Mathematics for Computer Scientists 1 is recommended.
To be determined from performance in examinations and tutorials. Exact modalities will be announced at the beginning of the module.
4 h lectures
+ 2 h tutorial
= 6 h (weekly)
90 h of classes
+ 180 h private study
= 270 h (= 9 ECTS)
The numbers in parentheses indicate the total number of 2 hour lectures.
LINEAR ALGEBRA
C. Algebraic structures (5)
29. groups (2)
30. rings and fields (1)
31. polynomial rings over fields (1/2)
32. Boolean algebras (1/2)
D. Linear algebra (21)
33. vector spaces (2)
- definition, examples
- linear maps
- subspaces
- linear span, linear dependence, basis, exchange theorem
34. linear transformations (image, kernel) (1)
35. matrix representations of linear transformations (1 1/2)
- interpretation as linear transformations
- multiplication by composition
- ring structure
- inverses
36. rank of a matrix (1/2)
37. Gaussian algorithmn for systems of linear equations (2)
- Gaussian elimination (1)
- Back substitution (1)
38. iterative methods for systems of linear equations (1)
39. determinants (1)
40. Euclidean vector spaces, scalar products (1)
41. functional-analytic generalisations (1)
42. orthogonality (2)
43 Fourier series (1)
44. orthogonal matrices (1)
45. eigenvalues and eigenvectors (1)
46. eigenvalues and eigenvectors of symmetric matrices (1)
47. quadratic forms and positive-definite matrices (1)
48. quadrics (1)
50. matrix norms and eigenvalue estimates (1)
51. numerical calculation of eigenvalues and eigenvectors (1)
To be announced before the start of the module on the relevant internet page.
This module is identical in content to the German-language module Mathematik für Informatiker 2.
This module is part of the following study programmes: