PDF for print
Find calendar
| Title |
Differential Geometry
|
| Semester |
E2025
|
| Master programme in |
Mathematical Bioscience / Physics and Scientific Modelling
|
| Type of activity |
Course |
| Mandatory or elective |
Mandatory/Elective Mandatory: Mathematical Bioscience. Physics and Scientific Modelling - Thematic profile 2 Elective: Physics and Scientific Modelling - General profile |
| 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 |
Morten Andersen (moan@ruc.dk)
|
| Head of study |
Jesper Schmidt Hansen (jschmidt@ruc.dk)
|
| Teachers |
|
| Study administration |
INM Registration & Exams (inm-exams@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 curve-length, 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 work-load of 135 hours. The stipulated workload distribution is:
|
| 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 1-2 short presentations to the rest of class of a selected part of the curriculum as well as presenting solutions to 2-4 exercises to the rest of the class. |
| ASSESSMENT | |
| Overall learning outcomes |
After the course the student will be able to
|
| Prerequisites |
|
| Form of examination |
Individual oral exam based on a portfolio. The character limit of the portfolio is 1,200-120,000 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: 7-point grading scale. Moderation: Internal co-assessor |
| Form of Re-examination |
Samme som ordinær eksamen / same form as ordinary exam
|
| Type of examination in special cases |
|
| Examination and assessment criteria (implemented) |
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
Regarding the use of generative AI at the exam In this course, generative AI tools (GAI) are allowed in the work on the exam if their use is declared. You must clearly indicate how you have used generative artificial intelligence (GAI). This can, for example, be included as part of a methodology section or as a brief statement at the end of your exam paper or submitted as an appendix to your assignment. This means that you must describe how you have used GAI, for example, for preparatory work on the assignment, to ask questions, search and process information, receive feedback and critique on your text, perform proofreading, or improve language and readability. It is important that you actively consider your choice of tools in this way, as it is part of the entire creation process of the assignment and thus part of your scientific method and academic communication. The use of any specific text that is GAI-generated requires citation, just like the use of any other sources from which direct quotes are taken. In the library's guide, you can see more about how to cite AI and how you can declare your use of GAI - find the guide here. Regular spell check and other language suggestions, as known from Word or other word processing programs, as well as programs for writing minutes and transcription, are allowed in all written exams and do not need to be declared. |
| Exam code(s) | |
| Last changed | 23/10/2025 |
Find calendar (1)
PDF for print (1)