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Geometri / Geometry

Semester
E2017
Subject
Mathematics *
Activitytype
master course
Teaching language
English
Registration

Please register via stads-self-service within the registration period announced here: https://intra.ruc.dk/en/students/student-hub/student-hub-find-the-answers-to-your-administrative-questions/

Tilmelding via stads selvbetjening Indenfor den annoncerede tilmeldingsperiode, som du kan se her: https://intra.ruc.dk/dk/for-studerende/student-hub/studieadministration/

Learning outcomes/Assessment criteria

After completing the course the student has obtained

Knowledge of

General properties of regular curves and surfaces in R3 Notions of Curvature for regular surfaces in R3 Abstract differential geometry Examples of concrete surfaces Skills in

Mastering differential geometric concepts, ideas and entities Correct use of the mathematical formalism, including the relevant notation, symbols and syntax Reading, understanding and conducting proofs within a differential geometric setting Applying mathematical analysis and linear algebra in differential geometry Competences to

Apply mathematical thinking in relation to geometric structures and problem solving Understand, evaluate and conduct mathematical reasoning and proofs in geometry Decode, interpret, distinguish and connect different mathematical representations, in particular geometric and algebraic representations Understand, formulate, formalize and solve problems in differential geometry Read and understand mathematical texts on differential geometry and communicate professionally both written and orally Apply numerical tools to investigate, solve and communicate differential geometric problems

Overall content

Fundamental elements of differential geometry:

• Regular curves in R3

• Regular surfaces in R3

• Notions of Curvature for regular surfaces and their relations

• Abstract surfaces and Riemannian metrics

• Concrete surfaces

Detailed description of content

Lectures and problem sessions including class room discussions and minor student presentations.

Teaching and working methods

Lectures and problem sessions including class room discussions and minor student presentations.

Course material and Reading list

The course will cover Chapters 5-13 in : John McCleary, Geometry from a Differential Viewpoint, Second Edition, Cambridge University Press 2013, ISBN 978-0-521-13311-1 (Paperback) or ISBN 978-0-521-11607-7 (Hardback) We shall occasionally refer to William R. Wade : An introduction to Analysis, Fourth Edition, Pearson Prentice Hall, 2010, ISBN 978-0-13-615370-2. You may benefit from consulting other sources, e.g.: Andrew Pressley, Elementary Differential Geometry, Springer 2010, SUMS, ISBN 978-1-84882-890-2. and Manfredo P Do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall 1976, ISBN 978-0132125895.

Form of examination

30 minutes oral examination, including voting based on a take-home question. the take-home question is handed out 72 hours prior to the oral examination. the examination is opened by the student giving a presentation of duration max. 10 min. addressing the question. after this, the student is questioned in the general curriculum for another 15 minutes.

all aids are allowed.

date: Submission of the take-home question 09/01-18 at 09:00 oral exams are on the 12th of jan.

Form of re-examination

as ordinary examination.

Information regarding sign up for the re-exam will be announced through moodle as we progress towards the date.

Examination type
Individual examination
Exam aids

all

Assessment
7-point grading scale
Moderation
External (i.e. course lecturer and an external examiner assess)
Evaluation- and feedback forms

See the section on exam

Responsible for the activity
Carsten Lunde Petersen (lunde@ruc.dk)
Teacher
Carsten Lunde Petersen (lunde@ruc.dk)
Administration of exams
INM Studieadministration (inm-studieadministration@ruc.dk)
STADS stamdata
Obligatorisk kursus
belastning : 10 ECTS aktivitetskode : U40460
prøveform : mundtlig bedømmelse : 7-trinsskala censur : Ekstern censur
Last changed 22/06/2018

lecture list:

Show lessons for Subclass: 1 Find calendar (1) PDF for print (1)

Monday 04-09-2017 13:15 - 04-09-2017 15:00 in week 36
1. kursusgang

Wednesday 06-09-2017 08:15 - 06-09-2017 10:00 in week 36
2. kursusgang

Monday 11-09-2017 13:15 - 11-09-2017 15:00 in week 37
3. kursusgang

Wednesday 13-09-2017 08:15 - 13-09-2017 10:00 in week 37
4. kursusgang

Monday 18-09-2017 13:15 - 18-09-2017 15:00 in week 38
5. kursusgang

Wednesday 20-09-2017 08:15 - 20-09-2017 10:00 in week 38
6. kursusgang

Monday 25-09-2017 13:15 - 25-09-2017 15:00 in week 39
7. kursusgang

Wednesday 27-09-2017 08:15 - 27-09-2017 10:00 in week 39
8. kursusgang

Monday 02-10-2017 13:15 - 02-10-2017 15:00 in week 40
9. kursusgang

Wednesday 04-10-2017 08:15 - 04-10-2017 10:00 in week 40
10. kursusgang

Monday 09-10-2017 13:15 - 09-10-2017 15:00 in week 41
11. kursusgang

Wednesday 11-10-2017 08:15 - 11-10-2017 10:00 in week 41
12. kursusgang

Friday 13-10-2017 10:15 - 13-10-2017 12:00 in week 41
13. kursusgang

Monday 16-10-2017 13:15 - 16-10-2017 15:00 in week 42
14. kursusgang

Wednesday 18-10-2017 08:15 - 18-10-2017 10:00 in week 42
15. kursusgang

Friday 20-10-2017 10:15 - 20-10-2017 12:00 in week 42
16. kursusgang

Monday 23-10-2017 13:15 - 23-10-2017 15:00 in week 43
17. kursusgang

Wednesday 25-10-2017 08:15 - 25-10-2017 10:00 in week 43
18. kursusgang

Friday 27-10-2017 10:15 - 27-10-2017 12:00 in week 43
19. kursusgang

Monday 30-10-2017 13:15 - 30-10-2017 15:00 in week 44
20. kursusgang

Wednesday 01-11-2017 08:15 - 01-11-2017 10:00 in week 44
21. kursusgang

Friday 03-11-2017 10:15 - 03-11-2017 12:00 in week 44
22. kursusgang

Monday 06-11-2017 13:15 - 06-11-2017 15:00 in week 45
23. kursusgang

Wednesday 08-11-2017 08:15 - 08-11-2017 10:00 in week 45
24. kursusgang

Friday 10-11-2017 10:15 - 10-11-2017 12:00 in week 45
25. kursusgang

Friday 17-11-2017 10:15 - 17-11-2017 12:00 in week 46
26. kursusgang

Monday 20-11-2017 13:15 - 20-11-2017 15:00 in week 47
27. kursusgang

Wednesday 22-11-2017 08:15 - 22-11-2017 10:00 in week 47
28. kursusgang

Monday 04-12-2017 13:15 - 04-12-2017 15:00 in week 49
29. kursusgang

Wednesday 06-12-2017 08:15 - 06-12-2017 10:00 in week 49
30. kursusgang

Friday 08-12-2017 10:15 - 08-12-2017 12:00 in week 49
32. kursusgang

Monday 11-12-2017 13:15 - 11-12-2017 15:00 in week 50
33. kursusgang

Wednesday 13-12-2017 08:15 - 13-12-2017 10:00 in week 50
34. kursusgang

Friday 15-12-2017 10:15 - 15-12-2017 12:00 in week 50
35. kursusgang

Monday 18-12-2017 13:15 - 18-12-2017 15:00 in week 51
36. kursusgang