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Fundamental Mathematical Structures

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

Read about the Master Programme and find the Study Regulations at ruc.dk

Læs mere om uddannelsen og find din studieordning på ruc.dk

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 (inm-studieadministration@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

  • present concrete mathematical structures in the field of set theory, topology, analysis and algebra

  • formulate proofs of common features and differences between such structures

  • exercise mathematical reasoning in relation to the subject

  • compare and differentiate between different types of mathematical arguments and proofs

  • critically and independently judge the validity of a mathematical proof

Form of examination

Individual oral exam based on a portfolio.

The character limit of the portfolio is 1,200-120,000 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: 7-point grading scale.
Moderation: Internal co-assessor
Form of Re-examination
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 am-le 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 hand-in times decided by the course professor.

Handing-in of portfolio elements for commenting is highly advised, but is not obligatory.

The assessment criteria for the written part of the exam

  • present concrete mathematical structures in the field of set theory, topology, analysis and algebra

  • formulate proofs of common features and differences between such structures

  • exercise mathematical reasoning in relation to the subject

  • compare and differentiate between different types of mathematical arguments and proofs

  • critically and independently judge the validity of a mathematical proof

The assessment of the oral exam is based on the student’s ability to meet the criteria mentioned above and their ability to

  • clearly present and communicate the scientific content of the portfolio

  • engage in a scientific dialogue and discussion with the assessor and co assessor

Furthermore, whether the performance meets all formal requirements in regard to both for the written og oral exam

Exam code(s)
Exam code(s) : U60167
Last changed 19/09/2022

lecture list:

Show lessons for Subclass: 1 Find calendar (1) PDF for print (1)

Monday 06-02-2023 10:15 - 06-02-2023 12:00 in week 06
Fundamental Mathematical Structures (MathBio)

Friday 10-02-2023 10:15 - 10-02-2023 14:00 in week 06
Fundamental Mathematical Structures (MathBio)

Monday 13-02-2023 10:15 - 13-02-2023 12:00 in week 07
Fundamental Mathematical Structures (MathBio)

Friday 17-02-2023 10:15 - 17-02-2023 14:00 in week 07
Fundamental Mathematical Structures (MathBio)

Monday 20-02-2023 10:15 - 20-02-2023 12:00 in week 08
Fundamental Mathematical Structures (MathBio)

Friday 24-02-2023 10:15 - 24-02-2023 14:00 in week 08
Fundamental Mathematical Structures (MathBio)

Monday 27-02-2023 10:15 - 27-02-2023 12:00 in week 09
Fundamental Mathematical Structures (MathBio)

Friday 03-03-2023 10:15 - 03-03-2023 14:00 in week 09
Fundamental Mathematical Structures (MathBio)

Monday 06-03-2023 10:15 - 06-03-2023 12:00 in week 10
Fundamental Mathematical Structures (MathBio)

Friday 10-03-2023 10:15 - 10-03-2023 14:00 in week 10
Fundamental Mathematical Structures (MathBio)

Monday 13-03-2023 10:15 - 13-03-2023 12:00 in week 11
Fundamental Mathematical Structures (MathBio)

Friday 17-03-2023 10:15 - 17-03-2023 14:00 in week 11
Fundamental Mathematical Structures (MathBio)

Monday 20-03-2023 10:15 - 20-03-2023 12:00 in week 12
Fundamental Mathematical Structures (MathBio)

Friday 24-03-2023 10:15 - 24-03-2023 14:00 in week 12
Fundamental Mathematical Structures (MathBio)

Monday 27-03-2023 10:15 - 27-03-2023 12:00 in week 13
Fundamental Mathematical Structures (MathBio)

Friday 31-03-2023 10:15 - 31-03-2023 14:00 in week 13
Fundamental Mathematical Structures (MathBio)

Monday 03-04-2023 10:15 - 03-04-2023 12:00 in week 14
Fundamental Mathematical Structures (MathBio)

Wednesday 12-04-2023 08:15 - 12-04-2023 12:00 in week 15
Fundamental Mathematical Structures (MathBio)

Friday 14-04-2023 12:15 - 14-04-2023 14:00 in week 15
Fundamental Mathematical Structures (MathBio)

Wednesday 19-04-2023 08:15 - 19-04-2023 12:00 in week 16
Fundamental Mathematical Structures (MathBio)

Friday 21-04-2023 12:15 - 21-04-2023 14:00 in week 16
Fundamental Mathematical Structures (MathBio)

Wednesday 26-04-2023 08:15 - 26-04-2023 12:00 in week 17
Fundamental Mathematical Structures (MathBio)

Friday 28-04-2023 12:15 - 28-04-2023 14:00 in week 17
Fundamental Mathematical Structures (MathBio)

Wednesday 03-05-2023 08:15 - 03-05-2023 12:00 in week 18
Fundamental Mathematical Structures (MathBio)

Wednesday 10-05-2023 08:15 - 10-05-2023 12:00 in week 19
Fundamental Mathematical Structures (MathBio)

Friday 12-05-2023 12:15 - 12-05-2023 14:00 in week 19
Fundamental Mathematical Structures (MathBio)

Wednesday 17-05-2023 08:15 - 17-05-2023 12:00 in week 20
Fundamental Mathematical Structures (MathBio)

Friday 19-05-2023 12:15 - 19-05-2023 14:00 in week 20
Fundamental Mathematical Structures (MathBio)

Wednesday 24-05-2023 08:15 - 24-05-2023 12:00 in week 21
Fundamental Mathematical Structures (MathBio)

Friday 26-05-2023 12:15 - 26-05-2023 14:00 in week 21
Fundamental Mathematical Structures (MathBio)

Wednesday 14-06-2023 10:00 - 14-06-2023 10:00 in week 24
Fundamental Mathematical Structures - Hand-in of portfolio (MathBio)

Monday 19-06-2023 08:15 - 19-06-2023 16:00 in week 25
Fundamental Mathematical Structures - Exam (MathBio)

Friday 30-06-2023 10:00 - 30-06-2023 10:00 in week 26
Fundamental Mathematical Structures - Hand-in of portfolio (reexam) (MathBio)

Wednesday 09-08-2023 08:15 - 09-08-2023 16:00 in week 32
Fundamental Mathematical Structures - Reexam (MathBio)