Self-study for math and physics or sticking with school material?

[Lisastronomy]

I am in the last year of my high-school with an aspiration to do a double-bachelor in Physics and Math. I am not sure if I am capable of doing so (I am not the smartest), but it is really one of my dreams to study both subjects, so I will try.

However, sometimes I experience some difficulty in high-school. My grades are fine, maybe not the highest, but they are good enough to pass. I truly love physics and math, but maybe that is also one of my failure points. Whenever we learn something in school, we learn to apply and be able to pass it on in an exam. Often, I don't really feel like I really understand the topics at all.

I know what the concepts do. For example, I know what a Lorentz force does, and for the most part I can apply that knowledge. However, knowing and fully grasping what is behind that theory, isn't covered in school and so for my knowledge, I barely have an idea what some concepts truly are deeply within the field of physics and math. I do often feel like, if I grasp such things, understanding and applying them becomes easier.

Now, whenever I dive into such concepts I often get this sense of overwhelming information. There is often so much behind a theory, that is not yet available for me with the skills that I have. (For example, we haven't had tensors in school yet, or matrices.) Another thing is, I don't know when to stop, or which road to even go. It never seems to be enough, because there is so much beauty to be explored!

Every theory leads to something new, something deeper and for me, I find it hard to see where to walk through, in order to find the right and enough information to satisfy my desire for that knowledge. The other point is, that because of this desire, I mostly think outside of the concepts I am learning, but of course I should remember, the exam of this topic is coming up soon too! I try to learn what is inside the book, by making exercises, and even though it is hard for me to admit, this often blinds me.

I feel like, whenever I have a question, and I am searching for the answer on the internet, for example, I figure out how I did know what I once applied to the exercises of school, but through all that repetition, I seem to fail to be able to think outside of that. All of this often makes me feel stressed or a bit sad, because I feel so curious, and even though I am not the smartest, I never let down of my dream to spend my life trying to understand the ideas made by these brilliant people!

I was hoping anyone could give me some tips about this. Any tip is welcome and don't hesitate to tell your outlook on this or your experience! Thank you in advance.

 

[PeroK]

I would say only one thing. The Internet is a vast resource and if you are studying from a textbook you should use it sparingly. Don't get sucked deeper and deeper into extra material.

Try to use the Internet as a practical resource to supplement what you are learning but not to get sidetracked into additional material. Focus on the core elements of the formal course you are studying.

 

[Lisastronomy]

I would say only one thing. The Internet is a vast resource and if you are studying from a textbook you should use it sparingly. Don't get sucked deeper and deeper into extra material.

Try to use the Internet as a practical resource to supplement what you are learning but not to get sidetracked into additional material. Focus on the core elements of the formal course you are studying.

Hi @PeroK , Thank you for your reply!

 

[hutchphd]

Any tip is welcome and don't hestite to tell your outlook on this or your experience! Thank you in advance.

At your stage my advice is to study the math. For me math took a while to "settle" and my high school was not great. You should try to study matrices (finite linear algebra) and of course calculus (as much as you can). The rest will be much easier

 

[Lisastronomy]

At your stage my advice is to study the math. For me math took a while to "settle" and my high school was not great. You should try to study matrices (finite linear algebra) and of course calculus (as much as you can). The rest will be much easier

Thank you so much for your reply!

 

[mathwonk]

here is a nice little book introducing matrices and linear algebra that i suggest you could read profitably:

https://www.amazon.com/dp/0879011211/?tag=pfamazon01-20

 

[Delta2]

As scientists and as human beings in general we are facing the infinite: All the possible knowledge is infinite, all the possible situations we can encounter in life are infinite as well, however our bodies and our brains are finite: our brain has finite memory and finite processing power.

So it seems to be an unfair battle: a finite brain against an infinite knowledge. So what can we do, we ll just learn as much as we can, yet knowing that no matter how much we ll learn there will still be infinite more to learn. You ll rediscover this in 5-10 years when you will have finished your bachelor studies and you will know a lot more than now, however even then you ll understand that there are always new things to learn and understand.

 

[mathwonk]

calculus is harder, but here is a book i think does a better job than average at motivating and explaining it. Unfortunately it seems to be available only in libraries, such as a university library: Lectures on Freshman Calculus, by Allan Cruse and Millianne Granberg. (I used to have a copy, long since gone.)

Here is another, shorter, book I like that is actually available, and a good place to start. It is also written by a friend of mine.

https://www.amazon.com/dp/0812098196/?tag=pfamazon01-20

 

[gleem]

For the record are you currently taking physics or did you take it as a junior? You mentioned Lorentz force which is usually covered in the second semester.

 

[CrysPhys]

OP:

* If you could fully understand the fundamentals of physics in high school, there would be no need for undergrad and grad courses and advanced seminars, would there? Learning physics (and most subjects) is an iterative process. So please don't get flustered that you don't understand everything at such an early stage (or ever).

* I'll suggest something different from, or in addition to, more math (depending on how much time you have). Do a small experimental science project. Does your school have science fairs? It will help you focus on a bounded problem that will result in a solution (of some degree). Even if you later specialize in theoretical physics, you will still need to know how to tie it to experimental results and stay grounded in reality. I know I'm expressing my personal bias: getting hands-on experience in a lab made physics more fun, more real, and more satisfying than studying theory in isolation (and you'll come to appreciate how more complex real-world scenarios are than the model scenarios in your texts).

 

[berkeman]

Do a small experimental science project. Does your school have science fairs? It will help you focus on a bounded problem that will result in a solution (of some degree). Even if you later specialize in theoretical physics, you will still need to know how to tie it to experimental results and stay grounded in reality

Yeah, it's similar in EE/electronics. I found that building electronics projects on my own really helped me to learn to "ask the right questions" of myself and my instructors. When you build a circuit that you've seen on paper and analyzed in the past, and it does not work the first time, you learn to figure out what is wrong, and modify how you think about circuits (into a more detailed and real-world way). You don't learn about circuit parasitics in standard intro EE/electronics classes, but boy do you learn about them when you build things!

 

[Lisastronomy]

here is a nice little book introducing matrices and linear algebra that i suggest you could read profitably:

https://www.amazon.com/dp/0879011211/?tag=pfamazon01-20

Thank you for the recommendation! I will buy it asap, including the calculus book you mentioned.

 

[Lisastronomy]

As scientists and as human beings in general we are facing the infinite: All the possible knowledge is infinite, all the possible situations we can encounter in life are infinite as well, however our bodies and our brains are finite: our brain has finite memory and finite processing power.

So it seems to be an unfair battle: a finite brain against an infinite knowledge. So what can we do, we ll just learn as much as we can, yet knowing that no matter how much we ll learn there will still be infinite more to learn. You ll rediscover this in 5-10 years when you will have finished your bachelor studies and you will know a lot more than now, however even then you ll understand that there are always new things to learn and understand.

Yes, that is true. Thank you for your reply!

 

[Lisastronomy]

For the record are you currently taking physics or did you take it as a junior? You mentioned Lorentz force which is usually covered in the second semester.

I live in The Netherlands. We don't really take classes, we have Physics through our entire high school. Lorentz force was covered the first time last year, which is the 5th year of high school.

 

[Lisastronomy]

OP:

* If you could fully understand the fundamentals of physics in high school, there would be no need for undergrad and grad courses and advanced seminars, would there? Learning physics (and most subjects) is an iterative process. So please don't get flustered that you don't understand everything at such an early stage (or ever).

* I'll suggest something different from, or in addition to, more math (depending on how much time you have). Do a small experimental science project. Does your school have science fairs? It will help you focus on a bounded problem that will result in a solution (of some degree). Even if you later specialize in theoretical physics, you will still need to know how to tie it to experimental results and stay grounded in reality. I know I'm expressing my personal bias: getting hands-on experience in a lab made physics more fun, more real, and more satisfying than studying theory in isolation (and you'll come to appreciate how more complex real-world scenarios are than the model scenarios in your texts).

I have noticed doing a small experimental science project really helps! This year I have been working on building a rocket with two classmates, and we need to make a project at the end of our last year of high school, which really helps to go through certain material. But still, I feel better about doing the theoretical work. But seeing how it works in practice, sometimes does help to see the reality in the material, as well. Thank you for your reply!