MAT9520 - Manifolds
The subject will give a thoroughly introduction to differetiable manifolds. The course will contain topics like the tangent - and the cotangent bundle, vector fields and flows (ordinary differential equations), differential forms, integration. Topological applications will give examples of how analysis on a manifold depends of the global structure.
The course will give a common background for further studies in topology and geometry and also for parts of real and complex analysis. The course will give proper background for geometry which is important in modern mathematics and theoretical elementary particle physics.
PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.
If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.
PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.
Formal prerequisite knowledge
Recommended previous knowledge
Overlapping courses10 credits overlap with MA152.
10 credits with MA252/352.
10 credits with MAT4520 - Manifolds.
*The information about the overlaps is not complete. Contact the Department for more information if necessary.
4 hours of lectures/exercises per week.
In addition, each phd student is expected to give a one hour oral presentation on a topic of relevance (chosen in cooperation with the lecturer). The presentation has to be approved by the lecturer for the student to be admitted to the final exam.
Language of examination
Students may, on subjects taught in Norwegian and the examination form is written exam, ask for the exam paper in Bokmål, Nynorsk or English. Closing date for registering the chosen examination language is September 1st for the fall semester and February 1st for the spring semester.
Please view the web page of the Faculty of Mathematics and Natural Sciences on how to proceed
Subjects taught in English will offer the exam paper in English only.
This rule also applies for subjects where the exam form is dependent on the number of students and written exam is chosen by the teaching staff.
Grades are awarded on a pass/fail scale. Read more about the grading system.
Resit an examination
Students who can document valid reasons for failing to attend their final exams within given deadlines may participate in deferred examinations. Deferred examinations are arranged either later in the same semester or early in the semester following the exam in question.
Students who have failed an exam, who withdraw during an exam, and students who wish to retake an exam to achieve a better grade may not participate in deferred exams, but may retake the exam when it is regularly scheduled.
Withdrawal from an examination
A student may sit this exam up to 3 times. If a student wishes to withdraw from the exam, s/he must do so in StudentWeb at least two weeks prior to the first day of the exam. Failure to do so will be counted as one of the three opportunities to sit the exam.
Special examination arrangements
If you have a disability or a health problem that entails significant inconvenience in an examination situation, you may be considered for special examination arrangements. Mothers who are breastfeeding may apply for extra time to complete the exam.
Feedback from our students is essential to us in our efforts to ensure and further improve the high quality of our programmes and courses. All courses are subject to continuous evaluation. At regular intervals we also ask students on a particular course to participate in a more comprehensive, periodic evaluation of this course.