Title 
Fundamental Mathematical Structures

Semester 
F2023

Master programme in 
Mathematics * / Mathematical Physical Modelling * / Mathematical Computer Modelling * / Mathematical Bioscience / Physics and Scientific Modelling

Type of activity 
Course 
Teaching language 
English

Study regulation  
REGISTRATION AND STUDY ADMINISTRATIVE  
Registration 
Sign up for study activities at stads selvbetjening within the announced registration period, as you can see on the Studyadministration homepage. When signing up for study activities, please be aware of potential conflicts between study activities or exam dates. The planning of 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. 
Number of participants 

ECTS 
10

Responsible for the activity 
Carsten Lunde Petersen (lunde@ruc.dk)

Head of study 
Jesper Schmidt Hansen (jschmidt@ruc.dk)

Teachers 

Study administration 
INM Studieadministration (inmstudieadministration@ruc.dk)

Exam code(s) 
U60167

ACADEMIC CONTENT  
Overall objective 
The overall objective of the course is to give the student an understanding of mathematical structures and proficiency in formulating mathematical logic, reasoning, and argumentation. 
Detailed description of content 
The course aims at giving the students an understanding of the axiomatic deductive structure of mathematics by introducing the students to classical fundamental examples of axiomatic deductive structures. Examples are propositional logic, set theory, abstract algebra, general topology, Real analysis, Probability theory, Euclidean geometry, Differential geometry and more. The concrete incarnation of the course will discuss a number of selected such fundamental structures. 
Course material and Reading list 
The course will introduce to and enlarge on a number of selected fundamental structurese.g. such as presented in the lecture notes by prof. Mogens Niss, which are freely available upon request 
Overall plan and expected work effort 
The course will be taught as a mixture of lectures, discussions and problem solving. The course load is 10 ECTS corresponding to approx. 270 hours of work. Of these approximately 84 hours will be classes, 80 hours should be preparations for classes, another 80 hours post processing of classes. The remaining time will be dedicated to repairing the portfolio elements for the final exam and the final exam. 
Format 

Evaluation and feedback 
The course includes formative evaluation based on dialogue between the students and the teacher(s). Students are expected to provide constructive critique, feedback and viewpoints during the course if it is needed for the course to have better quality. Every other year at the end of the course, there will also be an evaluation through a questionnaire in SurveyXact. The Study Board will handle all evaluations along with any comments from the course responsible teacher. Furthermore, students can, in accordance with RUCs ‘feel free to state your views’ strategy through their representatives at the study board, send evaluations, comments or insights form the course to the study board during or after the course. 
Programme 
The course will cover approximately 4 fundamental structures across approximately equal amounts of classes. 
ASSESSMENT  
Overall learning outcomes 
After the course the student will be able to

Form of examination 
Individual oral exam based on a portfolio. The character limit of the portfolio is 1,200120,000 characters, including spaces. Examples of written products are exercise responses, talking points for presentations, written feedback, reflections, written assignments. The preparation of the products may be subject to time limits. The character limits include the cover, table of contents, bibliography, figures and other illustrations, but exclude any appendices. Time allowed for exam including time used for assessment: 30 minutes. The assessment is an assessment of the oral examination. The written product(s) is not part of the assessment. Permitted support and preparation materials for the oral exam: All. Assessment: 7point grading scale. Moderation: Internal coassessor 
Form of Reexamination 
Samme som ordinær eksamen

Type of examination in special cases 

Examination and assessment criteria 
The exam is a 30 min oral exam including grade decision. At the exam the student draws a portfolio element to present without further preparation. The presentation should be timed to 10 min. In order to leave amle time for further questions across the entire curse curriculum. The students are offered to have their portfolio elements commented prior to the exam by the course professor after handin times decided by the course professor. Handingin of portfolio elements for commenting is highly advised, but is not obligatory. The assessment criteria for the written part of the exam
The assessment of the oral exam is based on the student’s ability to meet the criteria mentioned above and their ability to
Furthermore, whether the performance meets all formal requirements in regard to both for the written og oral exam 
Exam code(s)  
Last changed  19/09/2022 