[Note: For the MAT 4720 syllabus, please go here.]
Prerequisites: Math 3110 or permission of the instructor.
Texts: Our primary text will be Joseph Rotman's Galois Theory. I will most likely supplement Rotman with some other texts along the way. Depending on time constraints, we may spend some time to look at differential Galois theory.
Web Page: My webpage is located here:
https://BillCookMath.com
and
our course webpage is located here: https://BillCookMath.com/index.html?page=./courses/math4720-spring2024.
Meeting times: We meet Mondays, Wednesdays, & Fridays from 11:00am until 11:50am in Walker 308.
Final Exam: We will have final project presentations (tentatively in our usual classroom) during our final exam period. Our final exam period is Friday, May 3rd from 11:00am until 1:30pm.
Lecturer:
| Name: | Dr. William (Bill) Cook | |
| Office: | Walker Hall 345 | |
| Office Hours: |
Monday, Wednesday, & Friday before class Tuesday & Thursday 9:00am to 10:00am Friday 8:00am to 9:00am Other times by appointment. |
|
| Phone: | (828) 262-2367 | |
| Email: | cookwj@appstate.edu | |
| Webpage: | https://BillCookMath.com |
Technology: You are welcome to use any technology at your disposal to complete out of class assignments. We may occasionally use Maple or some other computer algebra system in class or on homework. If necessary, Maple should be available on all campus lab computers. If you would like a personal copy, download and activation information are available on our ASULearn page. Calculators and other computer technology will not be allowed on exams or quizzes. This includes cell phones. Your cell phone should never be out during an exam or quiz.
Course topics:
This course will include a review of basic group and ring theory. We will
cover some of the theory of vector spaces (linear algebra) and then study
field extensions. This will then allow us to show the impossibility of
obtaining certain compass-straightedge geometric constructions (eg.
trisecting angles, doubling cubes, squaring circles). Next, we will
develop the Galois correspondence relating field extensions to (Galois)
groups of automorphisms and then show the impossibility of solving certain
quintic equations.
If there is time, I also plan on sketching out some of "differential Galois
theory" and discuss solvability of differential equations.
Prerequisite details: MAT 3110. Although I will assume everyone has had an
introductory course in modern algebra and linear algebra, I will take time to
review necessary background material. I will assume that students are familiar
with the definition of a ring, but not that they remember any substantial ring theory.
A (mostly undetermined) very tentative course schedule can be found at:
https://BillCookMath.com/courses/math4720-spring2024/schedule.html.
Grades: Your term grade will be based on the results of your tests and final presentation as well as your scores on quizzes and homework and class participation. Here is more information about the individual components of your grade:
Tests: There will be two tests. Each test will make up 25% of your term grade. I have not attempted to fix dates for these tests presently. The actual dates will be negotiated/announced in class. It is likely that both tests will be take home exams or at least involve a significant take home portion.
Homework & Quizzes: I will regularly assign sets of homework problems to be turned in for a grade. We may have a few quizzes (if needed). I encourage you to work on your homework with your classmates. However, you must write up your solutions yourself. Do NOT merely copy your collaborators work and turn it in as your own. The homeworks (and quizzes) will make up 30% of your term grade.
Participation & Final Presentations:
Instead of having a final exam we will have final presentations. Everyone will pick a topic to present (this topic
will have to be approved and should be something related to what we covered in class). I will require that you create
a nice handout to go with your presentation. We will have presentations during the final exam period.
Also, I except you to come to class and participate in discussions. I may periodically ask (especially grad students) to present a homework problem. Participation as well as your final presentation and handout will make up 20% of your term grade.
Here are the components of the term grade with their weights:
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Differences between 5210 and 4720: This course is dual listed with MAT 4720. We have the same meeting times. However, your exams will include extra problems (most likely given as additional take-home portions of the exam) and most homework assignments will include additional problems just for 5210 students. In addition, your presentations and presentation handouts will be held to a higher standard. (Don't you feel special?)
Attendance: Don't miss class. If you miss class, you are responsible for the material covered during your absence. If you miss a quiz, test/exam, or workshop, you must bring in documentation proving that your absence is excusable or otherwise receive a zero. If a make-up quiz/test/exam is granted, it must be made up before the next quiz/test/exam.
Help! If you need help, please come to my office hours. If you are in Walker Hall and my office door is open, please feel free to stop by and ask questions – even if it's not during my posted office hours.
Fine Print: Copies of the academic integrity code, disability services information, religious observance policies can be found at https://academicaffairs.appstate.edu/resources/syllabi-policy-and-statement-information.