MM528: Mathematical perspectives (5 ECTS)

STADS: 13008601

Level
Bachelor course

Teaching period
The course is offered in the spring semester.

Teacher responsible
Email: jessica@imada.sdu.dk

Additional teachers
achim@imada.sdu.dk
duck@imada.sdu.dk
stephan.brandt@imada.sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Comment:
Ubegrænset deltagerantal. 4. kvartal.

Prerequisites:
None

Academic preconditions:
None

Course introduction
The aim of the course is two-fold. Firstly, the student will learn about the inner structure of mathematics. Modern mathematics employs a formal language using unambiguous symbols. The basis of this way of thinking stems from logic. In addition mathematics is considered to be built from axioms. The course provides an introduction to logic and gives examples of the axiomatic structure of mathematics – both within algebra and set theory. 

The second purpose is to give an introduction into the different disciplines of mathematics – and their interconnections. In addition to the division between discrete and continuous mathematics that the students meet in Mathematical Methods, there is a distinction between pure and applied mathematics. Furthermore within mathematics are a number of different disciplines, such as algebra, topology, analysis and geometry. The course gives a first description of some of these parts of mathematics.
 

Expected learning outcome
At the end of the course, the student is expected to:
• Formalize statements in a logically correct way.
• In a logically correct way solve problems involving sets, relations, functions and numbers within the syllabus of the course.
• Apply methods of proofs such as direct proof, indirect proof and proof by induction to prove statements within the syllabus of the course.

Subject overview
Subjects covered:
• Propositional logic and first order languages.
• Set theory and relations.
• Properties of the integers, real and complex numbers.
In addition the course will treat elementary subjects from different mathematical disciplines, such as algebra, analysis, geometry and applied mathematics.

Literature

Meddeles ved kursets start.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
a. Project assignment. Danish7 mark scale, external examiner. (5 ECTS)

 

Expected working hours
The teaching method is based on three phase model.
Intro phase: 21 hours
Skills training phase: 21 hours, hereof:
 - Tutorials: 21 hours

Educational activities Study phase: 8 hours

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.