MATH 340: Algebra II: Rings and Fields

Fall 2018

Instructor: Dr. Imin Chen, SC-K 10528, Generally speaking, it is preferable to see me in person than to correspond by email. Please note that in cases when the response will be of benefit to others in the class, instead of replying to your email, I will respond by making an announcement or clarification in the next lecture.

Office Hours: During semester: WF 1-2 pm SC-K 10528. Now changed to MW 1-2 pm SC-K 10528 starting week of Sept 30.

During exam period: MWF 1-2pm SC-K 10528.

Lectures: MWF 11:30 am -12:20 pm


Course Outline Additional course policies


Required: A First Course in Abstract Algebra: Rings, Groups, and Fields, by Marlow Anderson and Todd Feil, 2014 / 3E, CRC Press LLC. ISBN: 9781482245523.

Recommended: Abstract Algebra, David Dummit and Richard Foote, 2003/ 3E, Wiley. ISBN: 9780471433347


Assignments are to be handed in through Crowdmark by the due date. Assignments are posted on this course webpage in advance and a link will be sent to you a few days prior to the deadline of each assignment.

Selected solutions will be posted on or explained in the tutorials.

The lowest assignment grade (percentage terms) will be dropped from the grading scheme.


Course Table

  Coverage, due dates, holidays. Additonal materials and comments.
Week 1

The Natural Numbers: 1.1-1.5; The Integers: 2.1-2.4; Modular arithmetic: 3.1-3.3

Review of the rudiments of logic

Week 2

Polynomials with Rational Coefficients: 4.1-4.6

09.12 -> Assignment 1 due. Now due 09.14.

Week 3

Factorization of Polynomials: 5.1-5.3

09.19 -> Assignment 2 due.

Week 4

Rings: 6.1-6.5; Subrings and Unity: 7.1-7.4;

09.26 -> Assignment 3 due.


Week 5

Integral Domains and Fields: 8.1-8.6

10.03 -> Quiz [Solution Key]


Week 6

Ideals: 9.1-9.4; Polynomials over a Field: 10.1-10.4

10.08 -> Last day to drop courses with WD.

10.10 -> Assignment 4 due.

Week 7

Ring Homomorphisms: 11.1-11.4; The Kernel: 12.1-12.5; Rings of Cosets: 13.1-13.2

10.17 -> Assignment 5 due.


Week 8

The Isomorphism Theorem for Rings: 14.1-14.3

10.24 -> Assignment 6 due.

Week 9

The Chinese Remainder Theorem: 16.1-16.3

Practice Midterm Questions

Practice Midterm [Solution Key]

11.02 -> Midterm [Solution Key]

Screencast: CRT example
Week 10

Vector Spaces I & II: 39.1-40.4

Field Extensions and Kronecker's Theorem: 41.1-41.3

11.07 -> Assignment 7 due.

Week 11

Algebraic Field Extensions: 42.1-42.4

Finite Extensions 43.1

11.14 -> Assignment 8 due.

Week 12

The Splitting Field: 44.1-44.2; Finite Fields: 45.1-45.2

11.23 -> Assignment 9 due. (Note due date is on a Friday)

Week 13

Additional Topics

11.28 -> Additional Questions for the last tutorial.

Week 14


Selected Solution Keys (A9 & E) S1 S2

Summary of topics

Practice Final [Solution Key] Note: some corrections and clarifications have been made, there is an updated version.