2017 Spring Course Syllabus - Mathematics 4096.001

Course: Mathematics 4096.001.

Course Title: Senior Problem Solving (Math 4096).

Time: Tuesday and Thursday 9:30-10:50am.

Place: Tuttleman 007.

Instructor: Vasily Dolgushev.

Instructor Office: Wachman Hall Rm. 530.

Instructor Email: vasily.dolgushev@temple.edu

Instructor Phone: 215-204-7287.

Course Web Page: Please, go to the blackboard learn.temple.edu

Office Hours: Wednesdays 10-11:30am or by appointment.

Prerequisites: Math 2111 (Basic concepts of Mathematics) and Math 3096 (Introduction to Modern Algebra).

Textbook: No textbook is required for this course. However, the following books can be helpful: Introduction to Compact Riemann Surfaces and Dessins d'Enfants, by E. Girondo and G. Gonzalez-Diez; Graphs on Surfaces and their applications, S.K. Lando and A.K. Zvonkin; Group Theory, J.S. Milne, http://www.jmilne.org/math/CourseNotes/gt.html; Fields and Galois Theory, J.S. Milne, http://www.jmilne.org/math/CourseNotes/ft.html; Algebraic Number Theory, J.S. Milne, http://www.jmilne.org/math/CourseNotes/ant.html; Algebraic Topology, A. Hatcher, https://www.math.cornell.edu/ hatcher/AT/ATpage.html; Introduction to algebraic curves, by P. A. Griffiths.

Course Goals: To gain experience for doing an actual mathematical research.

Topics Covered: This course will be devoted to the group theoretic and combinatorial aspects of the Grothendieck's theory of child's drawings. I will start with a review of the necessary background on group theory and graph theory. I will then introduce the concept of constellation, the concept of hypermap and prove that there is a bijection between isomorphism classes of constellations and isomorphism classes of hypermaps. We will then talk about the fundamental group of a topological space and covering spaces. If time will permit, we will talk about Riemann surfaces and the relationship between hypermaps and Riemann surfaces. The course has a writing component and a programming component: students will work in groups on projects related to the topic of the course, they will also learn elements of the programming language Python and some packages which are useful for working with the symmetric groups and graphs.

Course Grading: Homeworks: 60% and the writing project: 40%.

Exam Dates: The will be no tests in this course.

Attendance Policy: Attendance will not be monitored but I strongly encourage you to come to each class and take notes.

Homeworks: Homework assignments will be posted on the blackboard. They will be collected every other Thursday. You have to justify all your steps in your work on homework 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. I will not accept late homeworks.

Writing Project: I will ask you to split into groups. Each group should choose a study project, work on this project, prepare a written report and give an in-class presentation. The purpose of the project is to broaden your knowledge, get an experience to work in a team, and an experience with writing about mathematics. Your report should be between 8 and 12 pages long. It should be typed using LaTeX (strongly preferred) or Word and submitted in the PDF format. The first draft of the report will be due on March 23 (Thursday) and the final version of the report will be due on April 27 (Thursday). In-class presentations will be scheduled during the week of April 17. The presentation of each group should be around 30 minutes long. The list of topics for projects will be posted on the blackboard during the first week of the semester.

Teaching Assistant: The TA for this course is William Worden. His office is in Wachman Hall, Rm. 517. His office hours TBA.

Enter note 10 heading here: Any student who has a need for accommodation based on the impact of a disability should contact me privately to discuss the specific situation as soon as possible. Contact Disability Resources and Services at (215) 204-1280, 100 Ritter Annex, to coordinate reasonable accommodations for students with documented disabilities.

Enter note 11 heading here: 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 at this website: http://policies.temple.edu/.

Any student who has a need for accommodation based on the impact of a disability should contact me privately to discuss the specific situation as soon as possible. Contact Disability Resources and Services at (215) 204-1280, 100 Ritter Annex, to coordinate reasonable accommodations for students with documented disabilities.

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.

Students will be charged for a course unless dropped by the Drop/Add deadline date. Check the University calendar for exact dates.

During the first two weeks of the fall or spring semester, students may withdraw from a course with no record of the class appearing on the transcript. In weeks three through nine of the fall or spring semester, or during weeks three and four of summer sessions, the student may withdraw with the advisor's permission. The course will be recorded on the transcript with the instructor's notation of "W," indicating that the student withdrew. After week nine of the fall or spring semester, or week four of summer sessions, students may not withdraw from courses. No student may withdraw from more than five courses during the duration of his/her studies to earn a bachelor's degree. A student may not withdraw from the same course more than once. Students who miss the final exam and do not make alternative arrangements before the grades are turned in will be graded F.

The grade I (an "incomplete") is reserved for extreme circumstances. It is necessary to have completed almost all of the course with a passing average and to file an incomplete contract specifying what is left for you to do. To be eligible for an I grade you need a good reason and you should have missed not more than 25% of the first nine weeks of classes. If approved by the Mathematics Department chair and the CST Dean's office, the incomplete contract must include a default grade that will be used in case the I grade is not resolved within 12 months.