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MM538: Algebra and linear algebra (10 ECTS)

STADS: 13011601

Level
Bachelor course

Teaching period
The course is offered in the autumn semester.

Teacher responsible
Email: duck@imada.sdu.dk

Timetable
Group Type Day Time Classroom Weeks Comment
Common I Monday 12-14 U30 37-41,44-51
Common I Wednesday 10-12 U157 38,40-41,45,47,50
Common I Wednesday 16-18 U91 44,46,48-49,51
Common I Thursday 08-10 U145 36
Common I Friday 10-12 U17 36
H1 TE Monday 16-18 U130 37-41,44-51
H1 TE Monday 14-18 U143 43
H1 TE Thursday 16-18 U130 44-47,49-51
H1 TE Friday 12-14 U131 48
M1 TE Wednesday 12-14 U157 37-41,43-51
M1 TE Friday 12-14 U14 36
M1 TE Friday 10-12 IMADA Seminarrum 44-45,47-51
M1 TE Friday 10-12 Studerende finder selv plads 46
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Prerequisites:
None

Academic preconditions:
None.

Course introduction
In this course the students learn basic algebraic concepts. These include linearity, which is fundamental in all areas of mathematics and its applications. In addition rings and their basic properties are introduced.

Qualifications
Problem solving, understanding principles of mathematical thinking, argumentation and ability to carry out and understand proofs, ability to handle abstract mathematical concepts, ability to present in written form precise mathematical arguments.

Expected learning outcome
By the end of the course the students are expected to be able to:
  • apply techniques and results from linear algebra  and algebra to solve problems within the syllabus of the course
  • argue for the individual steps in the solutions
  • formulate correct arguments
  • use mathematical terminology
Subject overview
  • Systems of linear equations
  • matrices, determinants
  • vector spaces
  • scalar product and orthogonality
  • linear transformations
  • eigenvectors and eigenvalues
  • diagonalisation
  • Basic number theory
  • polynomials
  • rings and fields
  • homomorphisms and factor rings
  • field extensions
  • algebraic closure
Literature
    Meddeles ved kursets start.


Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
  1. Mandatory assignments, evaluated by internal censorship on a pass/fail basis(5 ECTS). (13011602)
  2. Written exam, evaluated by external examiner by the danish 7 mark scale (5 ECTS). (13011612)
Expected working hours
The teaching method is based on three phase model.
Intro phase: 56 hours
Skills training phase: 73 hours, hereof:
 - Tutorials: 45 hours

Educational activities Study phase: 28 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.