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| Semester |
F2018
|
| Subject |
Mathematics *
|
| Activitytype |
master course
|
| Teaching language |
English
|
| Registration |
Engelsk: Please register via STADS-self-service within the annonced registration period, for more information see: https://intra.ruc.dk/en/students/student-hub/student-hub/ruc-uddannelsesjura-og-studieadministration/registration-periods/ Dansk: Tilmelding via STADS selvbetjening Indenfor den annonceret tilmeldingsperiode, for mere information se: https://intra.ruc.dk/for-studerende/student-hub/student-hub-sys-foldere/ruc-uddannelsesjura-og-studieadministration/tilmeldingsperioder/ |
| Learning outcomes/Assessment criteria |
Knowledge • Knowledge of specific mathematical structures within set theory, topology, analysis and algebra. • Knowledge of common features of and differences between such structures. • Knowledge of different types of reasoning and proofs, and their importance. • Construction and formalisation of such structures. Skills • The ability to recognise fundamental mathematical structures. • The ability to know and use symbols and other representations in accordance with the given formalism. • Skills in reading, understanding and reproducing proofs in the context of the structures studied. Competencies • Competency to apply mathematical thinking in relation to the fundamental structures of the subject. • Competency to be able to follow, assess and carry out mathematical reasoning and proofs. • Competency to decode, interpret, differentiate between and link different mathematical representations. • Competency to be able to decode and apply mathematical symbolic language within a given formalism, and to assess the strengths and weaknesses of an axiomatic system. • Competency to be able to read and understand mathematical texts concerning the basis of the subject and fundamental structures, and to communicate these both orally and in writing. |
| Overall content |
• Various fundamental, abstract mathematical structures and their interrelations. • Introduction to formal logic, including the concept of a formal theory. • Set theory, algebraic structures, metric and topological spaces, geometric structures and aspects of measure spaces. |
| Detailed description of content |
The aim of the course is to buildup the students understanding of mathematical structures. What constitutes a mathematical structure? How is a structure formed? What are the properties? What are the general principles (to the extend such principles can be determined). The course has two parts. The first is a rather quick (re)-introduction of various mathematical structures. The second part is a comparative analysis of the structures encountered in the course and in other courses. What is the general pattern in structure formation etc. |
| Teaching and working methods |
Lectures and solving of exercises with brief student presentations and discussions of the material. |
| Expected work effort (ECTS-declaration) |
The course is a 10 ECTS course and the student is expected to work 250-260 hours with the course during the semester. Off these 60 hours (40 classes of 1h45m) are is a combination of lectures and students supervised exercise solving. The students are expected to spend an equal amount of time (60 hours) in preparation for the class and 1.5 times this amount (90 hours) for working with the material after class. The remaining time is preparation for the exam. |
| Course material and Reading list |
Course notes written by Mogens Niss. The notes will be available from the Moodlepage of the course. The notes covers Formal logic Set Theory Algebraic structures Topological structures |
| Form of examination |
The course is assessed through an oral examination. The oral examination relates to written assignments/tasks prepared during the course. The examination duration is 30 minutes, including assessment. |
| Form of re-examination |
Re-examination takes the same form as the ordinary examination. |
| Examination type |
Individual examination
|
| Exam aids |
all |
| Assessment |
7-point grading scale
|
| Moderation |
Internal (i.e. course lecturer and an internal examiner assess)
|
| Evaluation- and feedback forms |
The course is evaluated according to the evaluation scheme developed by the study board for INM. This consists of a midterm evaluation and a final evaluation (both are discussions between the course professor and the class. The final evaluation is supplemented with a blinded written evaluation through survey exact. The teaching will be dialog based with ample possibilities for feed back both personally and as a class. |
| 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 | 27/06/2018 |
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