This is the homepage for Math 145-02, Abstract Algebra, taught by Prof. Moon Duchin. Note that section 01 is taught by Prof. Montserrat Teixidor and follows a different schedule and assignments!

Syllabus/course info sheet: here.

Here is a rough layout of topic timing. Obviously, real timing may vary from this plan. As you can see, it roughly follows the book, but the symbol * means that there is substantial extra material planned besides what you can find in the text.

1Tue Sep 3Intro to course; intro to proofs; intro to groups
2Thu Sep 5Ch 1 – the cyclic groups Z/nZ (cf Math 63)1
3Tue Sep 10Ch 2 – injection, surjection, bijection, permutation (Math 61)2
4Thu Sep 12Ch 1-2 wrapup1-2
5Tue Sep 17What is a group? discrete groups Z^d, Z[i], SLnZ, Fn, plus continuous versions3.1*
6Thu Sep 19generators and relations; Cayley graphs; subgroups3.2*
7Tue Sep 24examplepalooza: isometry (eg, dihedral) groups, fundamental groups, and more3.3*
8Thu Sep 26homomorphism and isomorphism3.4,3.7
9Tue Oct 1cyclic, abelian, nilpotent groups3.5*
10Thu Oct 3symmetric groups; permutations as matrices3.6*
11Tue Oct 8cosets3.8
12Thu Oct 10normality and the magic of quotient groups3.8

Thu Oct 17Midterm 1: Groups
13Tue Oct 22What is a ring? Z/pZ, matrices, R[x]
14Thu Oct 24polynomials and their roots4.1
15Tue Oct 29factorization and extensions4.2
16Thu Oct 31arithmetic in R[x]/I4.3
17Tue Nov 5more generalities on rings, ideals, fields, vec sps, modules5.1
18Thu Nov 7ring homomorphisms5.2
19Tue Nov 12PIDs and quotients5.3
20Thu Nov 14quotient fields
21Tue Nov 19Chapters 4-5 review

Thu Nov 21Midterm 2: Polynomials, Rings, Fields*
22Tue Nov 26topics: free groups and quotients, free groups and paradoxes*
23Tue Dec 3worksheet on free groups*
24Thu Dec 5wrap-up of Banach-Tarski paradox
Mon Dec 16Final Exam: Cumulative