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Mathematics classes that will help with physics (list included) 
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#1
Feb2213, 06:10 PM

P: 122

Hello folks,
I was wondering if anybody could give me some suggestions on which mathematics courses will be of the most use for theoretical physics. I am a sophomore at Wayne State university and am taking intro to quantum mechanics and a first course in optics this semester. I am taking linear algebra to finish the basic math sequence over the summer here, (calculus, differential equations, and linear algebra) And I was just wondering if somebody could help me with finding out which classes would be most helpful to pursue studies in theoretical physics. I am dual majoring in mathematics, but I am mainly concerned not with getting a degree, as with getting knowledge Here is a listing of the classes offered at my school http://www.bulletins.wayne.edu/ubko....73.html#47937 Thanks 


#2
Feb2213, 08:55 PM

P: 178

Numerical methods.



#3
Feb2213, 08:58 PM

P: 122

For theoretical physics mate?



#4
Feb2213, 09:01 PM

P: 1,071

Mathematics classes that will help with physics (list included)
I did biophysics theory as an undergrad and we used numerical methods. 


#5
Feb2213, 09:07 PM

P: 122

So I have to confine myself to an area and theorize there? The undergrad stuff at my school is this.. I have left (in semester order)
Thermodynamics/stat mechanics, mechanics 1 quantum physics 1, mechanics 2 Quantum physics 2, electromagnetism 1 Electromagnetism 2, modern physics lab 4 semesters. But over the summers they do not offer these classes, so I want to take a lot of math classes over the summers to be the best I can be, I really like quantum mechanics a lot, I want to take a lot of quantum mechanics classes as a grad student, if that helps isolate classes. I was told elementary analysis (which is the class required to get into all those upper level classes on that list) is good, as well as partial differential equations and complex analysis, but then I heard algebra was good, probability theory, basically every teacher I ask tells me something different so I don't know what to do. 


#6
Feb2313, 12:36 AM

P: 1,417

It is quite hard to say since little of math (at least at the level you are considering taking) is useless for physics... following your own interests towards math can help too!
But anyway definitely take an analysis class, and definitely an abstract algebra class (for QM). Taking classes like complex analysis, probability theory, more abstract algebra, more analysis etc can all definitely be useful, but understand that whenever math is necessary in a physics class, you usually learns that math within the physics class, just much more quick and dirty and bareboned than in a full math class, but it's not like you'll ever get stuck if you don't take them. That being said two very important mathematics topics that usually get taught quite shabbily within a physics context (although it is definitely very useful to know them properly) are: representation theory (very important for QM) and differential geometry (very important for GR). (The problem is that they might be grad courses in your math department.) If you are really planning on going to the mathematical physics sides of things, i.e. you know you will be studying a lot of math in the future, then take as much analysis, algebra and topology classes to ensure a firm foundation for selfstudy down the road! 


#7
Feb2313, 12:56 AM

P: 122

Thanks for the advice. They teach a class next semester called 'Methods of theoretical physics 1', where you learn differential equations with boundary conditions, Fourier transforms, PDEs, vector analysis, and probably some other stuff, matrix methods I believe if I recall correctly.
There is a class called elementary analysis which is the prereq for all the higher math courses. I'm not great at math, I mean, I get A's, but I don't really feel like I understand it, so I want to focus on the things that I can apply towards physics. Unfortunately the elementary analysis is not offered this summer so I will have to take it next year so next summer I can take some algebra and perhaps something else. They do offer a lot of topology and things like that. I should just become a monk and go to school for the rest of my life. 


#8
Feb2313, 01:00 AM

Emeritus
Sci Advisor
PF Gold
P: 9,415

I don't see a need for knowledge of more than the most basic definitions (groups, rings, fields, homomorphism, isomorphism) and maybe a few simple theorems about homomorphisms from abstract algebra. This is something like 1/4 of a typical abstract algebra course. So I'm not sure I'd even include abstract algebra on the list. 


#9
Feb2313, 01:21 AM

Emeritus
Sci Advisor
PF Gold
P: 9,415

If you want to go into mathematical physics, you also need topology, measure and integration theory, and functional analysis. 


#10
Feb2313, 01:45 AM

P: 122

Thanks a lot. I suppose I will just reference this thread and reopen the conversation as I get a bit closer. There is so much, it is a bit boggling. I suppose for right now I will content myself to focusing on understanding my classes now.
And thank you everybody else as well. This gave me a lot to think about and I plan to revisit this question as I, and you, progress. 


#11
Feb2313, 02:03 AM

P: 1,417

As for abstract algebra: actually I agree that the material itself in an abstract algebra is not that important for QM (as in, all the theorems) but what seems immensely valuable to me from such a class is the reasoning skills you obtain when thinking about algebra (and it is a kind of mathematical maturity that is the distinct from the maturity you get from an analysis class, at least in my own experience). My opinion is that once you get the basics down icecold, it is much more possible to add to that the specific relevant physicsrelated pieces that you can selfstudy (e.g. representation theory), whereas to get the basics down can easily take the length of a proper math course on analysis and abstract algebra respectively. 


#12
Feb2313, 12:08 PM

P: 836

Just to add some merit of abstract algebra i physics, here is a cheap book (a Dover) on QM and group theory: http://www.amazon.com/GroupTheoryQ.../dp/0486432475



#13
Feb2313, 12:51 PM

Mentor
P: 18,327

The weird thing about your classes is that the Advanced Linear Algebra class requires two previous Abstract Algebra Courses. I don't really understand that. I'm not saying that Abstract Algebra isn't useful to understand before Linear Algebra, but I wouldn't put it as prereq.



#14
Feb2313, 02:53 PM

P: 1,066

If I could redo my math education for theoretical physics I would:
Take all the mathematical methods courses your schools physics and math departments offer. Take some numerical courses. Take real analysis, probability theory, combinatorics, complex analysis (Diff geo if I were more interested in GR), UD ODE's, PDEs and LA. 


#15
Feb2313, 03:30 PM

P: 772




#16
Feb2313, 03:41 PM

Mentor
P: 18,327




#17
Feb2313, 06:52 PM

P: 122

Well this post got quite interesting. This is all obviously beyond me, but hopefully these responses and any continued will serve as a guide to me in the future, as well as others too.



#18
Feb2413, 11:22 PM

P: 341

Check out this thread too (and my post over there):
http://www.physicsforums.com/showthr...58#post4271758 


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