Course: MATH 103B
Title: Modern Algebra II
Credit Hours: 4
Prerequisites: MATH 103A or MATH 100A or consent of instructor.
Course Description: Second course in a two-quarter introduction to abstract algebra with some applications. Emphasis on rings and fields. Topics include definitions and basic properties of rings, fields, and ideals, homomorphisms, irreducibility of polynomials.
Main textbook: Contemporary Abstract Algebra by Joseph Gallian.
Other recommended textbooks:
- First Course in Module Theory by M. E. Keating.
- Rings, Modules and Linear Algebra by B. Hartley and T. O. Hawkes
- Concrete Abstract Algebra by Niels Lauritzen.
- Algebra by Michael Artin.
Piazza: This quarter we will be using Piazza for class discussion. The system is highly catered to getting you help fast and efficiently from classmates, the TA, and myself. Rather than emailing questions to the teaching staff, I encourage you to post your questions on Piazza.
Email policies
I get many emails every day. As such, it helps a lot if you can keep your emails short and to the point. If you do this, I will likely reply much more quickly.
Please refrain from using ChatGPT (or another LLM) to write your emails, as they tend to write very lengthy and wordy emails. As a result, if you write me a long email that was clearly written by ChatGPT, I will likely take much longer to reply, and I will also use ChatGPT in my response.
Grading policies
Weekly assignments will be posted on Gradescope.
- Submit your work on Gradescope.
- Typed-up solutions or photographed/scanned copies are both accepted.
- You must select the appropriate page(s) for each question when submitting your work on Gradescope. Points will be taken off if you fail to do this. If you do not know how to use Gradescope, have a look at this Gradescope guide.
- DO NOT email me your homework.
- Late homework will be accepted up to 24 hours after the deadline, with a 10% point penalty.
Final grade
Version 1: Homework (20%), midterm 1 (20%), midterm 2 (20%), final exam (40%).
Version 2: Homework (20%), best midterm (20%), final exam (60%).
At the end of the course, we will calculate both versions of your grade and give you the higher score. Letter grades will be assigned based on the following scale:
| Letter grade | Range |
| A+/A/A- | 90-100 |
| B+/B/B- | 80-90 |
| C+/C/C- | 70-80 |
I might adjust the scale to be more lenient, but I can guarantee that the grade corresponding to a given percentage will not be lower than specified by the above scale. For example, if your score is 89, then your grade will be at least a B+.
Note: The grades displayed on Canvas are only for Version 1 of your grade. Version 2 of your grade is calculated separately.
Homework policies
- As a main focus of this course is proof writing, your solutions must be written in complete English sentences, including punctuation.
- Discussing homework with others is OK, but it is expected that everyone writes in their own words the homework solutions.
- Homework must be uploaded onto Gradescope by 11:59pm on the due date (Tuesdays).
- No points will be given to solutions that are not readable.
- Late homework will be accepted up to 24 hours after the deadline, with a 10% penalty.
- Lowest homework score will be dropped.
- Note: There will be an assignment at the beginning of class for determining commencement of academic activity for financial aid purposes. This will not be part of your final score or grade.
Exam policies
The internet can be helpful when working through your homework. However, a computer should be used as an aid in the learning of concepts, not just as a means of computation. You should keep in mind that you will not be allowed access to any electronic devices during exams. Of course, this also means that you will not be asked to solve problems on exams that require the aid of an electronic device.
- The use of electronic devices will not be permitted during exams.
- Bring your student ID to the exams.
- No make-up exams will be offered.
Midterms: We will have two 50-minute midterms, which will be held during class time on
January 28 and February 20. There will be no make-up midterms under any circumstances.
Final exam: The final exam will take place on Saturday, March 14 at 11:30am-2:30pm in WLH 2111 (Section A), or WLH 2205 (Section B).
- It is your responsibility to ensure that you do not have a schedule conflict involving the final examination. You should not enroll in this class if you cannot sit for the final examination at its scheduled time.
- There are no make-up exams for any reason. Nor do we allow alternate times for taking exams.
- If you have a documented disability or must miss the exam for a university sponsored activity, then arrangements can be made using the standard procedures.
- If you cannot attend one of the midterms, grading Version 2 (described above) will ensure fairness by taking such cases into account.
- There may be different versions of exams involving different numbers and/or different orderings of questions.
- Bring pen or pencil and your student ID.
- You are allowed one letter size piece of paper of notes (front and back) for exams. The notes must be handwritten.
- Notes written on an iPad/tablet are not acceptable.
- If any part of your notes is typed or includes screenshots of my/other people's notes, they will be confiscated during the exam, and a point penalty may be applied.
- No calculators or electronic devices of any kind will be allowed during the examinations.
Regrade policy
Your homework and your exams will be graded using Gradescope. You will be able to request a regrade via Gradescope for one week after the scores have been released. Be sure to make your request within one week; no regrade requests will be accepted after the deadline.
The purpose of regrade requests is to correct grading errors (which can and do happen). You cannot lose points for regrade requests, provided your request was legitimate. Frivolous regrade requests in exams (in other words, obvious attempts at fishing for points, without any clear justification) will not be tolerated, and points will be taken off for such violations. This includes, but is not limited to:
- Asking for a regrade request for every question in an exam.
- Getting ChatGPT to generate a regrade request for you.
- Asking for extra points without any mathematical justification.
- Mentioning how close you are to the next letter-grade cut-off.
- Any mention of being close to a cut-off (e.g. "I am 1 point away from a B+") in a regrade request will result in your regrade request being ignored and points being removed.
As a result, when asking for regrade requests, you must do the following:
- Only submit regrade requests if you believe there has been a mistake when grading a particular question.
- Don't worry if it turns out that you simply misunderstood how your answer was graded. You will not lose any points if it's clear that you believe that there was a mistake and are not simply trying to fish for points.
- You must include a brief justification (1-2 sentences is usually enough) for why you believe your answer deserves more points.
- Overly long regrade requests may be ignored. Keep it short and to the point!
- Do not submit regrade requests for every single question in an exam.
Doing the above will give you the best chance at a successful regrade request, and will also guarantee that you do not lose points.
Accommodations
Students requesting accommodations for this course due to a disability must provide a current Authorization for Accommodation (AFA) letter issued by the Office for Students with Disabilities. Students are required to discuss accommodation arrangements with instructors and OSD liaisons in the department in advance of any exams or assignments.
There may be different versions of exams given. All versions of any exam will cover the same topics and will be calibrated to the same level of difficulty. It is standard Math Department practice to utilize different versions of exams, both within each lecture's exam, and between lectures whose exams are at different times.
Information about incomplete grades
According to university-wide regulations, a student's work must be of "non-failing quality" to be eligible for an incomplete grade. In this class, work of "non-failing quality" is taken to mean:
- At least 70% average homework score up to the day of the incomplete grade request.
- At least 70% in either Midterm 1 or Midterm 2.
Both of the above must be true. For example, you are not eligible for an incomplete grade if you scored over 70% in one of the midterms but your homework score is below 70%.
Academic integrity
Cheating will not be tolerated. See this link for information on how to promote academic integrity and the consequences of cheating.