/sci/ - Science & Math

[Anonymous No.5655448]

As a physicist, how deep ought I to go into maths? I understand/can use everything I have learnt/been taught so far, but I have often skimped over detailed derivations, focusing more on a general idea of where it came from, or ignored it completely. Is this going to fuck me over in the future? What should I really be doing, with respect to mathematics?

[Anonymous No.5655455]

I am your complete opposite, I tend to obsess over proofs and derivations when it comes to mathematics, and I'd say it wasn't really that helpful. At least if you are in the undergraduate Physics level. It might be more beneficial to grind you methodical maths skills, that extremely boring though, at least for me. That's why I'm considering leaving Physics after undergrad and do Mathematics in graduate school, and probably do some Theoretical (mathematical focused) Physics on the side.

[Anonymous No.5655466]

I think it depends on what you want to do in the long term. Theoretical physics requires you do be very adept when it comes to maths. In fact some of the best theoretical physicists have been mathematicians.

What is it that you want to do after undergrad?

[Anonymous No.5655464]

>>5655455

If it wasn't 'that helpful', is that to say it's helped you in certain situations? If so, which are they?
I plan on getting a PhD if things continue as they are, but so far, I've not come across a situation where knowing about proofs and derivations (I can do them; I just don't bother doing them because of time constraints) helps me solve a problem any better. I make sure I understand how everything is used/what they mean, etc.
Also, yeah, I spend a lot of time on mathematical methods; if anything, I've gotten used to it now and quite enjoy it.

[Anonymous No.5655470]

Are you planning on going into experimental or theory?

[Anonymous No.5655469]

>>5655448
you need the standard calculus, linear algebra, & ode. after that you need a math methods course. this will cover topics from advanced math that have actual application in stem. your physics/math department should offer this course. pure math course are a waste of time.

http://www.amazon.com/Mathematical-Methods-Physics-Engineering-Comprehensive/dp/0521679710

http://www.amazon.com/Advanced-Mathematical-Methods-Scientists-Engineers/dp/0387989315/

http://www.amazon.com/Introduction-Applied-Mathematics-Gilbert-Strang/dp/0961408804

[Anonymous No.5655485]

>>5655466
>>5655470

In a dream world, it'd be theory; I'd be a professor of theoretical physics. But let's face it, that simply isn't going to happen. So semi-ideal world is me going into experimental physics (Again, being a professor would be great), but again, not exactly easy to get into. So if we're being realistic, I don't know; it's a terrible idea to plan based on my ideal goals, because they're hugely unlikely. I remember as a child I'd ponder limiting questions, like "Just how close can you get to this wall before you can't get any closer?", so I'm very interested in tiny things, and in particular why they're different from big things, so GR, QM, and nanotech are all up my alley.

>>5655469

No, I know what mathematics I actually need to know (Thanks for the links anyway), but I am basically asking how rigorous I need to be. If I can use the principles/equations from mathematics in practice, do I need to know why they are true? Of course this is the case for physics; I can't use F=ma is mass is changing, for example, but is it so for mathematics? There won't be a time when the integral of cosine isn't sine, for example?

[Anonymous No.5655489]

>>5655485
Well if you think you have a chance at theoretical physics then it's worth being rigorous with the maths. Proving things will allow you do develop a deep understanding for why things work as they do and so will help you develop other ideas.

At the top levels you need to be able to create "new maths" rather than just apply formulas again and again.