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Fundamental Mathematical Structures

Semester
F2019
Subject
Mathematics / Mathematical Physical Modelling / Mathematical Computer Modelling
Activitytype
master course
Teaching language
English
Registration

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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.

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.
  • Knowledge of the construction and formalisation of such structures.

Skills

  • Skills to recognise fundamental mathematical structures.
  • Skills to know and use symbols and other representations in accordance with the given formalism.
  • Skills to read, understand and reproduce 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 calculation exercises with brief student presentations and discussions of the material. 3-7 small assignments are submitted either individually or in groups, for feedback.

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 70 hours (40 classes of 1h45m) are 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 may relate 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.

The responsible course lecturer
Carsten Lunde Petersen (lunde@ruc.dk)
Teacher
Carsten Lunde Petersen (lunde@ruc.dk)
Eva Uhre (euhre@ruc.dk)
Administration of exams
INM Studieadministration (inm-studieadministration@ruc.dk)
STADS stamdata
Kandidatkursus
Belastning : 10 ECTS Aktivitetskode : U40275 / U40467
Prøveform : Mundtlig (ua) Bedømmelse : 7-trinsskala Censur : Intern censur
Last changed 21/12/2018

lecture list:

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

Tuesday 05-02-2019 13:15 - 05-02-2019 17:00 in week 06
Mat: Fundamental Mathematical Structures - Lecture 1

Friday 08-02-2019 10:15 - 08-02-2019 12:00 in week 06
Mat: Fundamental Mathematical Structures - Lecture 2

Tuesday 12-02-2019 13:15 - 12-02-2019 17:00 in week 07
Mat: Fundamental Mathematical Structures - Lecture 3

Friday 15-02-2019 10:15 - 15-02-2019 12:00 in week 07
Mat: Fundamental Mathematical Structures - Lecture 4

Tuesday 19-02-2019 13:15 - 19-02-2019 17:00 in week 08
Mat: Fundamental Mathematical Structures - Lecture 5

Friday 22-02-2019 10:15 - 22-02-2019 12:00 in week 08
Mat: Fundamental Mathematical Structures - Lecture 6

Tuesday 26-02-2019 13:15 - 26-02-2019 17:00 in week 09
Mat: Fundamental Mathematical Structures - Lecture 7

Friday 01-03-2019 10:15 - 01-03-2019 12:00 in week 09
Mat: Fundamental Mathematical Structures - Lecture 8

Tuesday 05-03-2019 13:15 - 05-03-2019 17:00 in week 10
Mat: Fundamental Mathematical Structures - Lecture 9

Friday 08-03-2019 10:15 - 08-03-2019 12:00 in week 10
Mat: Fundamental Mathematical Structures - Lecture 10

Tuesday 12-03-2019 13:15 - 12-03-2019 17:00 in week 11
Mat: Fundamental Mathematical Structures - Lecture 11

Friday 15-03-2019 10:15 - 15-03-2019 12:00 in week 11
Mat: Fundamental Mathematical Structures - Lecture 12

Tuesday 19-03-2019 13:15 - 19-03-2019 17:00 in week 12
Mat: Fundamental Mathematical Structures - Lecture 13

Friday 22-03-2019 10:15 - 22-03-2019 12:00 in week 12
Mat: Fundamental Mathematical Structures - Lecture 14

Tuesday 26-02-2019 13:15 - 26-02-2019 17:00 in week 09
Mat: Fundamental Mathematical Structures - Lecture 15

Friday 29-03-2019 10:15 - 29-03-2019 12:00 in week 13
Mat: Fundamental Mathematical Structures - Lecture 16

Tuesday 02-04-2019 13:15 - 02-04-2019 17:00 in week 14
Mat: Fundamental Mathematical Structures - Lecture 17

Friday 05-04-2019 10:15 - 05-04-2019 12:00 in week 14
Mat: Fundamental Mathematical Structures - Lecture 18

Tuesday 09-04-2019 13:15 - 09-04-2019 17:00 in week 15
Mat: Fundamental Mathematical Structures - Lecture 19

Friday 12-04-2019 10:15 - 12-04-2019 12:00 in week 15
Mat: Fundamental Mathematical Structures - Lecture 20

Tuesday 16-04-2019 13:15 - 16-04-2019 17:00 in week 16
Mat: Fundamental Mathematical Structures - Lecture 21

Tuesday 23-04-2019 13:15 - 23-04-2019 17:00 in week 17
Mat: Fundamental Mathematical Structures - Lecture 22

Friday 26-04-2019 10:15 - 26-04-2019 12:00 in week 17
Mat: Fundamental Mathematical Structures - Lecture 23

Tuesday 30-04-2019 13:15 - 30-04-2019 17:00 in week 18
Mat: Fundamental Mathematical Structures - Lecture 24

Friday 03-05-2019 10:15 - 03-05-2019 12:00 in week 18
Mat: Fundamental Mathematical Structures - Lecture 25

Tuesday 07-05-2019 13:15 - 07-05-2019 17:00 in week 19
Mat: Fundamental Mathematical Structures - Lecture 26

Friday 10-05-2019 10:15 - 10-05-2019 12:00 in week 19
Mat: Fundamental Mathematical Structures - Lecture 27

Tuesday 14-05-2019 13:15 - 14-05-2019 17:00 in week 20
Mat: Fundamental Mathematical Structures - Lecture 28

Tuesday 21-05-2019 13:15 - 21-05-2019 17:00 in week 21
Mat: Fundamental Mathematical Structures - Lecture 29

Friday 24-05-2019 10:15 - 24-05-2019 12:00 in week 21
Mat: Fundamental Mathematical Structures - Lecture 30

Friday 31-05-2019 10:15 - 31-05-2019 12:00 in week 22
Mat: Fundamental Mathematical Structures - Lecture 31

Friday 14-06-2019 08:00 - 14-06-2019 14:00 in week 24
Mat: Fundamental Mathematical Structures - Examination

Monday 19-08-2019 08:00 - 19-08-2019 17:00 in week 34
Mat: Fundamental Mathematical Structures - Reexamination