Wondering which Math Class to take next

[AlexChandler]

Hello Everybody
I am a Physics Major transferring to Michigan State University next semester. I have completed Calculus based Physics 1 and 2, as well as Calculus 1,2,3, Linear Algebra, and Differential Equations. I am wondering which kind of math class some of you may recommend to take next.
I will be taking Thermodynamics and Modern Physics as well as General Chemistry next semester.
MSU requires that I take 2 300+ level math courses.. of course I would like to take more.
Here is a Math Course I am currently looking at:
Advanced Calculus...The real numbers; limits; continuity; sequences and series of functions; uniform convergence; power series; differentiation; integration.
Any other recommendations?
Thanks
Alex

 

[fss]

Advanced Calculus is probably a good one; does it cover Fourier transforms?

 

[AlexChandler]

It says Fourier Transforms are covered in MTH 922 Harmonic Analysis.. but that requires about six courses that I haven't taken yet. Fourier Series is covered in MTH 340 Ordinary Differential Equations I. But that requires a higher linear algebra course, which i would not mind taking. Are these used a lot in physics?

 

[hitmeoff]

It says Fourier Transforms are covered in MTH 922 Harmonic Analysis.. but that requires about six courses that I haven't taken yet. Fourier Series is covered in MTH 340 Ordinary Differential Equations I. But that requires a higher linear algebra course, which i would not mind taking. Are these used a lot in physics?

Before people chime in with suggestions on taking Analysis or Complex Analysis or something of that nature, Id like to state my opinion.

Im a Math/Physics major, and am currently taking the Abstract Algebra and Analysis series, as well as doing the junior level mechanics. My feeling is that pure math could be extremely useful for physics, especially if your looking to do theoretical. Not sure what your goal is, but if you are looking for a math class to help you out with your physics classes, understand that Analysis will take a while to pay off.

In Calc 1-3 you learned how to do calculus, in analysis you build up the calculus. You will be spending the better part of the semester going through properties of numbers, building up a definition of real numbers, sequences and limits. It'll probably be a while before much of what you learn will pay off with any kind of real application to physics. In this regard, a class that might have more immediate payoffs would be a course on (junior level) PDEs and ODEs.

On the other hand, I think you are going into sophomore level modern and thermo, right? Like the third semester of calc based physics? If this is the case, then you've pretty much have done all the math you need for those classes. Actually, quite a bit more. So u don't necessarily need a math class to pay off NOW. In this case, then yes Analysis is the way to go, because its typically a gateway class to other junior level math classes that are very immediately like Differential Geometry, Fourier analysis, Topology, etc.

Also a word of caution: junior/senior level math classes are completely different than what you are used to. Upper division classes are largely proof driven. You will be asked to prove alot, most of your work will involve proving things, you probably won't be doing much calculating and instead be working with very abstract concepts.

I know few people who DONT struggle with that first upper division math class, because they are simply not used "proofs." I have spent literally all day working on a single homework problem. I am not saying its not worth it. Of course its worth it, the harder you make your mind work, the more alert its going to be whenever you try to learn something else. Just be conscious that upper division math is very different from anything else you have done and will take quite a commitment .

 

[AlexChandler]

Haha! I like the sound of these higher math courses. I have the commitment for it, I am sure of that. I get so absorbed into my work I often will forget to eat or drink or other things humans should do. The Analysis course sounds great to me. And I've heard so much about differential geometry and topology in books! Its very exciting.
So are you a double major? I've been thinking about doing that. I know that I want to do Physics, but there is so much Math that I want to know as well. Is this common to double major?
I've done a bit more research and have found a small list of classes that I have the prereq's for.
MAT 5000 Proof Writing... prerequisite for Intro to Topology
MAT 5070 Advanced Calculus... (Analysis I)
MAT 5280 Methods of Diff EQ
MAT 5400 Elementary Theory of Numbers
MAT 5410 Applied Linear Algebra
MAT 5420 Algebra 1
MAT 5530 Elementary Differential Geometry

I think Advanced Calculus sounds the best at this point.
Im also wondering about another thing. I took Multivariable Calculus about a year ago (before I started really excelling in Math/Physics) and got an "A-" ...and really didn't learn nearly as much as i could have.. Would it be a good idea to retake the course? Or should I just look through my book and brush up a bit?
Sorry to ask so many questions.. but i don't know anybody else who can help!
Thank you,
Alex

 

[Bourbaki1123]

You have the prerequisites for Elementary Differential Geometry but you haven't taken proof writing? I don't even see how you could take that course without advanced calculus and topology as well. Maybe I don't know what they mean by 'Elementary'? What are the topics?

 

[AlexChandler]

5530 Elementary Differential Geometry and its Applications. Cr. 3

Prereq: MAT 2030 and 2250. Introduction to the differential geometry of curves and surfaces in three-dimensional space. Curvature, torsion, Frenet formulas, fundamental theorem of space curves. Gauss and mean curvature, asymptotic and principal curves, geodesics, Gauss-Bonnet theorem. Applications such as pursuit curves, roulettes, brachistochrones, precession of Foucault's pendulum, design of packaging machines, shapes and soap films. (I)

The Prereq's for this course are Calculus III and Elementary Linear Algebra

 

[Daverz]

5530 Elementary Differential Geometry and its Applications. Cr. 3

Prereq: MAT 2030 and 2250. Introduction to the differential geometry of curves and surfaces in three-dimensional space. Curvature, torsion, Frenet formulas, fundamental theorem of space curves. Gauss and mean curvature, asymptotic and principal curves, geodesics, Gauss-Bonnet theorem. Applications such as pursuit curves, roulettes, brachistochrones, precession of Foucault's pendulum, design of packaging machines, shapes and soap films. (I)

The Prereq's for this course are Calculus III and Elementary Linear Algebra

So we're talking about Wayne State University? I don't see an elementary differential geometry course on the MSU website.

Take this course if you can.

On the MSU website I see:

http://www.reg.msu.edu/Courses/Request.asp?SubjectCode=mth&Term=current

The 301 Foundations course looks like it might be useful for theoretical physicists. One ends up studying a lot of math on ones own anyway, and getting some basics would help in reading advanced math texts.

Also Applied Advanced Calculus looks kind of useful, though some of it may be redundant.

But since their physics department has a "math methods" course, LB 415 Methods of Theoretical Physics that covers most of what you need, I'd just take whatever math courses interest you.

 

[hitmeoff]

Haha! I like the sound of these higher math courses. I have the commitment for it, I am sure of that. I get so absorbed into my work I often will forget to eat or drink or other things humans should do. The Analysis course sounds great to me. And I've heard so much about differential geometry and topology in books! Its very exciting.
So are you a double major? I've been thinking about doing that. I know that I want to do Physics, but there is so much Math that I want to know as well. Is this common to double major?


I think Advanced Calculus sounds the best at this point.
Im also wondering about another thing. I took Multivariable Calculus about a year ago (before I started really excelling in Math/Physics) and got an "A-" ...and really didn't learn nearly as much as i could have.. Would it be a good idea to retake the course? Or should I just look through my book and brush up a bit?
Sorry to ask so many questions.. but i don't know anybody else who can help!
Thank you,
Alex

I am double major. And I feel the same as you do. Physics is where I want to be, but I also HAVE TO learn as much math as possible. My ultimate goal is to do Mathematical/Theoretical Physics, so I figured an undergrad degree in both should help me out with what it is I want to do.

As far as it being common...dont know about that. I personally know of several people that were "thinking" about doing both, but they eventually settle into one or the other. I only know of one other person (at my campus) personally, who is also doing both Math and physics.

It is NOT an easy double major to undertake. You would think there's a lot of overlap in the subject matter, but there really isn't at this level. For example, though group theory can be used in physics, don't expect your knowledge of group theory (for mathematicians) to be of much help in your QM class (Griffiths book, which is the standard for undergrad QM barely even mentions it and certainly doesn't use it). So you really are undertaking two very different majors that require two different approaches. Switching gears between high level math and high level physics is not easy.

Sounds like you are very motivated though, and if you truly love the subjects then you should definitely go for it. At one point in my life I was questioning my decision because it was so hard to do, but now I am motivated by the challenge of learning both.

As far as retaking Calc III, I will say this: You best know all of your freshman and sophomore level math very well. You will use it all as a physics major, Calc, Series, DEs and LA are all beyond important for all upper div physics courses. With that said, your physics dept should offer some sort of sophomore level mathematical methods course which will crush 2 years of lower division math into one semester/quarter long course. This type of class should tidy up all of your math skills. If this kind of course isn't offered, then just review on your own over the course of the the year, so by the time you take your first upper div class in physics, you'll be ready.

On the courses you listed. If you KNOW you are going to take upper div math, taking the proofs course could be useful. Personally, I didnt find that my proofs class was much help and it seems a lot of my class mates felt the same way, but maybe my schools course sucks. I'll just say that the most I got out the class was a familiarity with math symbols and some set theory concepts. Past that, the proofs we did in that class really didn't help me for the types of problems faced in Algebra.

Though Number Theory probably has the least amount of applications to physics in the whole list, the course will definitely sharpen your proof skills and will prepare you for things like Algebra.

I'm surprised the you didn't list (junior level) Linear Algebra as a class you can take. This is usually the first rigorous math class a math major takes. If there is any class PERFECTLY SUITED FOR YOU, this is it. You will still deal with a lot of proofs, but because you've seen the (computational side of the) material before, it is much more intuitive than Algebra as a first rigorous math class. Plus, outside of a PDE and ODE class, its probably the most directly and immediately applicable upper div class you will take.

 

[Mororvia]

In my days as a physics major at MSU, my 2 300+ level math courses were MTH 314 Linear Algebra (no proofs) and MTH 441 Ordinary Differential Equations II. One question should be, are you sure your version of Linear Algebra won't get counted as MTH 309 (proofs) or 314 when your transfer? MTH 309 opens up a lot more possibilities.

Anyway, others I would consider from the math department: MTH 442 Partial Differential Equations or MTH 443 Boundary Value Problems for Engineers (this would help in physics too)

Good luck

 

[AlexChandler]

In my days as a physics major at MSU, my 2 300+ level math courses were MTH 314 Linear Algebra (no proofs) and MTH 441 Ordinary Differential Equations II. One question should be, are you sure your version of Linear Algebra won't get counted as MTH 309 (proofs) or 314 when your transfer? MTH 309 opens up a lot more possibilities.

Anyway, others I would consider from the math department: MTH 442 Partial Differential Equations or MTH 443 Boundary Value Problems for Engineers (this would help in physics too)

Good luck

The LA course I took is only counted as GCU. So I think I will definitely take 309. I'm excited about PDE as well. Thats awesome that you went to MSU! I actually have not been accepted yet, still awaiting the letter in the mail. I expect to get in... but also looking at Wayne State. I may just go to WSU for a semester and reapply to MSU for next fall. The classes I have listed are those at WSU.
So what is the physics department like at MSU? Do they have good professors?

 

[AlexChandler]

I'm surprised the you didn't list (junior level) Linear Algebra as a class you can take. This is usually the first rigorous math class a math major takes. If there is any class PERFECTLY SUITED FOR YOU, this is it. You will still deal with a lot of proofs, but because you've seen the (computational side of the) material before, it is much more intuitive than Algebra as a first rigorous math class. Plus, outside of a PDE and ODE class, its probably the most directly and immediately applicable upper div class you will take.

Yes the courses listed are from Wayne State University. I am still waiting for acceptance from MSU so I am looking at WSU classes right now because I have already been accepted there. I was surprised as well to not see LA. They have applied linear algebra though:

5410 Applied Linear Algebra. Cr. 4

Prereq: MAT 2030 and 2250, or consent of instructor. Gaussian elimination, vector spaces, the four fundamental subspaces, orthogonality, least squares approximation, determinants, eigenvalues and eigenvectors, positive definite matrices, singular value decomposition, linear transformations, complex matrices. Applications such as differential and difference equations, Markov processes, graphs and networks, Fourier series, computer graphics, numerical linear algebra. (B)

MSU does actually have a junior level LA course with proofs, and if I'm accepted there, that may be the course I take. It will be between that or Analysis I. But I also have the Prereqs at MSU for PDE which I have been hearing a lot about.

One other thing I was wondering about is statistics. I have never taken a stats course.. not even in high school. Should I take a course in statistics? At WSU they have one lower level stats course:

2210 (MAT 6150) Probability and Statistics for Teachers. Cr. 4

Prereq: grade of C or better in MAT 1800; 2010 recommended. No credit after MAT 5700. Counting techniques, discrete sample spaces and probability, random variables, mean and variance, joint distributions, the binomial and normal distributions, the central limit theorem, estimation and hypothesis testing. (T)

 

[AlexChandler]

So we're talking about Wayne State University? I don't see an elementary differential geometry course on the MSU website.

Take this course if you can.

On the MSU website I see:

http://www.reg.msu.edu/Courses/Request.asp?SubjectCode=mth&Term=current

The 301 Foundations course looks like it might be useful for theoretical physicists. One ends up studying a lot of math on ones own anyway, and getting some basics would help in reading advanced math texts.

Also Applied Advanced Calculus looks kind of useful, though some of it may be redundant.

But since their physics department has a "math methods" course, LB 415 Methods of Theoretical Physics that covers most of what you need, I'd just take whatever math courses interest you.

I am very interested in Differential Geometry. When I read about Paul Dirac, it kept repeating how essential his background in differential and projective geometry was to his way of analyzing things in physics. I would also like to take a course in Technical Drawing. MTH 301 looks very useful actually, it looks to be a great first higher math course. I like the sound of Applied Advanced Calculus as well! but it also sounds like LB 415 will cover what I need there. Its very hard to decide.
I greatly appreciate the help!

 

[Mororvia]

So what is the physics department like at MSU? Do they have good professors?

Some are better than others, of course. Generally, everyone I had was alright. Just remember to go to office hours and ask for help if you need it. In fact, go to office hours occasionally anyway so you get to know some of them a little more. This will come in handy if you would like to get involved in research or if you will need recommendation letters later.