Which Fall Schedule Option Should I Choose as a Math and Physics Major at MSU?

[AlexChandler]

Hello,
I am a math and physics double major and a junior at Michigan State University. I have already taken introductory physics, the first semster of classical mechanics, a course in thermodynamics and modern physics, and linear algebra (along with the basic calculus and diff eq courses) I have recently decided to begin the advanced track program in mathematics which is supposed to be much more difficult than the normal math degree. This fall, I am having a difficult time deciding which schedule would be best for me. I definitely have to take Chemistry 142, and Classical Mechanics II (Phy 422).
I have two different options for which other two classes to take.

Option 1:

Quantum Physics I (Phy 471)

Description: Schroedinger equation, hydrogen atom, harmonic oscillator, and other one-dimensional systems.

and

Honors Algebra I (MTH 418H)

Description: Theory of groups, Sylow theory, the structure of finite Abelian groups, ring theory, ideals, homomorphisms, and polynomial rings.

or Option 2:

Electricity and Magnetism I (Phy 481)

Description: Electrostatics, dielectrics, magnetic fields of steady state currents, Faraday law of induction.

and

Intro to Advanced Analysis (MTH 327H)

Description: Real and complex numbers, limits of sequences and series, continuity, differentiation, Riemann integration of functions over R, uniform convergence.

Now if I take option 1 that means i have to take the second semester of quantum and algebra the following semester. If I take option 2 that means I have to take the second semester of E&M and Analysis the following semester. And each way I will have to wait until the following year to study the other option courses.

I am leaning toward taking option 2 (E&M and Analysis) simply because this is my first semester taking an advanced math course and I think Analysis would be the better course to take first. Also I feel that Analysis would help me with my understanding of calculus, which I will be using extensively in my physics courses.

My advisor is recommending that I take option 1 (Quantum and Algebra)

Any advice would be much appreciated.

Thank you

 

[G01]

If your main interest is physics, and you are considering grad school, I would suggest option 1.

You will to start thinking about the physics GRE if you plan to continue physics studies. Some 1st semester quantum mechanics will appear on the physics GRE, however, very little 4th year E&M will appear. So, I think putting E&M off until your last year will potentially be less troublesome.

 

[upsidedowntop]

My advice is to choose based on what sort of math you like more.

Quantum uses a lot of linear algebra, differential equations, probability, and a little abstract algebra.

Electromagnetism is much more similar to mechanics than quantum is. It relies more on vector calculus and differential equations. The reliance on PDEs in electromagnetism is much less than in quantum.

Regarding the math courses, I'll give you a description of what sort of thing you study in the course.

For abstract algebra, you study types of algebraic systems: groups, rings, fields, modules, vector spaces, etc... If you've already taken linear algebra you should know about vector spaces. A lot of different objects can be made into vector spaces: tuples of real numbers, matrices of real numbers, continuous functions from R->R, infinite sequences of complex numbers. The same applies to the other algebraic classifications. A lot of different objects are rings or fields or whatever, so it's useful to learn about all of them at once by studying the algebraic properties that they have in common.

For (real) analysis, you study the real numbers in depth. My first week real analysis assignment involved proving the existence of logarithms. Then we did a bit of topology and learned to deal with limit properly. For example, proving that lim n->infty (n)^(1/n) -> 1. After that we studying some of the properties of continuous functions, then on to proving various differentiation rules, FTC, MVT, IVT, etc. Then Defining integrals and proving various integration rules, then sequences of functions.

Pick whatever sounds interesting to you now and study that.

 

[AlexChandler]

Thanks so much for your comments. In light of this i suppose i will probably go with option 1 and wait for next year to do the other classes. I hadn't even thought of the GRE when putting together my schedule. Thanks for that reminder!