Josh0768
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My university offers two different two-semester sequences for learning abstract algebra, and I can't decide which one would be better for me, a physics major. Here are the two sequences and their course descriptions, copied and pasted from the university website:
Algebra 1: Theory of groups, Sylow theory, the structure of finite Abelian groups, ring theory, ideals, homomorphisms, and polynomial rings.
Algebra 2: Algebraic field extensions, Galois theory. Classification of finite fields. Fundamental Theorem of Algebra.
OR
Abstract Algebra I and Number Theory: Structure of the integers, congruences, rings, ring homomorphisms, ideals, quotient rings. A writing course with an emphasis on proofs.
Abstract Algebra II: Permutation groups, groups of transformations, normal subgroups, homomorphism theorems, modules. Principal ideal rings, unique factorization domains, noncommutative rings, rings of fractions, ideals.
Which one of these sequences would be the most beneficial for me (a physics major with aspirations to enter high energy physics) to take?
(It might be worth noting that the first sequence is an honors sequence, and as such, I would expect it to be taught in a smaller setting and I think it would be the harder of the two sequences.)
Algebra 1: Theory of groups, Sylow theory, the structure of finite Abelian groups, ring theory, ideals, homomorphisms, and polynomial rings.
Algebra 2: Algebraic field extensions, Galois theory. Classification of finite fields. Fundamental Theorem of Algebra.
OR
Abstract Algebra I and Number Theory: Structure of the integers, congruences, rings, ring homomorphisms, ideals, quotient rings. A writing course with an emphasis on proofs.
Abstract Algebra II: Permutation groups, groups of transformations, normal subgroups, homomorphism theorems, modules. Principal ideal rings, unique factorization domains, noncommutative rings, rings of fractions, ideals.
Which one of these sequences would be the most beneficial for me (a physics major with aspirations to enter high energy physics) to take?
(It might be worth noting that the first sequence is an honors sequence, and as such, I would expect it to be taught in a smaller setting and I think it would be the harder of the two sequences.)