Math 110B - Section 01 - Fall 2024
Subject to change.
Welcome to Abstract Algebra! I’m looking forward to meeting you all and starting our work together. Please let me know if you have any questions at all, about our course or anything else.
Continuation of MATH 110A. Topics include: rings and fields. Applications may be selected from lattice, machine, and coding theories. This is a 3 unit class.
Students should have successfully completed Modern Algebra 1 (Math 110A) with a grade of C- or better before taking this course. If you have any questions or concerns about this prerequisite, please check in with me as soon as possible.
In this course, students will (1) increase their capacity for critical thinking and fact-based reasoning, (2) develop the necessary competency with group theory for further work in mathematics and other fields, (3) improve their written and oral communication of mathematics, and (4) develop the skills and mindset for solving problems in a team. Specific content outcomes are for students to be able to
Members of this class represent a rich variety of backgrounds and perspectives. Our class commits to providing an atmosphere for learning that respects diversity and recognizes it as a source of strength. While working together to build this intellectual community, we ask all members to:
We will further develop this agreement together in class.
Overall grades for the course will be determined from the course components listed above with the following weighting:
Homework will usually be assigned each class meeting, and due at start of the next meeting. The goal of this daily work is for us all to critically engage with the material, uncover points of confusion, and deepen understanding. Confusion and struggle is an important part of the learning process that we’ll need to learn to embrace.
These assignments allow me to see your work outside of the classroom, before we come together to collaboratively revise. You are allowed and encouraged to work together, but you are expected to write up your solutions on your own. Please take care that your work is well-organized and fully-justified with proper grammar, punctuation, and spelling.
These assignments will be graded on the following ten-point system. (The score will be the highest one that applies.)
| 10 | At most one problem was skipped. All completed problems were seriously attempted with well-organized and fully-justified work |
| 8 | At most two problems were skipped. All completed problems were seriously attempted with well-organized and fully-justified work |
| 6 | At most half of the problems were skipped. All completed problems were seriously attempted with well-organized and fully-justified work |
| 4 | At least half of the problems were completed collaboratively in class when it is due. All completed problems were seriously attempted with well-organized and fully-justified work |
| 0 | None of the above |
Outside Resources
Please do not use resources from outside our class to complete the homework. It is acceptable to watch a video or go to our Math Lab for general conceptual questions, but please do not use such resources for direct assistance with the problems.
Learning to discuss mathematics is a highly valued part of this course. This component will evaluate your progress in areas such as ability to describe a solution (with clarity and thoughtfulness), ability to share and shed light on your difficulties, and ability to listen critically and respond accordingly. The best way to excel in this component is to be engaged in class each day, active in discussions, and prepared to present.
Presentations will be graded on the following scale. (The score will be the highest one that applies.)
| E | Exceeds Expectations. Thorough and detailed solution; exceptionally clear and thoughtful presentation. |
| M | Meets Expectations. Well-thought out approach capturing the key ideas; clear presentation. |
| I | In progress. Serious attempt, but has a significant flaw/gap or lack of clarity. |
| U | Unsatisfactory. Minimal or no progress was made. |
Participation will be graded on the following scale. (The score will be the highest one that applies.)
| E | Exceeds Expectations. Asking questions, contributing to meaningful discussion, or offering supportive comments essentially every meeting. |
| M | Meets Expectations. Asking questions, contributing to meaningful discussion, or offering supportive comments at least once per week. |
| U | Unsatisfactory. Never or very rarely participates in class or is disrespectful. |
The presentation and participation rubrics will be combined as follows. (The score will be the highest one that applies.)
| 90–100% | Receives M/E for participation; has at least 3 M/E presentations prior to each midterm. |
| 80-89% | Receives M/E for participation; has at least 2 M/E presentations prior to each midterm. |
| 70-79% | Receives M/E for participation; has at least 1 I/M/E presentation prior to each midterm. |
| 60-69% | Receives U for participation; has at least 1 I/M/E presentations over the semester. |
| 0–60% | Receives U for participation; never presents or all receive a U. |
There will be weekly assignments where you are asked to carefully revise and type up with $\LaTeX$ a small subset of the problems we covered. Becoming proficient with $\LaTeX$ is one of the aims of the course—I will support you as much as needed with this. Completed assignments are to be submitted via Canvas by the posted due date. Please take great care not to plagiarize or allow your own work to be plagiarized.
When writing up your solutions, you may work with one partner on this and turn in the same document for both of you. If you do this, please make sure that you have truly collaborated on both the mathematics and the writing.
There are 2 midterm exams. They are tentatively scheduled for Oct. 10 and Nov. 21. If an exam occurs during a religious holiday that you observe, I’m happy to reschedule it for you.
There is a Final Project tentatively due by Friday Dec. 13 at 12:00 PM. A detailed description of the final project and grading rubric will be posted via Canvas later in the semester. We will also meet during our scheduled final-exam time to work on the final project: Thursday, Dec. 12 from 12:45 AM – 2:45 PM.
This is a rough schedule of what we will cover, but please be aware that it is subject to change. The chapter numbers refer to our book.
| Week | Topics |
|---|---|
| 1 | Introductions + Motivating Questions (Chapters 1 and 2) |
| 2 | Complex Numbers + Roots of Unity (Chapter 3) |
| 3 | Quaternions + Abstract Fields (Chapter 3) |
| 4 | Fields, Subfields, and Extension Fields (Chapter 3) |
| 5 | Radical Extensions + Solvability by Radicals + Abstract Rings (Chapters 4 and 5) |
| 6 | Matrix and Polynomial Rings (Chapter 5) |
| 7 | Polynomial Rings: Division Algorithm and GCDs (Chapter 5) + Exam 1 (10/10) |
| 8 | Polynomial Rings: Irreducibility + Subrings and Ideals (Chapter 5) |
| 9 | Quotients + Generating Ideals + (Chapter 5) |
| 10 | Ring Homomorphisms + Algebraic Elements (Chapters 5 and 6) |
| 11 | Algebraic Elements + Eisenstein (Chapter 6) |
| 12 | Extension Fields as Vector Spaces (Chapter 6) |
| 13 | Field Isomorphisms and Automorphisms (Chapter 6) + Exam 2 (11/21) |
| 14 | Galois Groups (Chapter 7) + Fall Break |
| 15 | Galois Theory + Solvability by Radicals + End Game (Chapters 7 and 8) |
| – | Final Project |
Please come to class as much as possible! Our community will benefit greatly from a breadth of perspectives, and class will provide an opportunity to ask, clarify, and answer questions. However, I know that you all have varied and often challenging things going on in and beyond school, so missed classes will not directly affect your grade. If you need to miss class, please send me a quick email in advance, so I know what is going on.
Please strive hard to meet the deadlines, but if you need an extension for any reason, I am always happy to discuss it with you. Health related reasons will always be accommodated. Please send me a quick email as soon as you realize that extra time is needed—I really want you to be successful! Although late assignments may be subject to a reduced grade, I will usually grant short extensions with no penalty.
If you know or think that you might need academic adjustments or accommodations, of any kind, please speak with me privately as soon as possible. If you have one, please bring a copy of your accommodation letter from the Services to Students with Disabilities (SSWD) office. All discussions will remain confidential.
If you are sick, please do not attend any of your in-person classes, but do let your instructors know. If you are experiencing any COVID-like symptoms (fever, cough, sore throat, muscle aches, loss of smell or taste, nausea, diarrhea, or headache) or have had exposure to someone who has tested positive for COVID, please contact Student Health & Counseling Services (SHCS) at 916-278-6461 to receive guidance and/or medical care.
Academic dishonesty (including cheating and plagiarism) will result in disciplinary action and will be reported to the Office of Student Conduct. If you are unsure what constitutes cheating, please speak with me and review Sacramento State’s Academic Honesty Policy and Procedures document here: www.csus.edu/umanual/student/stu-0100.htm.
Please come talk with me if you have any questions! It is acceptable to watch a video or go to our Math Lab for general conceptual questions, but please do not use such resources for direct assistance with the problems.
If you are experiencing challenges with food, housing, financial or other unique circumstances that are impacting your education, help is just a phone call (916-278-5138) or email (cares@csus.edu) away. The CARES office provides case management support for any enrolled student.
Learn more about your options and resources here: www.csus.edu/student-affairs/crisis-assistance-resource-education-support
The ASI Food Pantry provides food and basic necessities to Sac State students in need at no cost. You just need to present a valid student OneCard. You can also utilize the Sacramento Food Bank & Family Services (SFBFS). In fact, SFBFS offers more than just food. From clothing for a newborn baby or a teenager heading out on a job interview, to Immigration Legal Services or English as a Second Language classes, and more, SFBFS is proud to offer support to the people of Sacramento County in a variety of different ways.
Learn more here:
If you or someone you know has experienced any type of sexual violence (including harassment, assault, dating or domestic violence, or stalking), there are many confidential and non-confidential resources available on campus. So you know, the University requires faculty and staff to report any personal disclosures of sexual misconduct including rape, dating/domestic violence and stalking to the Title IX Coordinator. Students who do not wish to report their experience to me or the Title IX Coordinator may speak to someone confidentially by contacting Student Health and Counseling Services (916) 278-6461. You can also contact WEAVE, Inc. Sacramento, which provides confidential support 24 hours a day at (916) 920-2952.
If you are in immediate danger or need immediate assistance, please call 9-1-1 or if you are on campus, campus police at 916-278-6000. If it is after hours or the weekend and you need immediate advocacy, please call WEAVE’s 24-hour hotline at 916-920-2952.
Learn more here: www.csus.edu/student-life/health-counseling/sexual-violence-support
Your physical and mental health are important to your success as a college student. Student Health and Counseling Services (SHCS) in The WELL offers medical, counseling, and wellness services to help you get and stay healthy during your time at Sac State. SHCS offers: Primary Care medical services, including sexual and reproductive healthcare, transgender care, and immunizations; urgent care for acute illness, injuries, and urgent counseling needs; pharmacy for prescriptions and over-the-counter products; mental health counseling, including individual sessions, group counseling, support groups, mindfulness training, and peer counseling; athletic training for sports injury rehabilitation; wellness services, including nutrition counseling, peerled health education and wellness workshops, and free safer sex supplies; violence and sexual assault support services. Most services are covered by the Health Services fee and available at no additional cost.
Confidential counseling services are available for Sacramento State students. Counselors are located on the second floor of the WELL. Appointments can be made 8:00am–5:00pm, Monday–Friday. Call 916-278-6461 or go here shc-pncweb.saclink.csus.edu/ to make an appointment.
If you are in immediate crisis, please call 9-1-1 or the Suicide Hotline at 1-800-273-TALK (8255).
Learn more here: www.csus.edu/student-life/health-counseling
Sacramento State is committed to ensuring an accessible learning environment where course or instructional content are usable by all students and faculty. If you believe that you require disability-related academic adjustments for this class (including pregnancy-related disabilities), please immediately contact Services to Students with Disabilities (SSWD) to discuss eligibility. A current accommodation letter from SSWD is required before any modifications, above and beyond what is otherwise available for all other students in this class will be provided. Please be advised that disability-related academic adjustments are not retroactive. If you know or think you need academic adjustments or accommodations of any kind but do not have a letter from SSWD, please speak with me privately as soon as possible.
SSWD is located on the first floor of Lassen Hall 1008. Phone is 916-278-6955 and e-mail is sswd@csus.edu. For a complete listing of services and current business hours visit www.csus.edu/student-affairs/centers-programs/services-students-disabilities
Sacramento State offers many more resources to support you and your peers. Reach out to me if you have any questions, or go here to learn more about many of them: webpages.csus.edu/wiscons/more/SacStateCampusResources.html.
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