Advise on math courses to supplement physics major

[connorb1542]

Hi, I am entering Rice University this fall as a Physics major, with the intention of double-majoring in Mathematics. Although I'd like to take every math class they have to offer, I need some advice on which math classes are crucial in providing a mathematical foundation and possibly a timeline for when to take such classes. My plan is to take these math classes BEFORE I get to the Physics classes that rely heavily on these topics to better understand the actual Physics going on and not getting tripped up by the math.

At Rice, its standard for a math major to start off with completing the calculus sequence, and also a class titled "Ordinary Diff. Eq.s and Linear Alg.". Then you complete eight courses at the 300 level or higher. I will list a few different branches of math below, but here is the full course offering http://courses.rice.edu/admweb/swkscat.main?p_action=CATALIST&p_acyr_code=2012&p_subj=MATH"

Analysis
Linear Algebra
Abstract Algebra
Geometry
Calculus on Manifolds
Lie Theory
Topology

Any advice is appreciated!

 

[connorb1542]

Also, here is a link to Computational and Applied Mathematics course offerings
http://courses.rice.edu/admweb/swkscat.main?p_action=CATALIST&p_acyr_code=2012&p_subj=CAAM

 

[micromass]

Hi connorb1542!

It is my personal opinion that every math major should take at least one course in abstract algebra, real analysis and topology. That way you get exposure to the three majors branches of mathematics: algebra, analysis and geometry.

However, you've not told us why you want to do a math major. Do you want the mathematics to help you with the physics? Or do you simply find it interesting? If so, what part of mathematics do you find most interesting? The more we know about you, the better our suggestions will be!

 

[Nabeshin]

A few words about the applicability of these courses to the physics major...

1) An advanced linear algebra course is perhaps the most helpful, even though 95% of what you need will likely be covered in your first course, and the extra 5% will be simply stated as fact in physics courses.

2) Some kind of differential geometry/knowledge of manifolds could be helpful for GR, but most likely at the graduate level rather than undergraduate.

3) Abstract algebra is a big part of theoretical physics, but likely not one which you will experience in your undergraduate education. At best, you might hear a bit about groups in classical mechanics or when taking a particle physics class, but this will be much more superficial than studying these structures in a mathematics class.

4) All the other classes you mention are not very applicable to undergraduate physics, so if you want to take them you should make sure you do it because you're interested rather than you think they will be beneficial.

Note: I like to try and downplay the importance of these abstract mathematics classes when giving people advice. A lot of people just think that all mathematics will somehow be applicable to physics, but the reality is that the entire undergraduate physics education rests just on calculus and linear algebra. Only really if you are planning to continue with graduate studies in a theoretical field, like particle physics, does the higher level math become useful. That said, taking math courses will never hurt you, and will only open your eyes to things that might be hinted at in an undergraduate education, but don't expect it to bolster your exam scores or anything like that!

 

[connorb1542]

Two things i should clarify:
1.) I find math interesting because i enjoy problem solving. In this sense, i also love math because i love being able to describe real-world phenomena with equations(ie, physics).

2.) I want to continue into graduate school for physics. I am not sure exactly what branch of physics i want to go into, but primarily i am considering theoretical (HEP or otherwise) and possibly biophysics(i find the field of quantum biology particularly interesting). Back to the issue: a big reason why i want a solid math foundation early on is so i can understand the physics THEORY going on without struggling to understand the math concepts used to describe the theory. In addition to bolstering my undergraduate education, i would also like the math to be helpful to my graduate studies/research as well.

 

[micromass]

Courses you should probably consider doing (other than what I already suggested) are
- Linear Algebra (you will need this all the time!)
- Partial Differential equations
- Calculus of Variations
- Functional Analysis (for quantum stuff)
- Lie Theory
- Differential geometry

Like Nabeshin already said, you probably won't need much of this in undergraduate, but once you're beginning in grad school, all of this becomes immensely important, certainly in theoretical physics!

 

[flyingpig]

4) All the other classes you mention are not very applicable to undergraduate physics, so if you want to take them you should make sure you do it because you're interested rather than you think they will be beneficial.

Ah damn it and i was going to take Analysis next year too...

 

[connorb1542]

thanks for the input!

@micromass - I am become grammar, the corrector of sentences!

 

[XiaoZheng]

Hey, I am a rice freshman studying physics too! which college are you from?