At my university, the following topics are covered between Linear Algebra and Abstract Algebra. Linear Algebra 1: Linear equations, matrices, vector spaces, linear transformations, determinants, eigenvalues and inner-product spaces Abstract Algebra 1: Sets and mappings, groups and subgroups, homomorphisms and isomorphisms, permutations, rings and domains, arithmetic properties of domains, and fields. Under the assumption that both courses are introductory first-time proof based: Are there any topics of abstract algebra that necessarily requires linear algebra to do? If so, which ones and are they necessarily abstract or computational. Which would you recommend taking first if you can only pick one for the semester?