The topics in the following syllabus are tentative, and might change. Check back here often for new versions! Our plan is to cover much of chapters 27: Chapters 2,3: Group theory, Chapter 4,5: Polynomials, commutative rings, and ideals, Chapter 6: Fields, Chapter 7: More group theory.
Version 0.95 (Last changed 5/10/2021)Lec  Date  Topic  Read  Problem sets (Generally due midnight Thursday) 

1  8 Feb 2021  Introduction notes  
2  10 Feb 2021  Functions notes  BB § 2.1  
3  12 Feb 2021  More functions, Equivalence relations notes  BB § 2.2  
4  15 Feb 2021  Permutations notes  BB § 2.3  
5  17 Feb 2021  More on equivalence relations, Z mod n notes  BB § 2.2  HW#1 Dweck reading latex logo  
6  19 Feb 2021  Groups notes  BB § 3.1  
7  22 Feb 2021  Groups (Zn, products, order of elements) notes  BB § 3.1, 3.3  
8  24 Feb 2021  Subgroups notes  BB § 3.2  
9  26 Feb 2021  Cosets and Lagrange's theorem notes  BB § 3.2  HW#2 latex  
10  1 Mar 2021 
Lagrange corollaries, homomorphisms, isomorphisms notes 
BB § 3.4, some of 3.7  
11  3 Mar 2021  Homomorphisms, isomorphisms notes  BB § 3.4, 3.7  
12  5 Mar 2021  Kernels, images, normal subgroups notes  BB § 3.7, 3.8  HW#3 latex  
13  8 Mar 2021  Examples of groups, symmetry groups notes  BB § 3.3, 3.5, 3.6  
10 Mar 2021  No class!  
14  12 Mar 2021  Factor groups notes  BB § 3.8  
15  15 Mar 2021  Review, more factor groups notes  BB §  HW#4 latex  
16  17 Mar 2021  Factor groups, continued. notes  BB § 3.8  
18 Mar 2021  First prelim, 6:30  8 pm, online  Usual class zoom link 
Get exam via gradescope at 6:30 pm 

17  19 Mar 2021  First isomorphism theorem notes  BB § 3.8  
18  22 Mar 2021  Group actions notes  BB § 7.3, and 7.2  
19  24 Mar 2021  Group actions and class equation notes  BB § 7.3  
20  26 Mar 2021  Applications of the class equation notes  BB § 7.3  HW#5 latex  
21  29 Mar 2021  First Sylow theorem notes  BB § 7.4  
22  31 Mar 2021  Applications of Sylow theorems notes  BB § 7.4  
23  2 Apr 2021  (Most of) proof of Sylow 2, 3. notes  BB § 7.4  HW#6 latex  
24  5 Apr 2021  Fields notes  BB § 4.1  
25  7 Apr 2021  Fields, ZZn, Commutative rings notes  BB § 4.1, 5.1  
26  9 Apr 2021  Polynomials over a field notes  BB § 4.1, 5.1  HW#7 latex  
27  12 Apr 2021  The division algorithm and roots notes 
BB § 4.2 BB § 5.3(to pg 264) 

28  14 Apr 2021  Ideals, GCD's, Euclidian algorithm notes  BB § 4.3, 5.3  
29  16 Apr 2021  Review, Factor rings, especially F[x]/f(x) notes  HW#8 latex  
30  19 Apr 2021  Extension fields notes  BB § 4.3, 5.3  
20 Apr 2021  Second prelim, take home, 10 am  10 pm Thursday 
Covers up through ideals, gcds, and HW8 

31  21 Apr 2021  Extension fields, cont. notes  
23 Apr 2021  No class!  
26 Apr 2021  No class!  
32  28 Apr 2021  Factorization of polynomials notes  BB § 4.4  
33  30 Apr 2021  Factorization of polynomials, II notes  BB § 4.4  
34  3 May 2021 
Commutative rings, domains, ideals, PIDS Homomorphisms and isomorphisms notes 
BB § 5.1, 5.2, 5.3  
35  5 May 2021 
Commutative rings II, prime and maximal ideals, quotient fields notes 
BB § 5.3, 5.4  
36  7 May 2021 
Maximal and prime ideals. Fields, algebraic extensions notes 
BB § 6.1  
37  10 May '21 
Fields, algebraic extensions, minimal polynomial
Degree of an extension 
BB § 6.2  
38  12 May '21  Compass and Straightedge constructions, I  BB § 6.3  HW#9 latex  
39  14 May 2021 
Compass and Straightedge constructions, II
Review 
BB § 6.3  
18 May 2021  Final Exam, 9:30 am  noon, online 