Should I take complex analysis or abstract algebra?

[hjg87]

Being a high school student who will be going into physics, should I take complex analysis or abstract algebra in the fall? I can't take both at once, and I am set to take intro to QM (I will already have taken Calc I-III, an introductory functional analysis course, and linear algebra. I also will probably have taught myself differential equations by then).

 

[fluidistic]

Being a high school student who will be going into physics, should I take complex analysis or abstract algebra in the fall? I can't take both at once, and I am set to take intro to QM (I will already have taken Calc I-III, an introductory functional analysis course, and linear algebra. I also will probably have taught myself differential equations by then).

Welcome to the forum!
I'm also a physics student and I didn't take an abstract algebra course (though one course of linear algebra). I'd go for the complex analysis course. Complex numbers are commonly used in physics, in optics/E&M dealing with waves or working with impedances of circuital components. I also believe knowing analyticity concepts are important for the upper undergrad courses. Maybe someone who took both courses could give you a better answer.

 

[lisab]

I agree with fluidistic. Complex analysis is extremely helpful for many branches of physics.

Perhaps abstract algebra would be helpful for more advanced physics courses, but complex analysis you'll use in most of your undergraduate classes.

 

[hjg87]

Okay. Thanks.

 

[rezeew]

I would recommend taking both complex analysis and abstract algebra if possible. Both of these subjects are highly relevant to physics and will provide a strong foundation for your future studies.

Complex analysis is a branch of mathematics that deals with functions of complex numbers. This is important in physics because many physical phenomena can be described using complex numbers, such as in quantum mechanics and electromagnetism. Understanding complex analysis will also help you develop a deeper understanding of calculus and its applications.

Abstract algebra, on the other hand, is the study of algebraic structures and their properties. This includes groups, rings, and fields, which are fundamental concepts in modern physics. Many mathematical models used in physics are based on abstract algebra, and a strong understanding of this subject will be beneficial in your future studies.

If you must choose between the two, I would recommend taking abstract algebra first. This subject builds upon the concepts learned in linear algebra and will provide a solid foundation for more advanced topics in physics. However, if you have the opportunity to take both, I would highly recommend it as they complement each other and will enhance your understanding of mathematical concepts in physics.

It is also worth noting that both complex analysis and abstract algebra are challenging subjects, but with the background you have described, I am confident that you have the necessary skills to succeed in both. Ultimately, the decision should be based on your personal interests and goals, but I highly encourage you to consider taking both courses if possible.