statistics/formulas everyone is talking about. Without understanding these math stuff I will not be able to go any deeper in these topics.

Do anyone have an idea of the minimum level of math should I reach? Or perhaps courses that I should be taking?

 

[gleem]

To help clarify your question so that we might help could you give an example of a concept that you understand but whose math you have a problem?

 

[YoungPhysicist]

For instance , I posted a thread "Do photon experience time" a few days ago on general/special relativity forum. A thing called "affine parameter" showed up at the discussion below. I searched it one the internet and found descriptions like this:

Thread: https://www.physicsforums.com/threads/do-photons-experience-time.953875/

https://www.encyclopediaofmath.org/index.php/Affine_parameter

These are the things that I can't understand.

 

[Wrichik Basu]

You need to cover up calculus completely, i mean limit theory, differentiation, integration, ordinary differential equations and Applications of derivatives.

Before starting with calculus, you have to do trigonometry. The topics are: basic ideas, compund angles, transformation of sums and products, multiple angles, submultiple angles, Inverse circular functions, general solution of trigonometric equations, and properties of triangles. These should be on your finger tips before you start with differentiation.

You need to have a good grip on coordinate geometery, like straight lines, circle, ellipse, parabola, and hyperbola, and 3d geometery topics like straight lines, planes and the like. These should be done simultaneously with calculus.

You should be conversant in topics like permutation and combination, progressions, matrices, determinants.

These are the minimum requirements to help you start out with any good book or lecture course. After that, topics like general relativity have their own requirements, like tensors and vector calculus. You can think about that later on.

 

[gleem]

Your level of education or knowledge seems inappropriate for the questions you are asking. And questions that you ask may not even be appropriate. Math is the language of physics. So you should start learning the language from the beginning which begs the question "what is your current level of knowledge of math?"
Once you have sufficient skill with the language you will be able to ask more realistic questions.

 

[berkeman]

anyone have an idea of the minimum level of math should I reach? Or perhaps courses that I should be taking?

what is your current level of knowledge of math?"

Are you on a math track at your school that will let you take calculus before you graduate? That would be a good goal for you, if the courses are available to you. If your high school does not offer calculus, you could check nearby community colleges to see if you can take calculus there and get credit for the courses. I took a couple of CC classes my senior year of high school.

Are you planning on going to college or CC after you graduate high school? You don't need to rush things too fast -- just keep taking math and science classes, and you will get there soon enough.

 

[plasmon_shmasmon]

You need to cover up calculus completely, i mean limit theory, differentiation, integration, ordinary differential equations and Applications of derivatives.

Before starting with calculus, you have to do trigonometry. The topics are: basic ideas, compund angles, transformation of sums and products, multiple angles, submultiple angles, Inverse circular functions, general solution of trigonometric equations, and properties of triangles. These should be on your finger tips before you start with differentiation.

You need to have a good grip on coordinate geometery, like straight lines, circle, ellipse, parabola, and hyperbola, and 3d geometery topics like straight lines, planes and the like. These should be done simultaneously with calculus.

You should be conversant in topics like permutation and combination, progressions, matrices, determinants.

These are the minimum requirements to help you start out with any good book or lecture course. After that, topics like general relativity have their own requirements, like tensors and vector calculus. You can think about that later on.

UM, this an overwhelming post. You DO NOT need to know all of this math before starting to learn physics. In fact, a lot of what was mentioned can be derived based on a simpler basis of knowledge (submultiple angles...really?). And a lot of these topics can be learned concurrently.

OP, what you are doing is exactly the way research is conducted and you have good learning instincts. You didn't know what an "affine parameter" was, so you looked it up. A little more digging will show you that it is related to abstract algebra (I think). So you have to ask yourself, how much abstract algebra do you need to learn to understand the physics concept that you were reading? It's hard to say, since you don't know what you don't know, so another strategy is to read similar/related physics posts/papers to get a better grasp of the context of the mathematics. Is "affine parameter" a common concept or tool that is thrown around in this field? What information does it provide? When did people start using "affine parameter" in the specific context that you read?

My point is that a lot of math can be contextualized, even when you don't understand it. A contextual understanding of the math will help you narrow down what you have to learn and how much of it you have to learn. Finally, the basic math that Wrichik Basu described can be learned in parallel.

I will end with this:

You don't need to rush things too fast -- just keep taking math and science classes, and you will get there soon enough.

 

[Wrichik Basu]

UM, this an overwhelming post. You DO NOT need to know all of this math before starting to learn physics. In fact, a lot of what was mentioned can be derived based on a simpler basis of knowledge (submultiple angles...really?). And a lot of these topics can be learned concurrently.

Of course, all these have to be learned concurrently. The OP has to refer to any standard school textbook, and not learn the topics by themselves. For example, trigonometry and topics like permutations, progressions, matrices, determinants, and conics are generally taken up simultaneously. It is followed by 3d geometery, calculus, and other topics like binomial series and so on.

But I DO think most of these are important to start with physics into some depth. Of course, you can start without all these, but then the OP will not be able to go into the depths at one go. That is what is done in school. But what I have written is from personal experience. For example, topics like Electromagnetism cannot be taken up without calculus.

Of course, there is no need to rush, as @berkeman has said. @Young physicist It will become boring if you continuing doing math only without any physics. And I do not support that. A good strategy that I was recommended by one of my professors was to start with physics, and if I reached an unknown topic, then I should look that up in some standard mathematics textbook, and then continue. That could be applicable in learning higher topics, but could be problematic at first, without the knowkedge of the basics. Many schools in my region teach maths in high school for the first two months without going into physics, so as to brief out topics like calculus and conics.

 

[YoungPhysicist]

OP, what you are doing is exactly the way research is conducted and you have good learning instincts. You didn't know what an "affine parameter" was, so you looked it up. A little more digging will show you that it is related to abstract algebra (I think). So you have to ask yourself, how much abstract algebra do you need to learn to understand the physics concept that you were reading? It's hard to say, since you don't know what you don't know, so another strategy is to read similar/related physics posts/papers to get a better grasp of the context of the mathematics. Is "affine parameter" a common concept or tool that is thrown around in this field? What information does it provide? When did people start using "affine parameter" in the specific context that you read?

Of course, there is no need to rush, as @berkeman has said. @Young physicist It will become boring if you continuing doing math only without any physics. And I do not support that. A good strategy that I was recommended by one of my professors was to start with physics, and if I reached an unknown topic, then I should look that up in some standard mathematics textbook, and then continue. That could be applicable in learning higher topics, but could be problematic at first, without the knowkedge of the basics. Many schools in my region teach maths in high school for the first two months without going into physics, so as to brief out topics like calculus and conics.

Thanks to everyone! These advices have been so useful!