Should I take complex analysis or abstract algebra?

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SUMMARY

The discussion centers on the decision between taking complex analysis or abstract algebra for a high school student entering physics. Participants unanimously recommend complex analysis, emphasizing its practical applications in physics, particularly in optics and electromagnetism, as well as its relevance to upper undergraduate courses. While abstract algebra may be beneficial for advanced studies, complex analysis is deemed more immediately useful for undergraduate physics coursework.

PREREQUISITES
  • Understanding of Calculus I-III
  • Familiarity with Linear Algebra
  • Basic knowledge of Quantum Mechanics
  • Introductory Functional Analysis
NEXT STEPS
  • Research the applications of complex analysis in physics, particularly in optics and electromagnetism.
  • Explore the concept of analyticity in complex functions and its significance in physics.
  • Investigate how abstract algebra can be applied in advanced physics courses.
  • Study the relationship between differential equations and complex analysis in physical contexts.
USEFUL FOR

This discussion is beneficial for high school students planning to pursue physics, educators advising students on course selections, and anyone interested in the mathematical foundations relevant to physics applications.

hjg87
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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).
 
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hjg87 said:
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.
 
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.
 
Okay. Thanks.
 

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