Intro Modern Algebra I · Mathematics
- broadly, finite group theory, elementary number theory, proof-writing
Group Theory, finite groups, introduction to abstract algebra
The first semester of this course focuses mostly on group theory.
The standard content of an introductory group theory course, up to semidirect products but not including fields and constructability.
Groups, Set theory, Equivalence classes, actions
10 weekly psets, but because things were so disorganized, many of them were dropped in pairs and were biweekly. PSets 30%, Midterms 30%, Final 40% 14.5: 2.5 hrs of class, 8 hrs per homework, 4 hrs re-teaching myself The workload is only so high because I had to do so much extra work to understand, via the homework/self-teaching, what probably should’ve been taught in lecture (which was a waste of time). TAs did all the grading and were fair, though occasionally a bit nitpicky with proofs, but otherwise responsive and understanding re: extensions and regrade requests.
The weekly homework and 3 exams were somewhat challenging but definitely doable, and office hours were really helpful for the homework. I think the averages for the exams were normally about 35/50. The homework was also very worthwhile (except the last one where we had to classify almost all groups up to order 30, which I thought was kind of tedious).
25% weekly homework, 10% quizzes (2 or 3), 15% each midterm, 35% final.
more specifically and in order, set theory and number theory review, group axioms, cyclic groups, dihedral groups, non-abelian groups (quaternions, etc...), Cartesian products of groups, permutation and symmetric groups, lagrange's theorem, normal subgroups, conjugacy classes, alternating groups, isomorphism theorems, finite abelian group classification, group actions, the class equation, solvable and nilpotent groups, sylow theorems, and the simplicity of alternating groups.
group theory, finite groups, homomorphisms,