**Textbook:**
*A first course in abstract algebra, seventh edition, by John B. Fraleigh.*

**Class time:** MWF 2:00pm-2:50pm

**Class location:** 141 Altgeld Hall

**Professor:** Igor Mineyev, 243 Illini Hall.
Email is not very efficient for discussions.
Please talk to me before/during/after classes and come to office hours.

**Office hours:** See below.

Because of COVID19, this course and many other courses will transition to an online format,

- Try not to travel, try to stay at your home location. If you absolutely need to travel outside Urbana-Champaign during the spring break, please
**take the textbook for this course with you**in case you experience difficulty returning back. This way you will be able to participate in class remotely. - I believe, the interactivity of classroom setting is important, this is why
it is important to meet in class regularly. The current situation with COVID19, of course,
prevents us from doing that for the rest of the semester. My plan for now is to use the regular
class time (MWF 2pm central time) both for discussions and office hours, via Zoom.
These meetings are not required, but I encourage you to use them.
Talking about math is so much fun, time is never enough. :)
In addition, as we agreed at our first meeting, for those in a very different time zone I will be available by Zoom at 7pm on Mondays and Wednesdays. For all meetings, please join
at the
**beginning of the hour**because we might finish earlier and leave. In those rare situations when you need to talk to me privately in person, mention this to me when we meet on Zoom, then continue by calling my office phone after the meeting ends. - I will try to record lectures and post videos for you to see.
Watching these videos
**is**required. If you have not done this before, please login at least once to https://mediaspace.illinois.edu/ (link on upper right) using your university NetID and password. This way I will be able to add you to the channel titled "2020s Math 417 by Igor Mineyev", where you can view videos for this class. If you can access the videos now, please watch the lectures any time**before**the class time the video is scheduled for (i.e. before we meet on Zoom). - Install the Zoom app on your device:
https://zoom.us/download
Make an account with Zoom. Please use your
**University email address**(ending with @illinois.edu) when creating that account. Type**your full name**in Profile, to be displayed during the virtual meetings. Get accustomed with the program. - To join Zoom meeting:
https://illinois.zoom.us/j/2059219133,
meeting ID is 205 921 9133.
It seems that https://illinois.zoom.us/
is the right address to use when joining a meeting, but I am not sure.
High-speed internet access is strongly recommended. 1.5 Mbps or more is recommended for Zoom. To minimize noise during the meeting,
**mute**your microphone (this is an option within Zoom, on the lower left). For the meetings, be in a non-distracting environment. I thought it is better to keep your web camera on during the lecture, but it looks like turning it off is better for bandwidth reasons. Let's try it both ways to see how it works. If you want to ask a question, there are 2 options: (1) raise your hand virtually or literally (if I can see you), or (2) unmute the microphone, ask, then mute it again. - I will be using Learn@Illinois Moodle for homework assignments.
Please scan your homework into a file, or type it in latex.
PDF files are strongly preferred for uploads, whenever possible.
If you scan it or take a picture, please write
**legibly**and scan with a**sufficiently high resolution**. To upload your file, log in using your NetID at https://learn.illinois.edu. For help with Learn@Illinois Moodle see these links: 1, 2. For the first assignment (HW7) I set the due date/time at Saturday, March 28, 2020, at 6pm to make sure that no one is late this time. For the future homework assignments the deadline will be at 1pm on Friday it is due (i.e. an hour**before**we start the new class meeting on Friday). Do not wait until the deadline, submit your homework as early as possible. - What to do with the exams will be decided later.
- For projects, coordinate within your group, meet virtually, discuss. We have agreed that, in addition to the report, each group will make a video for everyone to view. It looks like if I set permissions correctly in https://mediaspace.illinois.edu/ (after you logged in there at least once), you should be able to post videos to the channel. To test mediaspace, try to upload a short video to our channel now and then remove it. Let us plan for an about-50-minute video for each group. Talk to me at our meetings if this sounds reasonable. (It might take a while to upload, so save it on your computer first, then upload to mediaspace.) I will post the deadline for uploading the project video here later.
- It is hard for me to deal with email, I appreciate your understanding. Please talk to me during our virtual meetings/office hours.

The Integers Division algorithm. Greatest common divisor. Fundamental theorem of arithmetic. Congruence arithmetic. Permutations Cycle decomposition. Order of a permutation. Even and odd permutations. Group Theory Definition and examples. Subgroups, cosets and Lagrange's theorem. Normal subgroups and quotient groups. Homomorphisms. The Isomorphism Theorems. Group Actions. Cayley's theorem. Burnside's theorem. Conjugacy classes and centralizers. Applications of group actions, eg. to Sylow's theorem. Ring Theory I Definition and examples. Polynomial rings. Subrings, ideals and quotient rings. Homomorphisms of rings. The Isomorphism Theorems for rings. Integral domains and fields. Division algorithm for polynomial rings over a field. Roots of polynomials and the Remainder Theorem. The Fundamental Theorem of Algebra (without proof). Maximal ideals in polynomial rings over fields, with application to the construction of fields.

Homework will be listed here. If a newer version does not show up, restart your browser.

**Exams and grades.**
Do not miss the exams. There will be two midterm exams at the regular class time:

- Exam 1, Friday, February 28. Median score was 86, mean 84.9, standard deviation 8.3%.
- Exam 2, Friday, April 10.
- The final exam is at 8:00-11:00 a.m., Wednesday, May 13, 2020, in the regular classroom, as required by the Final Exam Schedule.

The highest-score midterm exam will count as 25%, the homework
25%, the project 20%, and the final exam 30%.
One lowest midterm exam and two lowest homework assignments will be dropped at the end of the semester to allow for emergency situations. Do not miss classes, exams or homework.
**If you miss seven or more classes during the semester** (counting regular classes, midterms, and the final exam), **a failing grade will be assigned** at the end of the course regardless of performance during the semester.
To see your current score for the class, click on the "Score Reports" link on the left in
www.math.illinois.edu/Classes/,
then enter your password. The dropped assignments and exams will be marked with "**" at the end of semester.

**The project.**
Closer to the second half of the semester, the students will be randomly split into groups
to work on a project, to write a report, and to present it to the class closer to the end of the semester. Select the topic of your project early and start working on it now. Take initiative, discuss it with me
and others in advance. The main requirements for the project:

- Most importantly, it should be interesting. Find what interests you, and make it interesting to others.
- It should be generally related to the course material, say, further developments, applications of the course material in other areas, or topics/concepts/theorems from other areas of mathematics that are related.
- It should be something that you did not know before taking this course.
- Type up the report or write neatly, provide pictures, diagrams, graphs, formulas, etc, whichever is needed. Include participant names, title. Hand the report to me at the time of your presentation. It also might be a good idea to provide copies to other students in the class during your presentation.
- Organize your thoughts and ideas in advance in order to fit into the time slot. Consider making you presentation interesting and inspiring.