So I'm currently a sophomore math/CS major. I'm interesting in taking the algebraic geometry sequence next year; however I don't have the formal prereqs for the class, first year graduate algebra, which I would be taking simultaneously with the algebraic geometry class. I'm wondering if this is doable? My current algebra background is all the standard undergraduate algebra, plus some module theory, some elementary homological algebra that I learned for the algebraic topology class I'm currently taking (like stuff in Dummit and Foote, a little bit of Chapter 6 from Rotman), plus some basic category theory. I also know a little about localization and spectrums, although not that much beyond basic definitions. The course description for the algebraic geometry class is: Algebraic geometry over algebraically closed fields, using ideas from commutative algebra. Topics include: Affine and projective algebraic varieties, morphisms and rational maps, singularities and blowing up, rings of functions, algebraic curves, Riemann Roch theorem, elliptic curves, Jacobian varieties, sheaves, schemes, divisors, line bundles, cohomology of varieties, classification of surfaces. The course description for the first year grad algebra which is formally a prereq for that is: Group theory: permutation groups, symmetry groups, linear algebraic groups, Jordan-Holder and Sylow theorems, finite abelian groups, solvable and nilpotent groups, p-groups, group extensions. Ring theory: Prime and maximal deals, localization, Hilbert basis theorem, integral extensions, Dedekind domains, primary decomposition, rings associated to affine varieties, semisimple rings, Wedderburn's theorem. Linear algebra: Diagonalization and canonical form of matrices, elementary representation theory, bilinear forms, quotient spaces, dual spaces, tensor products, exact sequences, exterior and symmetric algebras. Module theory: Tensor products, flat and projective modules, introduction to homological algebra, Nakayama's Lemma. Field theory: separable and normal extensions, cyclic extensions, fundamental theorem of Galois theory, solvability of equations.