General Information
Instructor
Professor Sarah Frei
Office: 314 Kemeny Hall
Office Hours: Wed 9:30-10:30, Fri 3:30-4:30
Contact via email: sarah.frei(at)dartmouth.edu (Replace the (at) with an @).
Teaching Assistant Luke Askew (first half of the term only)
Office: 243 Kemeny Hall
Office Hours: Wed 5:30-6:30
Contact via email: luke.a.askew.gr(at)dartmouth.edu (Replace the (at) with an @).
Scheduled Lectures
Section 1: Sarah Frei
(Block 2) MWF 2:10—3:15
(x-hour) Th 1:20—2:10
Kemeny 105
Textbook
David S. Dummit and Richard M. Foote, Abstract Algebra, 3rd Edition (ISBN: 978-0-471-43334-7).
▲Course Description
The sequence MATH 71 and 81 is intended as an introduction to abstract algebra. MATH 71 develops basic theorems on groups, rings, fields, and vector spaces. For a more detailed description on the topics we will learn in this class see the day to day Syllabus.
Goals of the course:
Weekly homework problems, midterm exams, and a final exam will provide students with opportunities to demonstrate the level of their abilities relative to the above learning goals.
More generally, mathematics courses should be viewed as an opportunity to develop and strengthen your problem-solving skills; you will be given numerous opportunities to grapple with complex problems and strategize solutions. These are skills you will certainly need to employ throughout as well as after your time at Dartmouth.
▲Expectations
I believe in the axioms* laid out by SFSU Professor Federico Ardila, and I will use them to guide my instruction of this course.1. Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
2. Everyone can have joyful, meaningful, and empowering mathematical experiences.
3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
4. Every student deserves to be treated with dignity and respect.
*Mathematically, an axiom is a statement accepted as truth, on which all other work is built.
Using these as guiding principles, I expect students in Math 71 to collaborate with me in developing and maintaining an inclusive learning environment where diversity and individual differences are understood, respected, and recognized as a source of strength. Racism, discrimination, harassment, and bullying will not be tolerated. I expect all participants in this course (students and faculty alike) to treat each other with courtesy and respect.
▲Resources
Our graduate teaching assistant, Luke Askew, will hold a weekly office hour on Wed 5:30-6:30. This will take place in his office, Kemeny 243. You can get help with any questions you have regarding the course topics and homework assignments. You don't need an appointment. Additionally, in the first three weeks, Luke will give lectures during the x-hour on set theory, logic, and proof writing.
The Academic Skills Center is available for everyone, and their primary goal is to assist students in becoming more efficient and effective learners.
The Peer Tutoring Program is also available if you would like to find a private one-on-one peer tutor. Tutors are recruited, having done well in the subject, and are trained by the Academic Skills Center. If a student receives financial aid the College will pay for three hours of tutoring per week. If you would like to have a tutor, please go to 301 Collis and fill out an application as early in the term as possible.
Mathematica and Wolfram|Alpha Pro are available at no charge to Dartmouth students. They are useful for solving technical problems, obtaining step-by-step solutions, and much more. To get access, go to wolfram.com/siteinfo and enter your Dartmouth email. Learn how to use Mathematica at wolfram.com/wolfram-u/.
▲The X-hour
In the first few weeks of the term, the X-hour will consist of an introduction to set theory, logic, and proof writing conducted by TA Luke Askew. After that, it will generally revert to office hours or midterm review, and occasionally will serve another purpose (e.g., extra or make-up lecture time) that will be announced in advance.
▲Grades
The course grade will be computed as follows:
| Percent of Final Grade | |
| Homework | 45 |
| Midterms | 30 (15 each) |
| Final Exam | 25 |
▲
Exams
There will be two take-home midterm exams (during weeks 4 and 7) and a cumulative final exam. The final is a 3-hour exam scheduled (by the registrar) for Sunday, Nov 24, 8:00-11:00.
▲Homework Policy
Homework assignments will be assigned once a week on Wednesdays and will be posted on Canvas. It will be collected the following Wednesday at 11:59pm via Gradescope. It can be hand-written or typed (more on LaTeX below).
Homework is a very important component of the course; as such, you should expect to spend a lot of time doing homework. An abstract mathematics class is in many ways similar to a language course: you must get lots of hands-on practice to internalize the definitions. Moreover, the homework is a chance for you to develop your mathematical communication skills. To this end, homework will be graded on correctness as well as clarity and exposition.
You may have a 24-hour extension on any three (3) written assignments you choose. You should notify me (via email) of your intention to use the extension before the assignment deadline. No explanation is required. If you believe you need a more significant extension, please email me at least 12 hours before the deadline with your proposed new deadline and a specific plan for how you will complete the assignment while staying current in this class. I will generally approve these requests, unless I notice a pattern of late work, in which case we'll need to have a conversation about necessary adjustments in order to stay better on-top of the material.
A note about LaTeX: LaTeX is a very useful program for typesetting mathematics nicely. If you haven't used LaTeX before and would like to learn, a good place to start is Overleaf, which is free and provides templates. Alternatively, here is a list of resources compiled by Rebecca Weber on LaTeX. I am also happy to help you get started with this during office hours.
Your lowest homework score above 50% from the term will be dropped.
▲Student Office Hours
These are times I have set aside specifically for you! Please come to office hours for any of the following reasons:
You are also welcome to schedule an appointment if you would like to meet outside of the above scheduled times (just send me an email).
▲The Honor Principle
The honor principle on homework: Cooperation on weekly homework is permitted (and encouraged), but you should write up the solution on your own. In other words, share your thoughts (say on a blackboard) to get started, but write up the solution afterwards using only your understanding. Please acknowledge any cooperative work (or external resources referenced) at the end of each assignment.External resources policy: Mathematical writing is very idiosyncratic; if your proofs are copied, it is easy to tell. You will not learn (nor adhere to the Honor Principle) by copying solutions from others, or from external sources such as internet forums and generative artificial intelligence (AI) output. Concerning internet forums (e.g., math.stackexchange), you are free to look at them and use any understanding you've gained from them in your course work, of course, subject to the above rules. Just be warned that these forums often contain incorrect or circuitous solutions, misleading discussions, use of techniques outside of the course material, and other material that may be detrimental to your learning process. Even the time that it takes to repeatedly search for solutions and read through dozens of forum posts could be better spent learning the material on your own or composing a question via email to me.
The honor principle on exams: Students may not give or receive assistance of any kind on an exam from any person except for the professor or someone explicitly designated by the professor to answer questions about the exam.
If you have any questions as to whether some action would be acceptable under the Academic Honor Code, please speak to me and I will be glad to help clarify things. It is always easier to ask beforehand than to have trouble later!
Plagiarism, collusion, or other violations of the Academic Honor Principle will be referred to the The Committee on Standards. If you have any questions as to whether some action would be acceptable under the Academic Honor Principle, please speak to me beforehand. For more information about standards of conduct, please see these resources.
▲
Student Accessibility and Accommodations
Students requesting disability-related accommodations and services for this course are required to register with Student Accessibility Services (SAS; Getting Started with SAS webpage; student.accessibility.services@dartmouth.edu ; 1-603-646-9900) and to request that an accommodation email be sent to their instructor in advance of the need for an accommodation. Then, students should schedule a follow-up meeting with their instructor to determine relevant details such as what role SAS or its Testing Center may play in accommodation implementation. This process works best for everyone when completed as early in the quarter as possible. If students have questions about whether they are eligible for accommodations or have concerns about the implementation of their accommodations, they should contact the SAS office. All inquiries and discussions will remain confidential.
▲Religious Observances
Dartmouth has a deep commitment to support students’ religious observances and diverse faith practices. 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 me as soon as possible — before the end of the second week of the term at the latest — to discuss appropriate course adjustments.
▲Mental Health and Wellness
The academic environment 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: the Counseling Center which allows you to book triage appointments online, the Student Wellness Center which offers wellness check-ins, and your undergraduate dean. The student-led Dartmouth Student Mental Health Union and their peer support program may be helpful if you would like to speak to a trained fellow student support listener. If you need immediate assistance, please contact the counselor on-call at (603) 646-9442 at any time. Please make me aware of anything that will hinder your success in this course.
▲Title IX
At Dartmouth, we value integrity, responsibility, and respect for the rights and interests of others, all central to our Principles of Community. We are dedicated to establishing and maintaining a safe and inclusive campus where all have equal access to the educational and employment opportunities Dartmouth offers. We strive to promote an environment of sexual respect, safety, and well-being. In its policies and standards, Dartmouth demonstrates unequivocally that sexual assault, gender-based harassment, domestic violence, dating violence, and stalking are not tolerated in our community.
The Sexual Respect Website at Dartmouth provides a wealth of information on your rights with regard to sexual respect and resources that are available to all in our community.
Please note that, as a faculty member, I am obligated to share disclosures regarding conduct under Title IX with Dartmouth's Title IX Coordinator. Confidential resources are also available, and include licensed medical or counseling professionals (e.g., a licensed psychologist), staff members of organizations recognized as rape crisis centers under state law (such as WISE), and ordained clergy (see https://dartgo.org/titleix_resources).
Should you have any questions, please feel free to contact Dartmouth's Title IX Coordinator or the Deputy Title IX Coordinator for the Guarini School. Their contact information can be found on the sexual respect website at: https://sexual-respect.dartmouth.edu.
▲