Instructor: John Perry
Office: Southern Hall, 317C
Office Hours: M-F 11⋅30a-1⋅00p
Office Phone: 601⋅266⋅5505
Email: john.perry@usm.edu
Instructor's web page: http://www.math.usm.edu/perry/
Class web page: http://www.math.usm.edu/perry/mat423/
Class meeting time and location: MW 9⋅45-11⋅15a SH 303
Elementary notions in groups, Fundamental Theorem of Finitely Generated Groups, permutation groups, quotient groups, isomorphism theorems, and applications of transformation groups.
Congruence, modularity, rings, fields, quotient rings, applications thereof.
MAT 326 (Linear Algebra I) and MAT 340 (Discrete Mathematics). These prerequisites constitute necessary preparation for the course; if you lack either you are at a tremendous disadvantage.
| Week | Sections |
| 1 | Introduction; Sets and relations |
| 2 | Integer division |
| 3 | Common divisors, Prime and composite numbers |
| 4 | Congruence, Linear equations |
| 5 | Public-key encryption, Catch-up |
| 6 | Test #1, Polynomial arithmetic |
| 7 | Polynomial division, Polynomial divisors |
| 8 | Factoring polynomials, Imagining something quite real |
| 9 | Catch-up, Test #2 |
| 10 | Rings, In the absence of division we have ideals |
| 11 | Cosets, Quotients of rings are also rings |
| 12 | Polynomial rings, Isomorphism |
| 13 | Factorization, Catch-up |
| 14 | Catch-up, Review |
| 15 | Test #3 |
| 100-90 A | 89.99-80 B | 79.99-70 C | 69.99-60 D | 59.99-0 F |
There is no curve.
| Tests (we’ll aim for four) |
60% of total |
| Homework and quizzes (problems may be graded randomly) |
30% of total |
| Participation (see below) |
10% of total |
Graduate students enrolled in MAT 523 must perform an independent research project. They must find an article in College Math Journal, Math Magazine, or a similar scholarly journal, read it, and write a brief summary of the article. The article must be related to the concepts of abstract algebra that we study in this class. Please check with me that the article is appropriate before getting too far into this. This counts as a test grade.
In 2010, the mathematics department voted to make the Major Field Test in mathematics a component of MAT 423. You will receive a grade for this test. We will discuss the details later in the semester.
I generally collect the homework for grading,
but in order to return it to you in timely fashion,
I might skip part of the assignment.
Nevertheless, it is important for you to understand every problem on the
assignment, so be sure to review the graded problems, try to fix what was
wrong, and ask me about any problem that wasn't graded, and which you did
not understand.
To earn the full credit for participation in this class, you must earn a full complement of “participation points.” A full complement is 2.5×(number of class meetings). In the summer 2019 session, there were 16 meetings, so a full complement was 16×2.5=40. In the fall 2019 session, there are 26 meetings, so a full complement is 26×2.5=69.
Earning fewer than a full complement will be pro-rated. For example, if a full complement is 40 points, and you earn only 34, then you earn 34/40=85% of the grade, which means that your final grade is penalized 1.5%. On the other hand, it is possible to earn bonus points through participation, capped at 10% of your final grade.
You can earn participation points in the following ways:
Other opportunities will present themselves throughout the semester, but notice that if all you do is attend class, and ask no questions nor try to answer any, then you earn only 16 of the 40 points, which comes to 16/40=40%. You would lose 6% of your final grade.
Feel free to suggest that a question you asked or answered should count as a participation point. Feel free to remind me that I owe you a point for asking or answering a good question. Note that an answer to a question I pose has to be “especially insightful.”
Students who try to game this by blurting out random or distracting answers will be penalized with a reduction in participation points. Negative points are possible!
Any assignment turned in past the specified due date and time will receive a grade lowered by ten percent for each school day late.
I do not give makeup tests/quizzes/etc. without an excused absence. If you must miss class, then you must also produce documentation of the reason for your absence. If you were sick, you can show me the receipt from the hospital or doctor; if you had a sports event, you can show me the schedule; if someone died, you can show me an obituary notice; if the tire on your car blew out, you can show me the receipt from the mechanic. Absences must be consistent with university policy; you may not submit a receipt from a night out at the Peg and Carousel (say) and expect to be excused from the test!
Tests are not multiple-choice. Tests are not easy. They do what the word says: they test your knowledge of the subject. If you have a problem with that, then you are in the wrong major.
I expect you to turn your phone off once class begins, and to leave it off. If you absolutely must use the phone, please step out of class, take care of business, then return. If you use the phone in the class, I will ask you to leave. If you do not comply with this request, you forfeit the next test. If you use the phone during a test, even as a calculator, you will forfeit the test.
I encourage you to work together on homework assignments, to look at each other's solutions, and to explain answers to each other. This is not the same thing as copying each other's homework. You take the tests alone and without help, so if you cannot explain to your tutor, classmate, or teacher how to solve the problem, then you have not learned how to solve it, and you need to study it more (perhaps by visiting me, the professor).
All students at the University of Southern Mississippi are expected to demonstrate the highest levels of academic integrity in all that they do. Forms of academic dishonesty include (but are not limited to):
Engaging in any of these behaviors or supporting others who do so will result in academic penalties and/or other sanctions. If a faculty member determines that a student has violated our academic integrity policy, sanctions ranging from resubmission of work to course failure may occur, including the possibility of receiving a grade of “XF” for the course, which will be on the student’s transcript with the notation “Failure due to academic misconduct.” For more details, please see the university’s Academic Integrity Policy: https://www.usm.edu/institutional-policies/policy-acaf-pro-12. Note that repeated acts of academic misconduct will lead to expulsion from the university.
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If a student has a disability that qualifies under the American with Disabilities Act (ADA) and requires accommodations, he/she should contact the Office for Disability Accommodations (ODA) for information on appropriate policies and procedures. Disabilities covered by ADA may include learning, psychiatric, physical disabilities, or chronic health disorders. Students can contact ODA if they are not certain whether a medical condition/disability qualifies. Address: The University of Southern Mississippi
Voice Telephone: (601) 266-5024 or (228) 214-3232
Fax: (601) 266-6035
Individuals with hearing impairments can contact |