The discussion revolves around the selection of mathematics courses beneficial for a double major in physics and mathematics, with a focus on developing tools for advanced physics topics such as quantum mechanics and relativity. Participants explore various mathematical concepts and their relevance to physics applications.
Participants generally agree on the importance of certain mathematical concepts for physics but have differing views on which specific courses to prioritize and the implications of switching majors. The discussion remains unresolved regarding the best course selection strategy.
Participants express uncertainty about the specific content of the courses available, which affects their decision-making. There are also unresolved questions about the foundational importance of certain mathematical areas and how they relate to the participants' future studies in physics.
Students pursuing a double major in physics and mathematics, particularly those interested in advanced topics like quantum mechanics and relativity, may find this discussion relevant.
Sounds reasonable from the physics point of view.Vitani11 said:I'm a double major in physics and math. I have taken Calc 1-3, ODE, and linear algebra. This summer I'm taking PDE and in Fall I'll be taking complex variables.
To achieve what?What other courses would you recommend?
For relativity, particle physics, Noether's theorem and things like that. It's the natural analogue to Euclidean geometry if you don't require an embedding into a surrounding space.Vitani11 said:Sorry I should have been more specific. I would like to develop as many tools as possible to tackle physics problems and "get deep" into topics such as quantum or relativity. So for example as you said differential geometry (I am assuming for relativity) and topology.
I mean that topological concepts are a) a generalization of all the metric stuff, which is only a part of all topology and b) include geometrical aspects which might be needed to understand e.g. cohomologies, differential forms and terms like AdS or Yang-Mills theory. The same is true for algebra: group, ring and field theory (mathematical fields, not physical) are fundamental structures like vector spaces are.I will be taking quantum in Fall so if that was a naive statement forgive me because I do not yet know the mathematics involved other than what I have learned in math physics. What do you mean by "..maybe topology and algebra as fundamental concepts like linear algebra is."?
Yes.Are you saying that topology is fundamental?
I think this is true and a good choice among the listed courses. To give a more detailed advice, it would be needed to know what these courses actually cover with respect to the realms I noted. Also Game theory might cover some useful aspects about probability theory and statistics, which are very much needed in experimental physics, like e.g. particle physics. But in doubt I personally would prefer a stochastic course over Game theory. LA2 is also likely a must-have.Here are the courses I must choose from: Advanced Calculus 1/2, Complex Variables, Numerical Analysis 2, Vector Calculus, Game theory, Optimization, Calc of variations, PDE 2, and Linear Algebra 2. I would love to take calculus of variations because I know it's important for things like deriving the Lagrange and it is a gateway to a lot of simpler physics (correct me if I am wrong).
There are many open questions that heavily depend on what you already have learned and where you want to go to. In the end it is more important to learn how to learn than what you learn, so you will always be able to get a good textbook on a subject and learn it from there.I've learned enough of calculus of variations in order to understand the lagrange and how to optimize things such as finding the maximum volume which can be inscribed in an ellipsoid etc. but not much more than that. To take calculus of variations I must first take Advanced Calculus 1 as it is a prerequisite. I can basically only pick 3 of these. Complex variables I will take regardless because I know it is important which leaves two. I would also like to take vector calculus but if I did that I could not do Calc of variations since I wouldn't have the advanced calc class down and I'm limited on how many courses I can take. Wow, I wish I could just take all of these math courses, lol. On the other hand I can switch from applied to regular mathematics and then the door would open to courses such as abstract algebra and topology but I don't know if that is worth the switch.