Title 
Differential Geometry

Semester 
E2023

Master programme in 
Mathematical Bioscience / Physics and Scientific Modelling

Type of activity 
Course 
Teaching language 
English

Study regulation  
REGISTRATION AND STUDY ADMINISTRATIVE  
Registration 
Sign up for study activities at stads selvbetjeningwithin the announced registration period, as you can see on the Studyadministration homepage. When signing up for study activities, please be aware of potential conflicts between study activities or exam dates. The planning of activities at Roskilde University is based on the recommended study programs which do not overlap. However, if you choose optional courses and/or study plans that goes beyond the recommended study programs, an overlap of lectures or exam dates may occur depending on which courses you choose. 
Number of participants 

ECTS 
5

Responsible for the activity 
Carsten Lunde Petersen (lunde@ruc.dk)

Head of study 
Jesper Schmidt Hansen (jschmidt@ruc.dk)

Teachers 

Study administration 
INM Registration & Exams (inmexams@ruc.dk)

Exam code(s) 
U60169

ACADEMIC CONTENT  
Overall objective 
The overall objective of the course in Differential Geometry is to give the student an understanding of its construction and formalism, which enables the student to apply differential geometry in the critical analysis of other mathematical contexts. 
Detailed description of content 
• The course starts with a general discussion of curves in Rn and their representations. • The course then continues into a discussion of regular surfaces in R3. • Starting from the very definition of a regular surface we discuss methods of constructing regular surfaces and prove that the change of coordinates on a regular surface is smooth. This naturally leads to a discussion of • The tangent space to a regular surface at a point of the surface, the differential of a differentiable mapping between two regular surfaces, the first fundamental form on a regular surface, the notion of curvelength, area and integration on a regular surface and notions of curvature of regular surfaces 
Course material and Reading list 
The exact currciulum will be announced on the Moodle site for the course 
Overall plan and expected work effort 
The course is a 5 ETCS credit course, corresponding to an expected student workload of 135 hours. The stipulated workload distribution is: Preclass 40 hours Classes 40 hours Post classes 40 hours Exam preparation 15 hours. 
Format 

Evaluation and feedback 
The course includes formative evaluation based on dialogue between the students and the teacher(s). Students are expected to provide constructive critique, feedback and viewpoints during the course if it is needed for the course to have better quality. Every other year at the end of the course, there will also be an evaluation through a questionnaire in SurveyXact. The Study Board will handle all evaluations along with any comments from the course responsible teacher. Furthermore, students can, in accordance with RUCs ‘feel free to state your views’ strategy through their representatives at the study board, send evaluations, comments or insights form the course to the study board during or after the course. 
Programme 
The course will consist of lecures and exercises. The students are required to show active participation in the course and give 12 short presentations to the rest of class of a selected part of the curriculum as well as presenting solutions to 24 exercises to the rest of the class. 
ASSESSMENT  
Overall learning outcomes 
After the course the student will be able to

Form of examination 
Individual oral exam based on a portfolio. The character limit of the portfolio is 1,200120,000 characters, including spaces. Examples of written products are exercise responses, talking points for presentations, written feedback, reflections, written assignments. The preparation of the products may be subject to time limits. The character limits include the cover, table of contents, bibliography, figures and other illustrations, but exclude any appendices. Time allowed for exam including time used for assessment: 30 minutes. The assessment is an assessment of the oral examination. The written product(s) is not part of the assessment. Permitted support and preparation materials for the oral exam: All. Assessment: 7point grading scale. Moderation: Internal coassessor 
Form of Reexamination 
Samme som ordinær eksamen / same form as ordinary exam

Type of examination in special cases 

Examination and assessment criteria 
The portfolio consists of a written presentation of the oral presentation which the student gives during the course on a topic assigned by the course organizer. During the oral examination the student should be able to
The assessment of the oral exam is based on the student’s ability to meet the criteria mentioned above and their ability to

Exam code(s)  
Last changed  12/04/2023 