Math 100B (Abstract algebra 2)
Contact information
- Instructor: Aaron Pollack; apollack@ucsd.edu
- TAs: Bryan Hu brhu@ucsd.edu; Finley McGlade fmcglade@ucsd.edu
Office hours
See Canvas for the Zoom links
- Pollack: Monday, Wednesday 1:00pm-1:50 pm (APM 5829); Thursday 11:00am-11:50am (Zoom)
- Hu: Tuesday 1:30pm-3:30pm (HSS 5086)
- McGlade: Wednesday, Friday 8:30am-10:30am (HSS 4085)
Lecture Topics
Recorded lectures can be found on Canvas
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Monday 9 January: Introduction to course
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Wednesday 11 January: Rings: definition and examples (11.1)
- Friday 13 January: Algebraic numbers; units of rings; polynomial rings (11.1,11.2) Sage notebook from Lecture 2 and 3
- Monday 16 January: University Holiday (MLK day)
- Wednesday 18 January: Ring homomorphisms (11.3)
- Friday 20 January: Kernels and ideals; characteristic of a ring; fields (11.3)
- Monday 23 January: More on kernels and ideals (11.3)
- Wednesday 25 January: Product rings; quotient rings (11.4)
- Friday 27 January: Exam 1
- Monday 30 January: Quotient rings (11.4); adjoining elements (11.5)
- Wednesday 1 February: Adjoining elements (11.5); Chinese Remainder Theorem (11.6)
- Friday 3 February: More on Chinese Remainder Theorem (11.6); Rings of fractions (11.7)
- Monday 6 February: Prime and maximal ideals (11.8)
- Wednesday 8 February: Euclidean domains and PIDs (12.2) Lecture notes
- Friday 10 February: GCDs, factorization into irreducibles, and UFDs (12.2) Lecture notes
- Monday 13 February: Review
- Wednesday 15 February: Polynomials over the real and complex numbers (12.2); Gauss's Lemma (12.3)
- Friday 17 February: Gauss's Lemma and Z[x] (12.3)
- Monday 20 February: University holiday (President's Day)
- Wednesday 22 February: Factoring integer polynomials (12.4)
- Friday 24 February: Exam 2
- Monday 27 February: Vector spaces (3.3)
- Wednesday 1 March: Bases and dimension (3.4)
- Friday 3 March: Bases and dimension (3.4); direct sums (3.6); quotients
- Monday 6 March: The dimension formula (4.1); applications of linear algebra to ring theory
- Wednesday 8 March: Algebraic and transcendental elements (15.2)
- Friday 10 March: Algebraic and transcendental elements (15.2)
- Monday 13 March: The degree of a field extension (15.3) Lecture notes
- Wednesday 15 March: Ruler and compass constructions (15.5) Lecture notes
- Friday 17 March: Ruler and compass constructions (15.5)
Homework Assignments
Homework is due by 10:00pm Pacific time on Gradescope on the days listed below
Exams