2024 Spring Course Syllabus - Mathematics 8012.001

Course: Mathematics 8012.001.

Course Title: Abstract Algebra II.

Credits: 3.

How this course will be taught: in person.

Time: TR 14:00-15:20.

Place: Wachman 617.

Instructor: Jaclyn Lang.

Instructor Office: Wachman 606.

Instructor Email: jaclyn.lang@temple.edu

Instructor Phone: Use email.

Office Hours: Tuesdays, Thursdays, Fridays 3:30-4:30pm.

Prerequisites: MATH 8011 or permission of instructor; the material covered last semester is assumed.

Course Materials: Hungerford's textbook "Algebra" GTM 73 (available to borrow from Temple libraries).

Course Goals: This course, the second part of a two-semester sequence, will give a thorough introduction to the methods and terminology of modern abstract algebra.

Topics Covered: The material to be covered in the upcoming Spring semester is roughly organized into three main parts: Field and Galois Theory (Chapters V--VI of the textbook), Linear Algebra (Chapter VII and possibly parts of Chapter IV), and Commutative Rings (Chapter VIII). The course will follow the textbook fairly closely, and students are responsible for all definitions and statements of lemmas, propositions, and theorems in the relevant sections, unless otherwise stated. The relevant reading from the textbook will be announced prior to each lecture, and it is recommended you at least have a look at the material before class. It is important that you attend class, take notes, and work through the notes afterwards. (Think about examples/nonexamples for definitions. What happens if a hypothesis in that proposition is removed? Read a statement of a proposition, close your notes/book, and think about how you would prove it.).

Course Grading: The course grade will be based on homework, weekly quizzes, a midterm exam and a comprehensive final exam. The final exam will count for 40% of your grade; the midterm 30%; the total score from all homework assignments 20%; the total score from all quizzes 10%. Improvements to homework and quiz scores can be made via written rewrites within three weeks of initial due date.

Exam Dates: The Midterm Exam will be given on Thursday, February 29, 2-4pm; the Final Exam on Tuesday, May 2, 1-3pm (as per the TU Examination Schedule). Both exams will be in person in Wachman 617.

Attendance Policy: You are expected to attend class unless you are ill or have extenuating personal circumstances. I will track the attendance for each class. If you cannot make a class, then please let me know beforehand.

Attendance and Your Health: To achieve course learning goals, students must attend and participate in classes, according to your instructors' requirements. However, if you feel unwell or if you are under quarantine or in isolation because you have been exposed to the virus or tested positive for it, you should not come to campus or attend in-person classes or activities. Students have the responsibility to contact their instructors to create a plan for participation and engagement in the course as soon as they are able to do so and to make a plan to complete all assignments in a timely fashion when illness delays their completion.

Homework: Home work will be collected at the beginning of every Tuesday lecture. Although you technically have three weeks from the due date to hand it in, I strongly encourage you to keep to the stated due dates as closely as possible. Due dates for rewrites are hard deadlines and will not be moved except in extenuating circumstances that last for several weeks. It is very important that you give the assigned problems your best effort--this is by far the best way to learn the material. I strongly encourage you to discuss the assignments with each other, but I expect everybody to write up their own solutions. While the internet is of course a source for solutions to all kinds of problems, you will not learn abstract algebra by relying on internet searches. If I suspect your solutions are not your own, I will ask you to come in and explain the solutions to me orally, and you will not receive credit for solutions you cannot explain in your own words. Ideally, you should write your homework solutions in LaTeX; this is not a requirement, but it is a good idea to learn LaTeX as early as possible. However, if LaTeX is getting in the way of your learning algebra, forget the LaTeX for now! If you handwrite your solutions, please do so legibly and leave plenty of space for comments. Your audience for your solutions is a classmate who failed to do this problem. You should write in complete sentences, define all terms not used in the problem, and avoid all abbreviations. Whether you handwrite or use LaTeX, your solutions should be polished; please do not hand in scratch work.

Canvas: Homework assignments and other materials will all be posted on Canvas.

Quizzes: Quizzes will be placed in a sealed envelope and given to you Thursdays after class and are due back (under my door) by 1pm on Friday. The quizzes are 30 minutes, no books, no notes, self-proctored (honor system). You will be asked simple questions about the material that has been covered during that week of lecture, mostly definitions and questions about particular examples. They are there to keep you on track with the material and encourage you to commit the fundamentals to memory. Obviously, do not discuss the quiz with students who have not yet taken the quiz. Please please PLEASE hand in the quizzes on time!.

Lowest scores: I'll drop your lowest quiz and lowest homework score when computing your grade.

Homework grading: The homework will be graded both for the mathematical content and the clarity with which your writing expresses your ideas. You can improve your homework grade through rewriting by corrected solutions for problems that you struggled with in the written assignment. This is not a punishment! It is meant to encourage you learn from your mistakes. Note however that this must be done within three weeks of the original due date of the assignment.

Covid: It is important that everyone feels comfortable with our classroom setting from a health perspective. If you are concerned about it, or if your situation changes during the term, please speak to me about it and we will explore other solutions.

Change in dates: There will be no class held on Thursday, January 25 or Tuesday, March 26. Instead we will have class on Monday, January 29 (Wachman 527) and Monday, February 5 (Wachman 617) from 3:30--4:50pm. Please mark these dates on your calendars!.

Disability Statement: Any student who has a need for accommodations based on the impact of a documented disability or medical condition should contact Disability Resources and Services (DRS) in Howard Gittis Student Center South, Rm 420 (drs@temple.edu; 215-204-1280) to request accommodations and learn more about the resources available to you. If you have a DRS accommodation letter to share with me, or you would like to discuss your accommodations, please contact me as soon as practical. I will work with you and with DRS to coordinate reasonable accommodations for all students with documented disabilities. All discussions related to your accommodations will be confidential.

Academic Freedom: Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here (opens in new tab/window).

Add/Drop Policy: Students will be charged for a course unless dropped by the Drop/Add deadline date. Check the University calendar (opens in new tab/window) for exact dates.

During the Drop/Add period, students may drop a course with no record of the class appearing on their transcript. Students are not financially responsible for any courses dropped during this period. In the following weeks prior to or on the withdrawal date students may withdraw from a course with the grade of "W" appearing on their transcript. After the withdrawal date students may not withdraw from courses. Check the University Calendar (opens in new tab/window) for exact dates. See the full policy by clicking here (opens in new tab/window).

AI Policy: The use of generative AI tools (such as ChatGPT, DALL-E, etc.) is not permitted in this class unless specifically announced for a particular assignment; therefore, any use of AI tools for work in this class may be considered a violation of Temple University's Academic Honesty policy and Student Conduct Code, since the work is not your own. The use of unauthorized AI tools will result in a grade of zero on the assignment; a second offense will be reported to the Student Conduct Board.

Incomplete Policy: The grade "I" (an "incomplete") is only given if students cannot complete the course work due to circumstances beyond their control. It is necessary for the student to have completed the majority of the course work with a passing average and to sign an incomplete contract which clearly states what is left for the student to do and the deadline by which the work must be completed. The incomplete contract must also include a default grade that will be used in case the "I" grade is not resolved by the agreed deadline. See the full policy by clicking here (opens in new tab/window).

Student Support Services: The following academic support services are available to students (all links open in a new tab/window):
    The Math Consulting Center
    Student Success Center
    University Libraries
    Undergraduate Research Support
    Career Center
    Tuttleman Counseling Services
    Disability Resources and Services
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