2024 Spring Course Syllabus - Mathematics 4096.001

Course: Mathematics 4096.001.

Course Title: Senior Problem Solving.

Credits: 3.

How this course will be taught: In person.

Time: Tuesday, Thursday 11am-12:20pm.

Place: Wachman 406.

Instructor: Vasily Dolgushev.

Instructor Office: Wachman 530.

Instructor Email: vasily.dolgushev@temple.edu

Instructor Phone: 215-204-7287.

Office Hours: Tuesdays and Thursdays 1:30-3pm and by appointment.

Prerequisites: Math 2111 (Basic concepts of Mathematics), Math 3096 (Introduction to Modern Algebra), Math 2101 (Linear Algebra) or Math 2045 (Differential Equations with Linear Algebra).

Course Materials: There is no specific textbook for our course. The syllabus on Canvas lists several books/notes and most of them are openly available.

Course Goals: To explore selected topics in mathematics: introduction to combinatorics, Grothendieck's child's drawings and constructions related to finite type invariants of knots; to improve writing skills that are critical to mathematicians: exposition and proof writing.

Topics Covered: The first part of the course is devoted to combinatorics (involving elements of graph theory). The second part is devoted to the group theoretic objects called Grothendieck's child's drawings. The third part of the course is devoted to chord diagrams and Jacobi diagrams. Although the latter objects are of combinatorial nature, they are related to invariants of knots.

Course Grading: Homework assignments 60% and the study project 40%.

Exam Dates: None.

Attendance Policy: I am not going to monitor the attendance.

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 page: I will use the Canvas page of this course to post homework assignments, announcements and additional materials.

Homework: Since this is a writing intensive course, each homework assignment will have two submission dates: you will get my feedback about your first submission; as for the second submission, in addition to my feedback, you will get a score. Homework assignments (with two due dates) will be posted on the Canvas page of this course. If possible, please submit hard copies of your work. If you submit your work electronically (e.g. via email), please submit it as a single (preferably PDF) file named: "YOURLASTNAME_HWNumberX.pdf" If an assignment contains programming exercises, you may also need to give me (or send me) a "print-out" of your Magma session and/or share your Magma script. Feedback about your solutions of selected homework exercises (as well as your work with Magma) will be given. Please justify all your steps in your work on all assignments. Also, please write legibly! Your score will be reduced for not writing legibly and for not justifying your steps. When computing your overall homework average, the lowest homework score will be dropped.

Programming Exercises/Magma: For our programming exercises, we will use the computer algebra system Magma http://magma.maths.usyd.edu.au/magma/handbook/. For Temple students, Magma is available through the high performance computing (HPC) server "compute". If you do not yet have an account at this server, please request one at https://www.hpc.temple.edu/ For working on your Magma scripts on the server "compute", you may need the openly available client FileZilla https://filezilla-project.org/.

Study Project: I will ask you to split into 3-4 teams. Each team should choose a study project, work on this project, prepare a written report and give an in-class presentation. Your report should be between 5 and 10 pages long. (If your study project has programming aspects, your team should also submit the final Magma script with carefully written comments.) The report should be typed using LaTeX (strongly preferred) or Word and submitted in the PDF format. Please submit the first draft of your report via email on (or before) April 19 (Friday). The due date for the final version of your report is May 6 (Monday). In-class presentations will be scheduled during the weeks of April 15 and April 22. The presentation of each group should be around 35 minutes long. Here are possible topics for a study project: 1) Cauchy-Frobenius-Burnside theorem and the Polya-Redfield enumeration theory. 2) Presentations of groups. 3) Fields and Galois theory. 4) The fundamental group of a topological space and covering spaces. 5) Riemann surfaces and Belyi pairs. 6) Lie algebras and weight systems for chord/Jacobi diagrams. The grade for your study project will depend on the mathematical correctness, clarity of the report and clarity of the presentation. If your study project has a programming part, I will also take into account correctness and readability of the code as well as helpfulness of the comments.

Letter Grades: 93-100 A, 90-92 A-, 87-89 B+, 83-86 B, 80-82 B-, 77-79 C+, 73-76 C, 70-72 C-, 50-69 D, 0-49 F.

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.