I have the option of taking one or both of these classes, but I am unfamiliar with algebra and don't know the difference between the following two courses based on their descriptions:
MATH 578. Algebraic Structures. 3 Credits. (NOTE: taught by a very well regarded professor) Permutation groups, matrix groups, groups of linear transformations, symmetry groups; finite abelian groups. Residue class rings, algebra of matrices, linear maps, and polynomials. Real and complex numbers, rational functions, quadratic fields, finite fields. (prerequisite is linear algebra/textbook is "First Course in Abstract Algebra" by Fraliegh)
MATH 534. Elements of Modern Algebra. 3 Credits. (NOTE: taught by a professor with mixed reviews) Binary operations, groups, subgroups, cosets, quotient groups, rings, polynomials. (prerequisite is discrete math/intro to proofs/textbook is "Abstract Algebra" by Beachy)
What course would you rather take/what course would you think is more useful and a better introduction into the world of algebra? Or would taking them both be ideal? Thank you so much!
I would take $578$ unless the other one is prerequisite for it in which case I take both.
$578$ sounds like a real solid higher algebra course which jumps into concepts right away and covers many important topics.