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) 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