2024 Spring Course Syllabus - Mathematics 3096.001

Course: Mathematics 3096.001.

Course Title: Introduction to Modern Algebra.

Credits: 3.

How this course will be taught: In person.

Time: Recitation: W 8:00-8:50am. Lecture: TR 2:00--3:20pm.

Place: Recitation: Wachman 009. Lecture: Wachman 016.

Instructor: Martin Lorenz.

Instructor Office: Wachman 528.

Instructor Email: martin.lorenz@temple.edu

Instructor Phone: Use email: lorenz@temple.edu.

Office Hours: TR 3:30--5:00pm and by appointment.

Prerequisites: Math 2111 (Basic Concepts of Mathematics).

Course Materials: Abstract Algebra: An Introduction, by Thomas Hungerford. 3rd ed.

Course Goals: This course will primarily deal with the theory of rings. A particular emphasis will be on writing mathematical proofs in the context of modern algebra. Written proofs must offer the reader a logical and well-organized narrative explanation of an approach to a solution of a problem; they should be written in carefully edited prose involving complete sentences. Students will also be expected to research a topic relevant to the course, write a paper on the topic, and report on the topic to the class.

Topics Covered: Integers, modular arithmetic, rings, polynomial rings, ideals and quotient rings. This material will largely be based on Chapters 1-6 of the textbook. However, since some of Hungerford's choices are unusual, I will occasionally adopt different conventions. This will be explicitly pointed out in class whenever it occurs. If time permits, then I may also cover a selection of topics from Chapters 7 & 8 (Group Theory).

Course Grading: There will be two midterm exams, each of which will count for 13% of your grade; a comprehensive final exam counting for 20%; and a presentation counting for 10%. In addition, there will be regular quizzes counting 14% total and written homework counting 30% total.

Exam Dates: The two midterms are tentatively scheduled for February 22 and April 11; both will be given during the regular class period. The final exam will be on May 2, 1:00am-3:00pm. All exams occur on a Thursday and will be given in our regular classroom; they will be open-book and open-notes tests. Materials on the Canvas page of this course can be accessed, but no other external resources are permitted.

Attendance Policy: Attendance will be recorded for both lectures and recitations; it will be considered in midterm ratings and in borderline grade cases at the end of the semester. Office hours may not be used to cover material missed due to unjustified absences.

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.

Canvas: This course will use Canvas. After each class, I will post my lecture notes on Canvas along with other important announcements.

Teaching Assistant: The TA for this course is Aniruddha Sudarshan. He will hold the recitations and grade all quizzes. Aniruddha's office hours are on ??? in Wachman ???. You can also find Aniruddha at the Math Consulting Center (MCC) in Wachman 1036 on ???. (To be completed.).

Recitations & Quizzes: Our weekly recitations will serve to (1) practice material covered in class, (2) answer any questions that you might have, and (3) give regular short quizzes, starting with Recitation #2 (on Sept 11). Each quiz will have a maximum score of 10. There will be no make-up quizzes, but your lowest two quiz scores will be dropped from the calculation of your course grade. Solutions to all quizzes will be posted on Canvas.

Homework: Written homework will be assigned approximately every other week; it will be posted and collected through Canvas. Each assignment will consist of four problems and will go through two rounds of grading, with one revision. Three of the assigned problems will only be checked for completeness, with possible scores being 0, 1 or 2. The fourth problem, chosen after the deadline, will be graded and annotated with detailed rewriting instructions (if needed). In the first round, I will assign a preliminary score to this problem. You will have the opportunity to resubmit a revised solution to improve your preliminary score up to the maximum of 6. Thus, the maximum score for each HW will be 12. Your lowest HW score will be dropped from the calculation of your course grade. Complete solutions of all homework problems will be posted on Canvas.

Presentations: Each student is expected to give a presentation to the class on a topic of their choice, which must be related to the material covered in this course. A list of possible topics will be discussed in class and posted on Canvas toward the end of the semester. Students are expected to work on their chosen topic in groups of two or three, with each member of the group being responsible for a particular aspect (background, theory, applications, etc). Further details will be communicated in due course.

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
If you are experiencing food insecurity or financial struggles, Temple provides resources and support. Notably, the Temple University Cherry Pantry and the Temple University Emergency Student Aid Program are in operation as well as a variety of resources from the Division of Student Affairs.