Mathematics 250A
Algebra

Fall, 2020
TuTh 8:10-9:30AM
Online University

Group theory, including the Jordan-Hölder theorem and the Sylow theorems. Basic theory of rings and their ideals. Unique factorization domains and principal ideal domains. Modules. Chain conditions. Fields, including fundamental theorem of Galois theory, theory of finite fields, and transcendence degree.
Professor Kenneth A. Ribet
email:
Non-pandemic office telephone: 510 642 0648
No point in sending a fax to: (510) 642-8204
Office hours (Not in Evans Hall)
A masked Ribet at the Berkeley Faculty Club

Graduate Student Instructor

Nicholas Brody will be the GSI for this course.

Textbook

cover of Lang book decorated forward page to Ribet's old copy of the book
Algebra by Serge Lang

Homework

Homework will be due on Tuesdays in general. Assignments will be posted on bCourses and announced on piazza.

Examinations

Grading

I have computed letter grades by calculating a "composite grade" for each student after the final exam papers have been graded. The composite grade will attempt to reflect the following weights: Homework 35%, midterm exams 15% each, final exam 35%.

Very approximate class schedule

This table suggests themes for the class meetings. It is based on the schedule of lectures in 2015. The slides for each course meeting can be found on bCourses. For a view of this class as taught by Elena Fuchs, see the 2012 class schedule.

DateThemes Sections
Aug. 26
Intro to the course
N/A
Aug. 27
Group actions
Sylow's theorems
§§ 1.5-1.6
Sept. 1 Sylow's theorems § 1.6
Sept. 3
More about Sylow
Jordan-Hölder
§ 1.3
Sept. 8
Jordan-Hölder
Abelian groups
§1.3, §§1.7-1.8
Sept. 10 Finitely gen. ab. groups § 1.8
Sept. 15 Elementary divisors §§ 3.4, 3.7
Sept. 17 Rings §§ 2.1-2.2, A.2
Sept. 22 Commutative rings §§ 2.2-2.4
Sept. 24 UFDs, PIDs §§ 2.5, 3.1
Sept. 29 First Midterm Exam
Oct. 1 Modules §§ 3.1-3.4
Oct. 6 Projective modules, categories,... §§ 1.11, 3.4
Oct. 8 Representable functors, tensor products §§ 16.1-16.3
Oct. 13 Representable functors, tensor products §§ 16.1-16.3
Oct. 15 Mostly flat modules §§ 16.1-16.3
Oct. 20 Flat modules and polynomials §§ 16.1-16.3, 4.1
Oct. 22 Polynomials §§ 4.1-4.3
Oct. 27 Yet more on polynomials §§ 4.1-4.4
Oct. 29 Second Midterm Exam
Election Day Polynomials, field extensions §§ 4.3, 4.4, 5.1
Nov. 5 Algebraic extensions, algebraic closure § 5.2
Nov. 10 Algebraic extensions §§ 5.1-5.2
Nov. 12 Normal extensions, separable degree §§ 5.3-1.4
Nov. 17 Finite fields § 5.5
Nov. 19 Primitive element theorem, Galois stuff §§ 5.4, 6.1
Nov. 24 Galois theory, fundamental theorem of algebra §§ 6.1-6.2
Dec. 1 Galois theory: examples and applications §§ 6.2-6.3
Dec. 3 Review
Dec. 8 Questions
Dec. 10 Questions

Practice and old exams

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