Algebra II
Math 504 - Spring 2021
Announcements
This page contains some information that can be helpful before you register for the course. After the registration, we will be using odtuclass. You should follow odtuclass and check your emails regularly for important announcements during the semester.
Lectures and Office Hours
I strongly encourage you to attend live lectures on Zoom. These lectures are tentatively scheduled to be on Wednesday and Friday starting at 13:40. The content of each lecture will be around as it is in the tentative schedule.
I plan to do lectures of approximately 75 minutes each day and leave the remaining time for questions as office hours. Feel free to request extra office hours by sending an email to me 24 hours in advance.
Homeworks, Exams and Grading
Homeworks will be assigned on a regular basis and there will be 6-8 homework sets by the end of the semester. There will be one midterm and a final. The time and the method of each exam will be announced later.
Midterm, 30 points - around the 8th week.
Final, 30 points - during the final exam period.
Homework, 40 points.
Homework Policy: You should write your solutions on your own. You are allowed to consult other people's solutions for homework problems, but you must express everything with your own words. If you copy a solution, which is referred to as cheating, you will probably gain nothing and may encounter penalties.
Textbook
We will use Algebra by Hungerford as the textbook. The course content and a tentative course outline can be found below.
Tentative Course Outline
Modules (6 weeks):
Week 1 - Modules, Homomorphisms and Exact Sequences.
Week 2 - Free Modules and Vector Spaces.
Week 3 - Projective and Injective Modules.
Week 4 - Hom and Duality. Tensor Products.
Week 5 - Modules Over a PID.
Week 6 - Modules Over a PID.
Fields (8 weeks):
Week 7 - Field Extensions.
Week 8 - Fundamental Theorem of Galois Theory.
Week 9 - Fundamental Theorem of Galois Theory.
Week 10 - Splitting Fields, Algebraic Closure and Normality.
Week 11 - Galois Group of a Polynomial.
Week 12 - Finite Fields.
Week 13 - Separability.
Week 14 - Cyclic, Cyclotomic, and Radical Extensions.
A note for undergraduate students
If you are an undergraduate student, you should know the following rules executed by the Mathematics Department:
If your CGPA is higher than 3.00 and if you are willing to take this course, you must send me an email before taking this course. Unfortunately, you cannot take this course if your CGPA is lower than 3.00.
An undergraduate student can take at most two 5XX courses, which are counted towards CGPA. You may either take both two courses as free electives or alternatively one free elective and one departmental elective.