This course will provide an introduction to fundamental algebraic structures. The majority of the course will consist of an introduction to the basic algebraic structures of groups and rings. We will also learn about further algebraic structures (like fields and integral domains), as well as polynomial rings.
Throughout the term, students will develop a mathematics portfolio with nicely written solutions and study into an application (to share with the rest of the class).
Prerequisites: MATH 22
Notice: As a result of the variable syllabus, this course may not serve as an adequate prerequisite for MATH 81. Students who contemplate taking MATH 81 should consider taking MATH 71 instead of this course
Textbook: A Book of Abstract Algebra (second edition) by Charles C. Pinter
- Learn the fundamentals of abstract algebra including groups and rings.
- Improve proof writing skills and various techniques (constuctive, contradiction, contrapositive).
- Improve mathematical creativity.
Course structure and expectations:
This course will be taught primarily asynchronously via pre-recorded video lectures, discussion boards, and class participation assignments. Synchronous portions of the course consist of weekly problem sessions on Mondays (during the D block) and office hours via Zoom. Some synchronous sessions may be recorded; please read the consent to record page.
Each week, a new module will appear in the Modules tab on Canvas. Each weekly module is broken up into 3 days of videos and activities. Students may complete the activities in any order, though the listed order is the intended progression. While I will not require that students complete each day's material on Monday, Wednesday, and Friday, I do expect that students interact with the course material at least 3 days per week.
Discussion boards are located on Canvas under the "Discussions" tab. There will be a "General" discussion board for questions and conversations about the course and a "Random" discussion board for classroom chatter (interesting articles or videos, student new or announcements, etc.), in addition to discussion boards related to various assignments. Please note, while questions related to assignments are welcome on discussion boards, it is a violation of the honor code to provide explicit answers to homework problems on discussion boards. Each discussion board will come with instructions for proper usage.
Because this course is being taught remotely, and we will not have the opportunity to interact with one another in person, it is worth noting some online etiquette. There are two points I want to emphasize:
- Remember the human. Remember that your instructor and your peers are human. It is important to communicate with respect and understanding. A general guideline: if you wouldn't say it in person, don't say it online.
- You can't over-communicate. Without face-to-face communication, much of tone and implication gets lost. So use more words than necessary. Over-explain yourself. Re-read your messages and posts and think of the perspective of your peers.
The course grade will be computed as follows:
|Exams (two, non-cumulative)||30%|
See below for details on each category.
In this course, class participation will consist of four components, each earning some of the available class participation points. The goal of class participation is for you to receive feedback throughout the week, for me to keep track of how everyone is doing, and to foster classroom community.
Each student's class participation score will be the number of class participation points earned (max 100). Because there are more than 100 points available (I expect about 125 points by the end of the term), students do not need to complete every exercise or attend each session in order to earn high marks in this category.
The categories and point values are described below:
- Check-in exercises
- Each weekly module will contain three assignments labelled "CP" (for Class Participation). Check-in exercises consist of submitting a solution to a simple problem, a short quiz on Canvas, or a discussion board post. These are each worth 3 points and are open for unlimited retries until the due date (generally the following Saturday at 11:59pm ET). No late check-in exercises will be accepted.
- Attendance and active participation in synchronous sessions
- Each Monday during the term, we will meet synchronously. See the Synchronous sessions page for more details. Students who attend and participate actively in the session will earn 3 points towards the class participation grade.
- (Active) attendance in office hours
- Students may earn up to 1 point per week for attending office hours. To earn this point, students must come prepared to ask a question or participate in the discussion. See the Office hours page for more details.
Written homework assignments will be assigned weekly. They are due each Wednesday at 11:59pm ET. Homework assignments will typically cover the material up through the previous Friday. So the first written assignment (soon to be available in the Week 1 module) covers the material from the Week 1 module and is due on Wednesday of Week 2. Homework submissions will be via Canvas; the use of LaTeX is highly encouraged.
For each student, the lowest homework score will be dropped at the end of the term. Because of this, no late homework will be accepted.
This course will have two (non-cumulative) exams taking place in Weeks 5 and 9, each worth 15% of the final grade. These will take place instead of a weekly homework assignment and will be take-home and open note/open Canvas (although no other resources will be allowed).
Throughout the course, each student will compile a portfolio consisting of
- 4 proofs/solutions from a set pool of exercises, and
- a paper or recorded presentation on an application of abstract algebra to the real world or another area of math.
Please see the Portfolio details page for more information.
The Honor Principle:
Academic integrity is at the core of our mission as mathematicians and educators, and we take it very seriously. We also believe in working and learning together.
Collaboration on homework is permitted and encouraged, but obviously it is a violation of the honor code for someone to provide the answers for you. On weekly homework, you are encouraged to work together, and you may get help from others, but you must write up the answers yourself. If you are part of a group of students that produces an answer to a problem, you cannot then copy that group answer. You must write up the answer individually, in your own words.
On exams, you may not give or receive help from anyone.
On portfolio problems, you may not give or receive help from anyone except the instructor.
Accessibility Services etc.
Students requesting disability-related accommodations and services for this course are encouraged to schedule a phone/video meeting with me as early in the term as possible. This conversation will help to establish what supports are built into my online course. In order for accommodations to be authorized, students are required to consult with Student Accessibility Services (SAS; email@example.com; SAS website; 603-646-9900) and to email me their SAS accommodation form. We will then work together with SAS if accommodations need to be modified based on the online learning environment. If students have questions about whether they are eligible for accommodations, they should contact the SAS office. All inquiries and discussions will remain confidential.
The academic environment at Dartmouth is challenging, our terms are intensive, and classes are not the only demanding part of your life. There are a number of resources available to you on campus to support your wellness, including your undergraduate dean (http://www.dartmouth.edu/~upperde), Counseling and Human Development (http://www.dartmouth.edu/~chd/), and the Student Wellness Center (http://www.dartmouth.edu/~healthed/).
Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with your instructor before the end of the second week of the term to discuss appropriate accommodations.
The syllabus page shows a table-oriented view of the course schedule, and the basics of course grading. You can add any other comments, notes, or thoughts you have about the course structure, course policies or anything else.
To add some comments, click the "Edit" link at the top.