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| Semester |
E2025
|
| Subject |
Subject Module in Mathematics
|
| Activity type |
subject Module course
|
| Teaching language |
English
|
| Registration |
Registration is happing through stads selvbetjeningwithin the announced registration period, as you can see on the Studyadministration homepage. When registering for courses, please be aware of the potential conflicts between courses or exam dates on courses. The planning of course 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. |
| Detailed description of content |
This course runs in Block C This course is a primer in abstract algebra and focuses on the definitions and properties of simple mathematical structures, in particular, groups and vector spaces. During the course the student is trained in mathematical thinking, to perform mathematical proofs, and communicate the curriculum in a concise mathematical manner. Note: To benefit fully from this course it is highly recommended that the student has passed the two basis courses Calculus and Linear Algebra or similar. |
| Expected work effort (ECTS-declaration) |
18 – 19 lectures combined with practical exercises (each 2 hours). The course is a 5 ETCS credit course, corresponding to an expected student workload of approximately 135 hours. About one third of these hours are contact hours while the remaining two thirds are dedicated to preparation. We expect that students will spend about at least 3-4 hours on preparation for a 2-hour lecture. Read more about expected work efford at Natbach here |
| Course material and Reading list |
Overall content Matrix transformations from R^n to R^m, Properties of matrix transformations, Complex vector space, Differential equations, Orthogonal matrices, Orthogonal diagonalization, Hermitian, unitary and normal matrices, General linear transformations, Isomorphismic vector spaces, Compositions and inverse transformations. The Integers Groups, Cyclic groups, Permutation groups, Cosets and Lagranges theorem, Group isomorphisms, Homomorphisms and factor groups |
| Evaluation- and feedback forms |
Three portfolio assignments with feedback, oral presentations by students, working on problem solving in class |
| Administration of exams |
INM Registration & Exams (inm-exams@ruc.dk)
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| Responsible for the activity |
Jesper Schmidt Hansen (jschmidt@ruc.dk)
|
| ECTS |
5
|
| Learning outcomes and assessment criteria |
|
| Mandatory or elective |
Mandatory course |
| Overall content |
Advanced linear algebra. Quantities with compositions. Basic algebraic structures (e.g. groups, rings and vector spaces), their properties and distinctive components as well as their results. The algebraic properties of the various number areas. Important specific examples of algebraic structures (such as vector spaces, symmetry groups, matrix groups, and finite fields). |
| Teaching and working methods |
Lectures and arithmetic exercises with brief student presentations and discussions of the material. |
| Form of examination |
Individual oral exam without preparation time.
The starting point for the exam is a question that will be drawn when the examination begins. The student begins the exam with a short presentation followed by a dialogue. There may be posed questions in any part of the curriculum. Time allowed for exam including time used for the drawing of question and for assessment: 30 minutes. Permitted support and preparation materials: All. Assessment: 7-point grading scale. Moderation: Internal co-assessor. |
| Form of Re-examination |
Samme som ordinær eksamen / same form as ordinary exam
|
| Exam code(s) | |
| Last changed | 23/10/2025 |
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