What kinds of math do I need to understand the world around me?

[Evanish]

My understanding of science has always been limited by my lack of adequate math skills. Eventually I reach explanations and studies filled with equations, symbols and variables I don't understand and I find myself at a dead end. I've done pretty well with my limited skills, but I kind of want to understand more. I don't think I'll every understand it all, but I think I can do better then I'm doing now. In order to have a better understanding of science what types of math do I need to focus on learning?

 

[HallsofIvy]

It's not a matter of "focusing" on a specific type of mathematics. It's a matter of each form of mathematics depending on previous kinds of mathematics. If you have not already, start with algebra. Then go to trigonometry and some geometry. By then you will be ready for Calculus. Then differential equations and differential geometry.

 

[micromass]

My understanding of science has always been limited by my lack of adequate math skills. Eventually I reach explanations and studies filled with equations, symbols and variables I don't understand and I find myself at a dead end. I've done pretty well with my limited skills, but I kind of want to understand more. I don't think I'll every understand it all, but I think I can do better then I'm doing now. In order to have a better understanding of science what types of math do I need to focus on learning?

Your post is pretty vague. What science exactly do you wish to understand? And what do you mean with understanding? For example, a understanding of the mathematical foundations of QM should need a different skillset than understanding evolution in biology.

 

[Evanish]

Your post is pretty vague. What science exactly do you wish to understand? And what do you mean with understanding? For example, a understanding of the mathematical foundations of QM should need a different skillset than understanding evolution in biology.

I'm a curious person. I'm interested in a lot of different subjects. If my post seems vague it's because my motivation is somewhat vague as well. Mostly I just want to understand the things I want to understand when I want to understand them. Not a very realistic objective, but still something to strive for. The latest thing I've been struggling with is spectroscopy. I don't really get diffraction grating especially when Rowland Circles are involved.

 

[homeomorphic]

Calculus, differential equations, linear algebra, prob/stat.

 

[symbolipoint]

I'm a curious person. I'm interested in a lot of different subjects. If my post seems vague it's because my motivation is somewhat vague as well. Mostly I just want to understand the things I want to understand when I want to understand them. Not a very realistic objective, but still something to strive for. The latest thing I've been struggling with is spectroscopy. I don't really get diffraction grating especially when Rowland Circles are involved.

... as in "optics", then you want Trigonometry, along with what the other has mentioned.


For spectroscopy, discrete math would be helpful more than you would first imagine. If you are just interested in transmittance and absorbance, then intermediate algebra is enough.

 

[Astronuc]

My understanding of science has always been limited by my lack of adequate math skills. Eventually I reach explanations and studies filled with equations, symbols and variables I don't understand and I find myself at a dead end. I've done pretty well with my limited skills, but I kind of want to understand more. I don't think I'll every understand it all, but I think I can do better then I'm doing now. In order to have a better understanding of science what types of math do I need to focus on learning?

It depends on how deeply one wishes to understand many phenomena and physical systems.

Basically one needs calculus through partial differential equations, linear analysis, complex analysis, and perhaps vector/tensor calculus, and a few others like HallsofIvy mentioned, and micromass and others will probably mention more. There is also numerical analysis with one does computational physics.

 

[Evanish]

Thanks for the suggestions everyone. I was using khan academy for a while and I think I was making progress, but then I took a break from it over which I seemed to forgot most of what I learned. The biggest problem I seem to run into with learning math is that I've gone about learning in such a sporadic undisciplined manner that I'm not really sure what I know and what I don't know. My math skills are like a road where parts are newly paved and other parts are giant gaping potholes. Knowing where those holes are so I can fill them in is the difficult part. Maybe I should try to put in a few hours everyday on the subjects suggested here. Eventually I'll manage to fill in the missing pieces even if I have to go over the same stretch of road over and over again.