Admission requirements
Topology (required)
Linear Algebra 1,2 (required)
Analysis 2,3 (required)
Algebra 1 (required)
Algebra 2 (recommended)
Complex Analysis (recommended)
Curves and Surfaces (recommended, NOT required)
Description
In this course, we introduce the concept of abstract smooth manifolds, generalizing the notion of a smooth surface in three-dimensional space, which serves as a motivating example. We will discuss the main properties of manifolds and structures on them, including vector bundles, vector fields and derivations, flows, differential forms, orientation, and integrals. Towards the end we will discuss Stokes’ theorem. This will pave the way for a discussion on De Rham cohomology, its fundamental properties, and its relation to topology.
Course objectives
Obtain a thorough understanding of the geometry and topology of manifolds.
Develop the ability to carry out explicit calculations of differential and integral calculus on manifolds in a concrete setting.
Apply these techniques in examples from geometry and dynamical systems.
Schedule
In MyTimetable; you can find all course and programme schedules; allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.
Additionally; you can easily link MyTimetable to a calendar app on your phone; and schedule changes will be automatically updated in your calendar. You can also choose to receive email notifications about schedule changes. You can enable notifications in Settings after logging in.
Questions? Watch the video; read the instructions; or contact the ISSC helpdesk.
Note: Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.
Teaching method
Lectures.
Assesment method
70% Final written exam + 30% Quiz
There will be \~7 Quizzes throughout the semester. Only the top 4 grades will contribute to the 30%.
Resit, review & feedback
Students can request to review their graded exam with me or the TA, by appointment.
Resit is written, unless few students wish to take a resit, in which I will suggest an oral exam.
The written resit review is as with the final. In case of oral resit, I would give verbal feedback immediately after deciding on the grade.
Reading list
Tu, Loring W. “An Introduction to Manifolds”. Springer, 2011
The book can be downloaded on Springerlink and a hardcopy can be ordered via the Mycopy option.
Registration
As a student; you are responsible for enrolling on time through MyStudyMap.
In this short video; you can see step-by-step how to enrol for courses in MyStudyMap.
Extensive information about the operation of MyStudyMap can be found here.
There are two enrolment periods per year:
Enrolment for the fall opens in July
Enrolment for the spring opens in December
See this page for more information about deadlines and enrolling for courses and exams.
Note:
It is mandatory to enrol for all activities of a course that you are going to follow.
Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.
Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.
Contact
Dr. Emre Can Sertöz - e.c.sertoz@math.leidenuniv.nl
Contact details for the TA will be provided at the beginning of the course.