FeDeX_LaTeX
Science Advisor
- 436
- 13
Hello,
I too am 16, and I'd like to pursue a career in either mathematics or physics. I agree that your mathematics need to improve. When I was 13-14, I 'stepped it up' a little bit; it was a period where I learned an incredible about using the internet and books. I recall asking on a maths forum at 13 how to calculate a derivative, and, of the 20 or so replies I received, none were helpful, a few were condescending, and many were downright rude. I had told them my age, and they told me things like "make sure you have a mastery of pre-calculus, memorise all those trig identities, build up a knowledge of logarithms and study a programming language before you start calculus, wait a few years before you bother trying, learn how to do other maths first". Then I found a website (edugratis) with simple videos that introduced calculus step by step; limits, differentiation, integration, related rate problems, cusps, etc. and by 15 I was really making a lot of progress in calculus. In fact, I'd say keep using YouTube. But stay away from the really hard stuff (things where you understand 0% of the stuff they're talking about). It's not very productive.
I think a good start for you would be problem-solving. The NRICH website has many problems for 11-19 year olds, with problems ranging from counting, to calculus and group theory (don't be fooled by the pretty colours, some of those problems are really tough).
For me, I was 15 when I first realized that I liked physics, but the mathematics of the physics was what made me appreciate it the most. Learn to love mathematics. During this period (13-15) I discovered things like fractional calculus and the Bernoulli numbers, and it was the problem solving that led me to learn about concepts like groups, difference equations and so forth. Right now, I'm working on Fourier series. Put the time in, but love it while you're doing it too.
It's good that you're a member here; spend a lot of time here reading topics that interest you (or random ones) related to physics or maths. Do this on other forums too, like mathisfunforum.com. You will pick up some of the mathematics, trust me. A few years ago I learned about double summations and Maclaurin series just by reading people talk about them. I know you can get a lot of things off of YouTube, but you need to do a bit more than that to learn, in my experience. For instance, I thought I was great at integrating by u-substitution, but then I encountered a really tough exercise someone had made where you could only use u-substitution to get the answer. As someone said in this thread; solving problems will make you better. The more you do them, the more you'll start to think like a mathematician (or a physicist, I suppose).
If your algebra or trig (not sure how the US system teaches it) isn't quite up to scratch, ask people here, or on other forums (like the one I mentioned), or look it up on YouTube. You can even PM me if you like. I know what it's like to want to get better at something but not know where to start. You're 16 -- you've realized, more or less, what you want to do. This is your coming of age, so to speak. Like me, I presume you're reading about a lot of advanced topics in physics but without the right mathematical background. I am the same. I have read about topics like string theory and quantum mechanics, and would love to understand them more, and I know that with every day the passes, I'm getting closer and closer to understanding the mathematics of it.
Good luck. And please don't become one of those people that love physics but think maths is a waste of time (like my old physics teacher). :P
However, although it might contradict this post a bit, you do not have to learn everything in a step-by-step fashion. You don't necessarily have to become a master of everything covered in trig to become good at calculus. But it helps a lot. Bit of trivia - I didn't know how to do long division until I was 14. I had devised my own method that was much slower until I heard about this new method that apparently people 8 years younger than me could do. Isn't that embarrassing?
Although, don't get into the habit of learning about doing things like differentiation without knowing what you're doing. It's easy to just understand that the derivative of x^n is nx^(n-1), but it's much nicer if you understand what you've just done.
Don't worry if you don't understand the terminology that well yet -- a couple of years ago if someone mentioned 'complex analysis' to me, I wouldn't be certain what they were talking about. But I already knew a lot about it.
I too am 16, and I'd like to pursue a career in either mathematics or physics. I agree that your mathematics need to improve. When I was 13-14, I 'stepped it up' a little bit; it was a period where I learned an incredible about using the internet and books. I recall asking on a maths forum at 13 how to calculate a derivative, and, of the 20 or so replies I received, none were helpful, a few were condescending, and many were downright rude. I had told them my age, and they told me things like "make sure you have a mastery of pre-calculus, memorise all those trig identities, build up a knowledge of logarithms and study a programming language before you start calculus, wait a few years before you bother trying, learn how to do other maths first". Then I found a website (edugratis) with simple videos that introduced calculus step by step; limits, differentiation, integration, related rate problems, cusps, etc. and by 15 I was really making a lot of progress in calculus. In fact, I'd say keep using YouTube. But stay away from the really hard stuff (things where you understand 0% of the stuff they're talking about). It's not very productive.
I think a good start for you would be problem-solving. The NRICH website has many problems for 11-19 year olds, with problems ranging from counting, to calculus and group theory (don't be fooled by the pretty colours, some of those problems are really tough).
For me, I was 15 when I first realized that I liked physics, but the mathematics of the physics was what made me appreciate it the most. Learn to love mathematics. During this period (13-15) I discovered things like fractional calculus and the Bernoulli numbers, and it was the problem solving that led me to learn about concepts like groups, difference equations and so forth. Right now, I'm working on Fourier series. Put the time in, but love it while you're doing it too.
It's good that you're a member here; spend a lot of time here reading topics that interest you (or random ones) related to physics or maths. Do this on other forums too, like mathisfunforum.com. You will pick up some of the mathematics, trust me. A few years ago I learned about double summations and Maclaurin series just by reading people talk about them. I know you can get a lot of things off of YouTube, but you need to do a bit more than that to learn, in my experience. For instance, I thought I was great at integrating by u-substitution, but then I encountered a really tough exercise someone had made where you could only use u-substitution to get the answer. As someone said in this thread; solving problems will make you better. The more you do them, the more you'll start to think like a mathematician (or a physicist, I suppose).
If your algebra or trig (not sure how the US system teaches it) isn't quite up to scratch, ask people here, or on other forums (like the one I mentioned), or look it up on YouTube. You can even PM me if you like. I know what it's like to want to get better at something but not know where to start. You're 16 -- you've realized, more or less, what you want to do. This is your coming of age, so to speak. Like me, I presume you're reading about a lot of advanced topics in physics but without the right mathematical background. I am the same. I have read about topics like string theory and quantum mechanics, and would love to understand them more, and I know that with every day the passes, I'm getting closer and closer to understanding the mathematics of it.
Good luck. And please don't become one of those people that love physics but think maths is a waste of time (like my old physics teacher). :P
However, although it might contradict this post a bit, you do not have to learn everything in a step-by-step fashion. You don't necessarily have to become a master of everything covered in trig to become good at calculus. But it helps a lot. Bit of trivia - I didn't know how to do long division until I was 14. I had devised my own method that was much slower until I heard about this new method that apparently people 8 years younger than me could do. Isn't that embarrassing?
Although, don't get into the habit of learning about doing things like differentiation without knowing what you're doing. It's easy to just understand that the derivative of x^n is nx^(n-1), but it's much nicer if you understand what you've just done.
Don't worry if you don't understand the terminology that well yet -- a couple of years ago if someone mentioned 'complex analysis' to me, I wouldn't be certain what they were talking about. But I already knew a lot about it.
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