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Vitani11
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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. What other courses would you recommend?
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.
The level of mathematics courses you should take for physics depends on your specific goals and interests within the field. Generally, it is recommended to take courses in calculus, linear algebra, and differential equations at the very least. For more advanced studies in theoretical physics, courses in abstract algebra, complex analysis, and topology may also be beneficial.
It is not necessary to take advanced mathematics courses for a career in physics, as many physics programs offer introductory courses in mathematics that are relevant to the field. However, taking advanced courses can provide a deeper understanding of mathematical concepts and potentially open up more opportunities for research and specialization.
While computer science courses may involve some mathematical concepts, they cannot fully substitute for mathematics courses in physics. A strong foundation in mathematical principles is essential for understanding and applying the complex theories and equations in physics. Additionally, many physics programs require specific mathematics courses as prerequisites.
Mathematical proficiency is crucial for success in physics. The subject is heavily reliant on mathematical concepts and equations, and being able to understand and manipulate these concepts is essential for solving problems and conducting research in the field.
Yes, there are many resources available for improving mathematics skills for physics. Some options include online tutorials and courses, textbooks, practice problems, and seeking help from a tutor or professor. It is also recommended to actively practice and apply mathematical concepts in the context of physics problems.