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In summary, Abstract Algebra is used in physics and can be helpful in some upper-level courses. However, another class may be more relevant for you.f

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http://en.wikipedia.org/wiki/Abstract_algebra

In physics, groups are used to represent symmetry operations, and the usage of group theory could simplify differential equations. In gauge theory, the requirement of local symmetry can be used to deduce the equations describing a system. The groups that describe those symmetries are Lie groups, and the study of Lie groups and Lie algebras reveals much about the physical system; for instance, the number of force carriers in a theory is equal to dimension of the Lie algebra, and these bosons interact with the force they mediate if the Lie algebra is nonabelian.[2]

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I know, but Abstract Algebra is the only math class I could get into. My school is so small that most math and physics courses only have one section each. I've been looking for reasons to stay in Abstract Algebra. I think I found a book that might help me. It's entitled "Group Theory and Quantum Mechanics" and was written by Michael Tinkham. Based on the reviews, it's very helpful for understanding the relationship behind abstract algebra and quantum mechanics.

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Courses
Physics and Abstract Algebra

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