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Math 31: Topics in Algebra

General Information

Instructor: Vladimir Chernov

Office: 414, Bradley Hall

Meeting time: MWF 10:00 - 11:05, Bradley 104

x-Hour: Th 12:00-12:50

Office hours: MWF 3-4:30





The textbook for this course will be Joseph Gallian: “Contemporary Abstract Algebra”, 5th Ed. Published by Houghton Mifflin Company


General Course Outline


Roughly the first half of the course will be focused on the study of groups. We will learn what they are, explore examples, and examine various properties. The second half of the course will be devoted to the study of rings and fields. We will see how everything we learned about groups still applies to rings and fields, but that the addition of abstract structure allows us to also say much more.




Homework will be collected each Monday for all the lectures from the previous week. Late Homework will not be accepted. However, in calculating your final grade, your lowest homework score will be dropped. Collaboration in doing homework is permitted and encouraged but no copying.

It is important that you keep up to date with your homework. For many of you, abstract algebra will be different from the math that you have studied to date. For this reason, it will take some time and effort to adjust to the new style of problems. In addition, the pace of the class will be quick and the material will build on itself. In order to follow what is going on, you will need to give yourself time to play with problems and build intuition.


Quizzes and Examinations


There will be 3 in-class quizzes, a  midterm exam and a  final exam. The midterm and final exams tentatively will be take-home, but this may be changed to the standard in-class 2-3 hour exams, if it is decided that it would be better for material learning.



The three 30-minute quizzes will be on Wednesday January 21, on Monday February 16, and on Monday March  1.

The take home midterm exam will be given on Monday February 2 and it will be due Friday February 6.

The take home final exam will be given on Friday March 12 and will be due Tuesday March 16, so you will have the whole final examination period to work on it, though of course it should not require more than a few hours if you know the material. 

You are expected to work alone on take home exams. If the exam is take-home, then you may consult any printed matter you like but you may not consult one another or other humans. If the exam is in-class, then you can not use any book or class-notes, unless explicitly allowed to do so. If you have any questions you are welcome to ask your instructor for clarifications. The honor principle applies.





The x-hours will be often used for this course. In particular, we shall have an optional  problem solving x-hour on Thursdays January 15 , January 29, and February 26.  These are x-hours before the quizzes and a midterm exam and they will, in particular, give you an opportunity to prepare better for the quizzes and exams. Attending these three x-hours is not required but is highly encouraged for all students.

We will also have a regular lecture during the x-hour on Thursdays January 8, January 22,  and February 12. These x-hours are held instead of the lectures January 10, January 19 and February 13..We might also have other x-hours if we will need to catch up with the syllabus etc.


Office Hours


Scheduled office hours are Monday, Wednesday, Friday 3-4:30 PM. You are encouraged to use these either individually or in groups to discuss homework problems or other material covered in class.


I also have office hours by appointment. If for whatever reason you can not make it during the regular office hours please do not hesitate to blitz me and I will try my best to meet you at the time when you are free.


Class Attendance and Participation

Class attendance is not a part of the grade, so if you need to miss a class this is not a problem. However as you already know there is a strong correlation between regular class attendance and learning the material. So please make mature choices.

Class participation will be a important learning tool for you in this course. Class participation includes asking questions, answering questions, generally speaking up in class, and coming to the x-hour problem sessions. Notice that you don't have to have a correct answer in order to speak up. Your participation in class reflects that you are engaged in the material and are working to learn it. While class participation is not formally part of your grade, it can help you when the final calculations are made.




Grades for the course will be determined based on the following percentages:

Quiz 1


Quiz 2


Quiz 3




Midterm Exam


Final Exam



The Honor Principle


The Honor Principle applies to this class in the following way: You are encouraged to work together on homework, but the final written copy you turn in must be your own understanding of the material. Copying someone else's work is not permitted.

All quizzes and the final must be completely your own work, with no outside help from other students, professors and other humans.

The take home exams are open notes and open books. On the quizzes and on in-class exams you are not allowed to use your notes, textbooks and other printed matter, unless explicitly allowed to do so.

If you aren't sure if something is a violation of the Honor Principle, ask before doing it.




If you are a student with a disability, including an "invisible" disability such as a chronic disease or a learning disability, I encourage you to discuss with me any appropriate accommodations that I could make on your behalf. Also, stop by the Academic Skills Center to register for support services.