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Abstract Algebra II
Math 4201-1
Louisiana State University
Spring Semester, 2020
Prof. Stephen Shipman
Place: Room 203 of Woodin Hall
Time: Monday, Wednesday, and Friday from 9:30 to 10:20
Office: Room 314 of Lockett Hall
Telephone: 225/578-1674
Email: shipman@lsu.edu
Office Hours: Monday 10:30-12:20; Wednesday 1:30-2:30; or by appointment
4201 life during corona
Starting on March 30, all classes will be held at the usual time by video conference using Zoom through LSU. A few minutes before class, I will send an e-mail to the students in the course, containing a link to our Zoom meeting.
Assignments are to be submitted electronically by e-mail to shipman@lsu.edu. If you write your assignment by hand, please scan it. There are scan apps for smart phones, such as the one that is part of the Dropbox app.
All office hours will be by appointment and will be conducted through video conference.
The third exam and the final exam will transpire at the original date and time. Shortly before the beginning time of an exam, I will send it to all students by e-mail, and students will have one hour for the third exam and two hours for the final exam to complete it and send it back to me electronically in scanned form.
I plan to post some notes on this website, but they are not intended to take the place of class discussions.
As usual, I will be sad if students do not attend class. Please do not make me sad.
Textbook
Introduction to Abstract Algebra, by W. Keith Nicholson, Fourth edition.
Course Description
Ideals in rings, factorization in polynomial rings, unique factorization and Euclidean domains, field extensions, splitting fields, finite fields, Galois theory.
Prerequisite: MATH 4200.
Course Content
- Chapter 4: Polynomial rings
- Chapter 6: Fields and roots of polynomials
- Chapter 10: Galois theory of automorphism groups of field extensions
Notes
Here are some of my notes, which are not supposed to take the place of the textbook or class discussions.
- Section 10.1
- Section 10.2 (check for updates)
Assignments
Problems will be assigned weekly and will usually be due on Fridays. All submitted work must adhere to the statement of ethical conduct at the bottom of this page. There is a grader for this course, but I (SS) will also review some of your work. I encourage you to discuss your mathematical thoughts with me and with others and to seek enlightenment (not copy solutions) from other sources, such as books, Wikimedia, etc. I am aware that solutions to problems in standard textbooks are easily available, and students must resist any temptation to use them. Trying to solve a problem on your own, even if you don't succeed completely, is infinitely more valuable and ethical than using someone else's solution.
Besides the problems listed below, do as many problems as you can and to keep practicing until you are confident with the material.
This is a 4000-level mathematics course, and all submitted work is expected to be logically coherent. This applies to all problems, whether they emphasize computation, verification, or proof.
Due date |
Section |
Problems to be submitted |
| Friday, Jan. 24
| Section 4.1
| 2, 5, 8, 13, 16, 31
|
| Friday, Feb. 7
| Section 4.3
| 1bd, 5bd, 7b, 10a, 14b, 16
|
| Friday, Feb. 7
| Section 6.1
| 2, 3, 18, 20, 31
|
| Monday, Feb. 10
| Chapter 4
| Exam 1
|
| Friday, Feb. 21
| Section 6.2
| 4, 7, 11, 12abc, 15, 30
|
| Friday, Feb. 21
| Section 6.3
| 4abdf, 5, 9, 13, 18, 21
|
| Friday, Mar. 6
| Section 6.4
| 3, 4, 5, 9, 11, 14, 21, 22, 23
|
| Friday, Mar. 13
| Chapter 6
| Exam 2
|
| Wednesday, April 8
| Section 10.1
| 5, 6, 8, 10, 13, 16a, 17, 26
|
| Friday, April 24
| Section 10.2
| 1, 8, 10, 13, 16, 17, 18, 19
|
| Monday, April 27
| Chapter 10
| Exam 3
|
Exam schedule
- Exam 1: Monday, February 10
- Exam 2: Friday, March 13
- Exam 3: Monday, April 27
- Final Exam: Monday, May 4; from 10:00 to 12:00
Evaluation
Evaluation of performance in the course is based on scores on the exams, assignments and the final exam as follows:
- Assignments: 15%
- Exam 1: 20%
- Exam 2: 20%
- Exam 3: 20%
- Final exam: 25%
Grading scale:
| A+: at least 95% |
A: at least 90% |
A-: at least 88% |
| B+: at least 85% |
B: at least 80% |
B-: at least 78% |
| C+: at least 75% |
C: at least 70% |
C-: at least 68% |
| D+: at least 65% |
D: at least 60% |
D-: at least 50% |
| F: less than 50%
|
Ethical Conduct
Students may discuss problems with each other and other people and consult other literature; however, all work that is turned in must ultimately be that of the submitter alone. If a student receives aid on an assigned problem from discussions with people or other sources, he or she must begin from scratch in writing the solution so that the result is the product of his or her own understanding alone. No joint work in any capacity may be submitted for evaluation.
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