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Abstract Algebra I
Math 4200-1
Louisiana State University
Fall Semester, 2019
Prof. Stephen Shipman
Place: Room 132 of Lockett Hall
Time: Monday, Wednesday, and Friday from 8:30 to 9:20
Office: Room 314 of Lockett Hall
Telephone: 225/578-1674
Email: shipman@lsu.edu
Office Hours: Monday 9:30-11:20; Wednesday 1:30-2:30; or by appointment
Textbook
Introduction to Abstract Algebra, by W. Keith Nicholson, Fourth edition.
Course Description
Elementary properties of sets, relations, mappings, integers; groups, subgroups, normal subgroups, quotient groups, homomorphisms, automorphisms, and permutation groups; elementary properties of rings.
MATH 2085 or 2090. Credit will not be given for both this course and MATH 4023.
Course Content
The course will cover Chapters 0-2 and part or all of Chapters 3 and 7 of the text book. Some of the key ideas are the following:
- Chapter 0: Pre-algebra stuff on sets, mappings, proofs, etc.
- Chapter 1: New stuff about algebraic structures we already know (integers, permutations).
- Chapter 2: Abstract groups and lots of examples; group theory.
- Chapter 3: Rings--algebraic structures with two binary operations.
- Chapter 7: Modules
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.
Page numbers refer to the page on which the problem set begins.
Due date |
Section |
Problems to be submitted. |
| Friday, Aug. 30
| Section 0.1
| 2, 3, 4
|
| Friday, Aug. 30
| Section 0.2
| 4, 6, 7, 8
|
| Friday, Aug. 30
| Section 0.3
| 15
|
| Friday, Sept. 6
| Section 0.4
| 1, 2, 8
|
| Friday, Sept. 6
| Section 1.1
| 5, 19
|
| Friday, Sept. 13
| Section 1.2
| 10, 12, 16, 29, 39
|
| Friday, Sept. 13
| Section 1.3
| 7, 12, 30, 34
|
| Friday, Sept. 20
| Section 1.4
| 3, 6, 7, 26, 29
|
| Friday, Sept. 20
| Chapter 1
| Exam 1
|
| Friday, Sept. 27
| Section 2.1
| 14, 18, 21
|
| Friday, Sept. 27
| Section 2.2
| 2, 3, 6, 7, 13, 28
|
| Friday, Oct. 4
| Section 2.3
| 2, 5, 15, 19
|
| Friday, Oct. 4
| Section 2.4
| 2, 4, 25, 28
|
| Friday, Oct. 11
| Section 2.5
| 3, 5, 12, 17, 27
|
| Friday, Oct. 11
| Section 2.6
| 3, 7, 17, 27
|
| Friday, Oct. 16
| Section 2.7
| Find the group of motions and group of symmetries of any 3D object of your choice (just one).
|
| Friday, Oct. 25
| Section 2.8
| 1, 18, 20
|
| Friday, Oct. 25
| Section 2.9
| 1, 9, 14
|
| Friday, Oct. 25
| Section 2.10
| 4, 6, 30
|
| Wed., Oct. 30
| Chapter 2
| Exam 2
|
| Friday, Nov. 8
| Section 3.1
| 3, 4, 10, 13
|
| Friday, Nov. 8
| Section 3.2
| 5, 7, 11, 19
|
| Friday, Nov. 15
| Section 3.3
| 1, 4, 15, 18, 22
|
| Friday, Nov. 22
| Section 7.1
| 2, 4, 8, 11, 16
|
| Mon., Dec. 2
| Sec. 3.1-3.3, 7.1
| Exam 3
|
| Mon., Dec. 9
| 10:00-12:00
| Final exam
|
Exam schedule
- Exam 1: Friday, September 20
- Exam 2: Wednesday, October 30
- Exam 3: Monday, December 2
- Final Exam: Monday, December 9; 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%
One regular exam score will be replaced by the highest score on any of the regular exams.
The assignments will be padded with a 100-point "free" assignment.
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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