Geometry
Faculteit  Science and Engineering 
Jaar  2017/18 
Vakcode  WIMTK08 
Vaknaam  Geometry 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester II a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Geometry  
Leerdoelen  1. The student is aware of the main developments in Differential Geometry since Euler, Gauss and Riemann, in particular regarding the distinction between extrinsic and intrinsic geometry. 2. The student is able to reproduce basic concepts and theorems from Differential Geometry, such as curvature and torsion of curves in threespace, lengths of curves on surfaces in threespace, the First and Second Fundamental Form and the Gaussmap of surfaces in threespace, principal curvatures, principal directions and curvature lines on surfaces in threespace, asymptotic directions and asymptotic curves on surfaces in threespace, geodesics, Christoffel symbols, the intrinsic geometry of abstract surfaces, parallel transport and covariant differentiation, the Theorema Egregium. 3. The student is able to understand and apply the theory from textbooks and elementary papers on Differential Geometry autonomously. He/she has developed a critical learning attitude regarding theory and problems in Differential Geometry. He/she is able to assess the validity and scope of definitions and theorems in Differential Geometry. 4. The student is able to give a clear and coherent written presentation on parts of Differential Geometry. 5. The student can solve problems strategically 

Omschrijving  Differential geometry of curves and surfaces is the central theme of this course. Both local and global aspects will be discussed. After a discussion of regular surfaces in threespace the local theory of surfaces will be discussed, emphasizing the role of the Gaussmap in the definition of curvature. Elementary aspects of Riemannian Geometry will play a central role in the intrinsic properties of surfaces. The course concludes with a number of lectures on global aspects of the theory of surfaces, like Hilbert's theorem on the nonrealizability of complete surfaces of constant negative curvature as (immersed) surfaces in threespace.  
Uren per week  
Onderwijsvorm  Hoorcollege (LC), Opdracht (ASM), Werkcollege (T)  
Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE)
(Assessment takes place through 3 homework assignments and a final written exam. The final grade E = 0.3 H + 0.7 , rounded to the nearest integer, where H = average of homework assignments, T = final exam. If E is greater than 5, but either H or T is less than 5, the final grade will be equal to 5.) 

Vaksoort  bachelor  
Coördinator  A.V. Kiselev  
Docent(en)  A.V. Kiselev  
Verplichte literatuur 


Entreevoorwaarden  Prior knowledge from the second year course Group Theory is required.  
Opmerkingen  
Opgenomen in 
