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Algebra I
Math 503 - Fall 2020


Announcements

This page contains some information that can be helpful before you register for the course. After the registration, we will be using odtuclass and possibly gradescope. You should follow odtuclass and check your emails regularly for important announcements during the semester. If you want to follow the course as a guest student, please send me an email.

The meetings will be on Webex. You may download the software from https://metu.webex.com. Students can join as a guest and you do not need to have a Webex account to participate in the course. Please consult this page for F.A.Q..


Lectures and Office Hours

I strongly encourage you to attend live lectures. The content of each lecture will be around as it is in the tentative schedule. The lecture videos and notes will be posted on odtuclass for convenience. The tentative live lecture hours are as follows.

Monday, 13:40-15:30.
Link for Monday Lectures.
Webex Meeting Number: 137 080 1855
Password: fermat

Wednesday, 14:40-16:30.
Link for Wednesday Lectures.
Webex Meeting Number: 137 312 1733
Password: fermat

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.


Textbooks

Math 503 is the first part of a classical graduate algebra course. This course covers some basic concepts in the theory groups and rings. We will use the following textbooks:

Dummit and Foote - Abstract Algebra, 3rd ed.

Hungerford - Algebra

We will follow Dummit and Foote most of the time. The course content and a tentative course outline can be found below.


Tentative Course Outline

Groups (8 weeks):

Week 1 - Introduction to groups. Some examples.

Week 2 - Subgroups. Centralizer, normalizer, stabilizer. Cyclic groups.

Week 3 - Quotient groups and isomorphism theorems.

Week 4 - Group Actions.

Week 5 - Sylow Theorems.

Week 6 - Direct products and sums. Finitely generated abelian groups.

Week 7 - Nilpotent and solvable groups.

Week 8 - Free groups, generators and relations.

Rings (6 weeks):

Week 9 - Polynomial rings, matrix rings and group rings.

Week 10 - Ideals and quotient rings.

Week 11 - Euclidean domains, principal ideal domains, unique factorization domains.

Week 12 - Continued.

Week 13 - Polynomial rings and formal power series.

Week 14 - Continued.


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.