How to Determine Aptitude for Mathematics

[Payton]

Unfortunately, the American education system is impartial toward passionate minds lacking an overabundance of financial stability. With a recently developed appreciation for mathematics I feel as if I should be pursuing the study of theoretical physics; however, I simply do not know the right way to approach this interest. If I were to study physics formally, I fear two possible and probable outcomes: 1) I don't have the mind for it, and/or 2) I don't have the passion for it. I do not see the value in obtaining a "higher education" in any field of mathematics if it is even possible that the time and money invested into attempting to satisfy my curiosity could effectively disappear.

Before committing myself to any specific path, I would like to have some sort of base for any potential decisions I may have to make. So, I ask of anyone who might be able to answer:

How does one accurately determine one's own aptitude for mathematics?

Thank you.

 

[Angry Citizen]

How does one accurately determine one's own aptitude for mathematics?

Are you getting C's in high school math? If so, you're not cut out for mathematics -- probably. Do proofs make you squirm uncomfortably in your seat? If so, you'll learn later.

In my opinion, don't be so damned timid. Take a chance. You've never encountered real mathematics. You've also never encountered real physics. The only way to know if you're a) good at it, and b) interested in it, is to jump in with both feet, and that means enrolling at a university. It is possible to transfer to a lucrative career such as engineering if you find your interest waning in pure maths/sciences during school. If you're American, you're going to take general education courses that'll expose you to non-scientific fields that might interest you away from STEM.

 

[AlephZero]

How does one accurately determine one's own aptitude for mathematics?

The same way as for any other skill. Try doing it, and see how good you are compared with other people.

From your OP, it seems clear you don't have much passion for it - not yet, anyway.

 

[Jack21222]

I do not see the value in obtaining a "higher education" in any field of mathematics if it is even possible that the time and money invested into attempting to satisfy my curiosity could effectively disappear.

So you want to be 100% sure? If you want 100% certainty in anything in life before trying it out, then I'm afraid life isn't for you. You'll end up never doing anything.

 

[PhDorBust]

Don't worry so much, there's lots of room for mediocrity in the world. The average university student (at lesser schools) probably spends less than 10 hours a week studying, and that's whom you'll be competing against. Moreover, there's nothing unique about your individual constitution. There is a certain elegance to mathematics and physics, and you will undoubtedly find it if you invest the proper time.

 

[mathwonk]

the same way you find out whether you can climb a hill, you start up it (after warming up and carrying water and good shoes and socks).

 

[Duderonimous]

Are you getting C's in high school math? If so, you're not cut out for mathematics -- probably.

I beg to differ...I was a flake in high school and graduated having only taken algebra I and geometry(barely passed geometry). Mind you this was in Hawaii where your only motivation is either smoking pakalolo (weed) or getting barreled (surfing). When I moved to live with my dad in California I attended the local community college. My interest in math and the sciences greatly increased and I can't get enough of it. Even more so for the rigorous proof oriented math classes. Constructing a proof is an art form. Maybe I'm the exception to the rule.

 

[Payton]

I suppose the more appropriate question should have been, If I were to attempt to teach myself mathematics, where would I start?

 

[Angry Citizen]

I beg to differ...I was a flake in high school and graduated having only taken algebra I and geometry(barely passed geometry). Mind you this was in Hawaii where your only motivation is either smoking pakalolo (weed) or getting barreled (surfing). When I moved to live with my dad in California I attended the local community college. My interest in math and the sciences greatly increased and I can't get enough of it. Even more so for the rigorous proof oriented math classes. Constructing a proof is an art form. Maybe I'm the exception to the rule.

You missed my point. I did say 'probably'. My point was simply that there is no way to predict one's skill at higher mathematics.

 

[jtbell]

If I were to attempt to teach myself mathematics, where would I start?

From wherever you are right now, of course.

How much math do you already know or have studied?

 

[FourierFaux]

If you have the passion for it, you can develop a mind for it. Every single person on this board started off where you are right now at some point.

What really matters in the long run is your interest in a subject. Practicing physics or engineering or math isn't really that much different from becoming a professional musician. The ones that shine are the ones that spend hours every day refining their art. Burning the midnight oil as it were. They can do it because they love it, they couldn't not do it. There are plenty of interesting things to do in life, pick one.

The answer to your question:
You determine your aptitude in mathematics. Find a book on a branch of mathematics that you understand. Read it. How much math can you stomach in a day? Feel free to take small breaks... they can help you to digest difficult material.

To learn any branch of math and any technique in math is eerily similar:
0) Time to play. (This is where your passion kicks in)
1) Identify what you know.
2) Identify what comes next.
3) Find a book that merges what you know with what comes next.
(They are easy to find)
4) Start from what you know.
5) Practice lots of problems to test what you know.
6) If you understand and can solve the practice problems and if you can reproduce the technique... you understand the material. Teach it to yourself so that you never forget it.
7) By this point you should be ready to move on.
8) Ask yourself, "Did I enjoy this?", if yes; repeat all the previous steps.

This is in a nutshell what the educational system should be designed to teach. Not having the mind for something in most peoples cases (ie those who don't suffer from a real physiological brain problem) is an illusion. If you're not passionate about something, you won't have the interest that will act as the catalyst for the enormous amount of discipline that will be necessary to master it. Your passion is the limiting factor.

 

[Payton]

thanks for the replies.

The highest level of mathematics I have been exposed to is Calculus... What kind of book should I pick up?

 

[FourierFaux]

I learned from James Stewart. Somebody else may have a better recommendation.

 

[General_Sax]

Stewart here too. I think his text lends itself well to self-study, because it's relatively simple examples and it's easy to find solution manuals.

Plus I think I heard somewhere that one can download it easily...