Hey guys, rising freshman here. I’m planning on double-majoring in physics and chemistry and already wondering what math classes I should take freshman year xD I’m primarily talking to my department about this but since I’ve received so much good advice on CC I thought I’d widen the net.
Here’s my situation: I’ve taken physical chemistry already but also love math and dislike the cultural attitude in physics of introducing mathematical tools sloppily when you need them. I like having a rigorous grasp of the math I’ll need before I need to use it, so I feel I really understand what I’m doing. The physics department is telling me to take real analysis if I want that but I’ve already taken it.
What math classes would you recommend for physics? I’m ok with drawing my own connections outside class but want understand the math before I need it. I plan to take quantum mechanics and relativity, both topics in which I have no prior rigorous background. I’ve considered taking some college algebra and geometry classes but I don’t know if they’ll be applicable.
PS: I’m at a flagship state school, so whatever class you can think of they probably have it. Don’t worry about the exact name, I can probably find the equivalent if given what the major topics are
@rejectedlion2016 What have you already taken? It seems like you’ve already taken real analysis but not college algebra or geometry.
Most courses labeled “college algebra” tend to be at the level of high school algebra II or pre-calculus, and while it’s definitely important, you shouldn’t take it if you already have a solid understanding. There are certainly more advanced algebra and geometry courses though!
You will almost certainly need calculus (up to multi-variable), differential equations, and linear algebra as a physics major - I am not a physics or chemistry major myself but I’ve seen enough applications of these subjects in physics, including quantum mechanics/computing. I would suggest taking these if you haven’t already. Other courses such as statistics, partial differential equations, and abstract algebra might come in handy at the higher level.
I agree with MITer94, you’re probably going to need calculus (througn multi-variable), differential equations, and linear algebra. Those are standard intro STEM math classes. If you haven’t taken those yet, I recommend them. And of course, keep talking with your department about this.
@thatrunnerkid@MITer94 ??? LOL guys, I don’t think there’s any more calculus I can take. Sorry I was unclear, I mean classes at real analysis-level or above (i.e., advanced undergrad or grad). I finished those classes last year. That’s why I’m taking real analysis now.
I’m thinking about abstract algebra or differential or algebraic geometry (what I meant by algebra and geometry - not remedial algebra and geometry rotfl). Wikipedia seems to confirm they would be useful but I don’t know if I want to do them now if I won’t use anything beyond lecture 3 until senior year. What about applied math classes? I know next to nothing about applied math and the department hasn’t been helpful either - what are the keywords I should be looking for?
@rejectedlion2016 Ah, sorry lol. I saw “college algebra” and geometry and wasn’t 100% sure what you meant…
PDE may not be a bad idea. Besides PDE and abstract algebra, I can’t really think of much atm. You may want to go to your university’s course catalog, search for some upper-level physics or chemistry classes that look interesting and see what math pre-reqs are required. Because I’m not a physics or chem major, I can’t really say much first-hand.
Is it correct that you have taken the usual frosh-soph level courses:
single variable calculus
multivariable calculus
linear algebra
differential equations
?
Beyond those, real analysis and complex analysis may be suggested for physics majors. But lots of other advanced math courses like abstract algebra, partial differential equations, differential geometry, etc. can also be applied to physics (based on looking at some web pages for physics and applied math majors).
Here are some suggested courses by one math department for applied math majors with various areas of application: https://math.berkeley.edu/programs/undergraduate/major/applied . You may want to pay attention to the listings for classical mechanics, quantum mechanics, and relativity, and reference the course listings at http://guide.berkeley.edu/courses/math/ to see the course descriptions, so that you can select similar courses at your own school.
@MITer94 yeah that’s the thing, most of them don’t have massive math prereqs beyond just calculus/lin alg/diff eqs, preferring to introduce higher math as you need it. I like to have an understanding of the math before I need it, or at least in parallel
@ucbalumnus yes that’s correct. Huh, I hadn’t considered complex analysis, are you sure? It’s interesting to me but also very different from real analysis. That’s a really useful link, thanks. Numerical analysis looks like another useful class
Does your current analysis class cover multi-variable topics such as implicit function theorem? If not, look for a class like that. Also a rigorous course in probability would be good. A class that develops Fourier series and transform rigorously would be useful as well. If there is an algebra class that focuses on matrix groups (or anything involving real/complex matrices like Horn and Johnson), that would be useful, but you may want to take a general algebra class first. The other suggestions people have made are also good. I would start with either prob, multi-variable analysis, PDE’s or complex. If you care about rigorous background, you will also want to take a course in measure theory eventually.
tl;dr any analysis course (including complex, harmonic, PDE’s and probability) or course on matrices would be a good place to start.
Yes it does cover MV topics. I’m fortunate to be in the analysis class with graduate students, not the undergrad math major weeder xD. Probability sounds good at some point, though shouldn’t I take measure theory before that? I know a bit about Fourier analysis but I think there is a class I can take specifically about Fourier analysis.
So far I’m thinking PDE and abstract algebra for the fall. I might add numerical analysis but I plan to take things slow in my first semester so I’ll see how those go first (and will obviously be taking some chemistry or physics and humanities). FA is usually offered in the spring I think so I’ll definitely take that. What class is tensor calculus taught in? That’s really a huge gap in my education so far - my knowledge stops quite abruptly at multilinear forms and I barely know what tensors are.
I would recommend taking calc based prob before measure theory based, as there are many, many interesting and important things you can learn about prob before taking measure theory. And the measure theoretic approach obscures some of the intuition for most students, so it is better to have a solid background first.
My understanding is that differential geometry is where you would learn about tensor calculus, but I don’t think you will get the computational practice that you will need for physics from the math department. Not 100%, though.