What is it like to experience math in physics?

[ChrisisC]

I'm a 15 year old sophomore in high school who absolutely loves physics (more of quantum mechanics and Einsteins theories of relativity and how it is incorporated into everyday life). I want to grow up and be a Physicist and that's all i would like to do because nothing fascinates me quite like physics does. But i am writing this for a reason in the career guidance category because i am not very strong in math, and i need advice on how to go about my physics career lacking a strong understanding of mathematics. I can easily understand how math concepts can apply to real world problems, i am just bad at actually performing the math, numbers just don't come to me, but science does. No matter what i will go into Physics even if i suck at math, but can you guys give me some information on what it's truly like to experience math in physics. Is it really that hard? is it really that grueling?

 

[Drakkith]

But i am writing this for a reason in the career guidance category because i am not very strong in math, and i need advice on how to go about my physics career lacking a strong understanding of mathematics.

Simple. You learn math. There's no way to get around it.

No matter what i will go into Physics even if i suck at math, but can you guys give me some information on what it's truly like to experience math in physics. Is it really that hard? is it really that grueling?

Yes it is. Though I'd rather call it "time consuming". Whether or not it's hard or difficult is too subjective. There are people out there who do math for fun and wouldn't call any math "hard". And there are others that avoid it like the plague because it is so difficult for them.

Also, unless you've spent a LOT of time doing math (or you've been diagnosed with a learning disorder), then I don't believe you can say that you just bad at it or that it doesn't come to you. If you've barely made any effort and/or spent any time learning something, then of course it's going to be difficult. I assume that you've spent about the same amount of time learning math as the average high school student who doesn't enjoy it, and believe me, it's not enough. In my college calculus class I spent 10-20 hours every week just doing homework. And even that wasn't really enough time.

I've also been a tutor for math, chemistry, and physics. I've tutored people who told me they were abysmal at math and just couldn't get it, but they managed to learn it and get through their classes because they put in the time they needed to do so. I recently tutored a girl in high school who was on the verge of failing her math class and kept telling me she "just didn't get math". We only met for about 2 hours per week, but after 2-3 months of tutoring she managed to pass her math class with an A. A big change from when we first met and she was in tears because she was so frustrated.

So while I can't say that you do or do not "get math", I expect the real reason you're not doing well is because you haven't put more time into it and haven't had anyone else who was interested in math help you.

Note: I'm not saying that you should be putting more time into it, only that if you haven't put a significant amount of time into learning math then don't fool yourself into believing that you're no good at it and you never will be. Almost everything worth doing is difficult at first. If it wasn't, everyone would be doing it!

 

[ChrisisC]

I do see your point. But i strongly believe Algebra does not come to me naturally, however a subject such as geometry is trivial to me, it's almost as if I'm learning 5th grade material. Are there any ways to experiment with mathematics on my own outside of school curriculum? I would like to explore mathematics in a way that is not taught, but more as discovered. Of course i won't be able to do much until i learn the basics of future math, but i just want to know how i can explore the world of mathematics on my own

 

[Drakkith]

Are there any ways to experiment with mathematics on my own outside of school curriculum?

That I don't know. I've only ever used the standard textbooks.

 

[symbolipoint]

I do see your point. But i strongly believe Algebra does not come to me naturally, however a subject such as geometry is trivial to me, it's almost as if I'm learning 5th grade material. Are there any ways to experiment with mathematics on my own outside of school curriculum? I would like to explore mathematics in a way that is not taught, but more as discovered. Of course i won't be able to do much until i learn the basics of future math, but i just want to know how i can explore the world of mathematics on my own

Maybe. One thing for sure, is that Physics and Engineering rely on Mathematics, more than just basic algebra, to codify situations and descriptions. Mathematics becomes much alive in applying to those kinds of topics. Any GOOD algebra book will have purely symbolic and conceptual exercises, AND application exercises, so that some chance of helping the Mathematics become alive is also possible in the instruction.

 

[Dr. Courtney]

I'm a 15 year old sophomore in high school who absolutely loves physics (more of quantum mechanics and Einsteins theories of relativity and how it is incorporated into everyday life). I want to grow up and be a Physicist and that's all i would like to do because nothing fascinates me quite like physics does. But i am writing this for a reason in the career guidance category because i am not very strong in math, and i need advice on how to go about my physics career lacking a strong understanding of mathematics. I can easily understand how math concepts can apply to real world problems, i am just bad at actually performing the math, numbers just don't come to me, but science does. No matter what i will go into Physics even if i suck at math, but can you guys give me some information on what it's truly like to experience math in physics. Is it really that hard? is it really that grueling?

My story:

https://www.physicsforums.com/insights/trials-tribulations-physicist-became-math-geek/

 

[Dr. Courtney]

Are there any ways to experiment with mathematics on my own outside of school curriculum? I would like to explore mathematics in a way that is not taught, but more as discovered. Of course i won't be able to do much until i learn the basics of future math, but i just want to know how i can explore the world of mathematics on my own

Sure you can, depending on what you really mean by "on your own." You will likely need a mentor to help guide you to productive and approachable problems where your skills can grow based on what you already know, but a lot of progress can be made outside of the "school curriculum."

I've mentored students in math projects at levels varying from school science fairs (ISEF-affiliated) to senior theses of undergraduate math majors. (Being a PhD in Physics, I am not quite qualified to mentor PhD level work in math.) But in most cases, students are "experimenting with math" on their own in a subfield that is interesting, educational, and relevant but nowhere near covering all of the algebra and trig needed as a solid basis for future work.

You might read my article, "Secrets of Successful Science Projects" and begin considering how you apply the principles there to selecting and executing a project in mathematics. See: https://www.physicsforums.com/insights/secrets-successful-science-projects/

I am happy to discuss any ideas or brainstorms you have by PM.

 

[Aufbauwerk 2045]

I'm a 15 year old sophomore in high school who absolutely loves physics (more of quantum mechanics and Einsteins theories of relativity and how it is incorporated into everyday life). I want to grow up and be a Physicist and that's all i would like to do because nothing fascinates me quite like physics does. But i am writing this for a reason in the career guidance category because i am not very strong in math, and i need advice on how to go about my physics career lacking a strong understanding of mathematics. I can easily understand how math concepts can apply to real world problems, i am just bad at actually performing the math, numbers just don't come to me, but science does. No matter what i will go into Physics even if i suck at math, but can you guys give me some information on what it's truly like to experience math in physics. Is it really that hard? is it really that grueling?

This is a great question. I am sure many students have the same problem.

You say "I need advice on how to go about my physics career lacking a strong understanding of mathematics." The short answer is that you need to develop that strong understanding of mathematics which you currently lack! You will need to know lots of mathematics in order to get anywhere in physics.

Please do not think it's impossible for you. On the contrary, make up your mind that since you need to know a certain amount of mathematics to move forward in physics, you will do it because you simply have no choice. Where there is a will, there is a way.

I won't say mathematics is easy but if you focus and work at it you should be able to overcome any obstacles with school mathematics.

I know this because I was in your situation until I realized that I had some mental blocks, mainly a lack of self-confidence, regarding mathematics. This was because I did not have much experience learning mathematics and doing problems, due to my previous mathematics courses which were not very good. I knew my mathematics skills were poor so I told myself I am not a "mathematics person."

For me, this problem vanished once I went to a school with better mathematics teachers. I did well in my high school geometry class. It helped that the teacher was a nice guy, he explained things very well, and he encouraged me. Then I realized that if I settle down, concentrate, and do lots of mathematics problems, it will sink in. Sometimes it is difficult but the reward is worth it.

Sometimes you won't see the point of some topics in high school mathematics but you should have confidence they are all important. You are building the foundation for calculus and differential equations which you must learn in order to understand physics.

Perhaps you could start by reviewing all the school mathematics you had problems with. Remember that there is no shortcut. Think of the skyscraper analogy. You start with the foundation and then build each floor in order. You must begin with arithmetic and geometry, then move on to algebra, trigonometry, and calculus. Just take it one step at a time and try to master one topic before you move on to the next.

You say "I am just bad at actually performing the math." No worries, just work at it and you can improve! Others have done it, including me. Please don't convince yourself that you are not a "mathematics person." Can you add, subtract, multiply, and divide? If so, then you are a mathematics person. And if you have any difficulties with basic arithmetic, go back and practice until it's second nature! Soon you will be good at "actually performing the math", which by the way is essential if you want to learn physics. I suppose we can learn some things from "conceptual physics" without lots of mathematics, but at the end of the day the language of physics is mathematics. There is no way around that.

Don't worry if some topics are hard at first. This is normal. Just keep trying. The more you learn, the more you will develop the mathematical part of your brain. Then one day you will be able to look back at the hard problems and they will seem easy.

You ask "can you guys give me some information on what it's truly like to experience math in physics?." I'm not sure if this totally answers your question. But every time I work out a physics problem I am experiencing math in physics because math is the language I am using.

You can experience this yourself by reading some solved problems in pre-calculus level physics. These problems use arithmetic, algebra, geometry, and trigonometry. There are many books that have such problems. You might take a look at Schaum's Outline series because it has lots of problems with carefully explained solutions. Perhaps they have a good pre-calculus physics book. Fortunately their books are not expensive.

I think it helps to work out the solutions to the example problems yourself using pencil and paper. This is better than just reading them. Then try to solve the rest of the problems on your own before you look at the answers.

I'll stop now. Please ask if you have any questions about what I've posted.

I hope you keep posting about your progress.

 

[Aufbauwerk 2045]

I do see your point. But i strongly believe Algebra does not come to me naturally, however a subject such as geometry is trivial to me, it's almost as if I'm learning 5th grade material. Are there any ways to experiment with mathematics on my own outside of school curriculum? I would like to explore mathematics in a way that is not taught, but more as discovered. Of course i won't be able to do much until i learn the basics of future math, but i just want to know how i can explore the world of mathematics on my own

When you say you want to experiment with mathematics on you own, that is a good thing. It shows you have the instinct of a scientist. However, as a practical matter, your primary goal at this time should be to master your school mathematics and do well on tests. You will be glad you did.

You say algebra does not come to you naturally. I don't think it comes naturally to anyone. It took civilized humans thousands of years to develop algebra. Don't worry about that. Just be happy that it has already been developed. All you need to do is learn it, which certainly you can do.

I read a relevant interview with a Nobel laureate in particle physics. Sorry his name escapes me at the moment. He said that doing physics research is basically a matter of learning what is already known, then adding to it. He said once you learn what is known, it is not so difficult to push it ahead somewhat. But you need that foundation. Creativity, imagination, and exploring on your own is what it's all about -- once you have the necessary background knowledge! Even the greatest scientists had to learn the basics thoroughly before they could add their own contribution. As Newton said, if he saw further than others it was because he stood on the shoulders of giants.

 

[Aufbauwerk 2045]

Just a follow-up. I gave the link to Prof. t'Hooft's list of topics. Since you are still in high school and asked about algebra, maybe you could start with a free online course in Beginning Algebra which he recommends.

http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/index.htm

The very first article in this tutorial is How to Succeed in a Math Class. I think this will be very helpful for you.