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 | |
Last changed | 22/06/2018 |