What extra Maths course should I take (Physics major)?

[Ryker]

I'm going to be a second-year student next year, and since for the first semester I only have three courses I need to take, and there are no optional Physics modules other than the already prescribed core courses everyone needs to take anyway, I was thinking I'd pick another Maths course. Trouble is, I don't know which one, and a lot of them seem interesting, so it's hard to make a decision based upon that alone.

So here are the ones I'm choosing between:
- Introduction to Discrete Mathematics,
- Algebra: Introduction to Ring Theory,
- Geometry,
- Graph Theory,
- Elementary Number Theory,
- Algebra: Introduction to Group Theory,
- Set Theory,
- Numerical Methods I.

I didn't list the content of the courses, since I didn't want to make this post too long, but I can do that if it isn't clear what they cover.

So I guess my question is whether anyone of those stands out in terms of usefulness for a Physics major or even later on when looking for jobs. Are there any specific advantages to taking any of them?

And just to add, I will have taken the usual Calculus, Advanced Calculus, Linear Algebra, Complex variables, ODE and PDE by graduation, as they are required by default.

 

[Shackleford]

Well, that depends on your future graduate degree plans, if you have any. But, for a job, maybe Numerical or Discrete (often CS flavored).

 

[Ryker]

I do plan on pursuing graduate studies, but since I'm only a first-year student, I'm keeping my options open and I really don't know what direction I'd like to go in yet.

 

[Shackleford]

I do plan on pursuing graduate studies, but since I'm only a first-year student, I'm keeping my options open and I really don't know what direction I'd like to go in yet.

Honestly, the required math cores for physics set you up pretty nicely already with the topics they cover. You could really just pick the extra math classes that sound interesting to you and be okay.

 

[ParticleGrl]

Numerical methods is extremely useful for practical applications of mathematics. It has the broadest applications of the courses you listed.

 

[Ryker]

Honestly, the required math cores for physics set you up pretty nicely already with the topics they cover. You could really just pick the extra math classes that sound interesting to you and be okay.

Yeah, I figured the required ones were already enough, but since I want to take some additional ones, I just thought I'd ask to see if any of the listed ones stick out, even though they're not required per se. I really enjoy linear algebra, so right now intro to ring theory, intro to group theory and elementary number theory sound the most interesting. But that might also be because I don't really know what set theory or graph theory are. I've checked wikipedia and by the description they both sound pretty cool, as well, but it's hard to pin them down. When I was doing my first degree, I pretty much knew what each optional course covered and how it would translate to real life or usefulness in other courses, but here I'm completely lost.

Numerical methods is extremely useful for practical applications of mathematics.

Another vote for numerical methods then, eh? Here's the description for it.

Numerical Methods I

Approximation of functions by Taylor series, Newton’s formulae, Lagrange and Hermite interpolation. Splines. Orthogonal polynomials and least-squares approximation of functions. Direct and iterative methods for solving linear systems. Methods for solving non-linear equations and systems of non-linear equations. Introduction to computer programming.

 

[Sankaku]

The numerical methods course is probably the most immediately "practical" for physics but you may want to look into the others if you would like to understand the foundations of mathematics better.

Discrete is useful for Computer Science (algorithms, etc.). You probably need discrete for Graph Theory. Quite often a basic discrete class covers some set theory, so I assume the Set Theory course is more advanced.

Algebra is foundational to most things in math, if you are going into something more theoretical. Group theory usually comes before Ring theory, though.

However, my interpretation of your courses could be completely wrong. Look at the standard sequence for the math majors to see which comes before which.
:-)

 

[Ryker]

I think Honours Math majors would take Introduction to Group Theory next semester, but they're essentially going to cover almost all of those courses, so I'm not sure if it's best for me to just take their route and cut it off at the point where I can't fit in any more modules. Today I was told it might be good taking a probability course or set theory, and that does sound pretty interesting. The former would be something very applicable to Physics, as well, but the bad thing about probability is that there is no such course offered and I don't want to take a statistics course. So that is unfortunately not a viable option.

Also, looking at it closer, it seems a lot of the courses I listed have pre-requisites that I would actually only be taking concurrently, so supposing I get that requirement waived, would it even be sensible for me to take some of those courses with only two courses in Calculus and Linear Algebra (both Honours and proof-based) under my belt?

 

[A. Neumaier]

So here are the ones I'm choosing between:
- Introduction to Discrete Mathematics,
- Algebra: Introduction to Ring Theory,
- Geometry,
- Graph Theory,
- Elementary Number Theory,
- Algebra: Introduction to Group Theory,
- Set Theory,
- Numerical Methods I.

Group theory may be very useful when you later go into theoretical physics; numerical methods when you go into computational physics. probability theory would be good no matter how you specialize.

What about a good programming course? Proficiency in programming (no matter how you learned it) is most important if you want to work later outside academia - and it takes lots of time to get really skilled at it.

 

[Ryker]

I've taken a course on Java in the previous semester, and was planning on just honing my skills in my free time (which is non-existent this semester, unfortunately, so I hadn't had the chance to do any programming on my own since then). I was thinking of maybe choosing the second course in Java next semester, as well, but I think I'd rather go with some maths course, and try and improve my programming in my own time, like I planned. For said maths course, it seems group theory and numerical methods are strong contenders then.

 

[A. Neumaier]

For said maths course, it seems group theory and numerical methods are strong contenders then.

What you actually need from group theory is Lie groups (basic for the description of symmetries in physics). But to do this well on a math level needs some differential equations and differential geometry. A first course in group theory will therefore be on a more general level, in a purely algebraic setting. (You'll soon notice that the division into subfields is quite arbitrary. If you learn how to learn from books on your own, you'll be much better off since you can then pick books that suit your style, and read topics in any order that you find useful or necessary.)

 

[Ryker]

For what it's worth, this is the description of the course.

Groups, subgroups, homomorphisms. Symmetry
groups. Matrix groups. Permutations, symmetric group, Cayley’s Theorem. Group
actions. Cosets and Lagrange’s Theorem. Normal subgroups, quotient groups,
isomorphism theorems. Direct and semidirect products. Finite Abelian groups.

We're already covering some of the stuff in our linear algebra classes, so I'm not sure how much of the stuff would be new or more in-depth.

 

[A. Neumaier]

For what it's worth, this is the description of the course.
We're already covering some of the stuff in our linear algebra classes, so I'm not sure how much of the stuff would be new or more in-depth.

This is OK. You'll need all that, though in the more specialized context of Lie groups - matrix groups are interesting examples of the latter. Thus I recommend that you take this course. Plus Numerical methods, if there is time left.

 

[flyingpig]

What about Linear Programming?

 

[Ryker]

What's linear programming? I've looked it up on Wikipedia, but I can't see where it fits in and it's not offered as a separate course.

 

[Ashuron]

for those numerical methods..which language are usually used..?

 

[A. Neumaier]

What's linear programming? I've looked it up on Wikipedia, but I can't see where it fits in and it's not offered as a separate course.

It is about minimizing or maximizing a linear function under given linear constraints. Very useful in many business applications; much less so for physics.

 

[flyingpig]

It is about minimizing or maximizing a linear function under given linear constraints. Very useful in many business applications; much less so for physics.

Circuit problems...? I am using them now, but at the very basic level.