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 2-7: 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) |
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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 |
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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 |