Linear Algebra and Geometry I
Syllabus, Bachelor's level, 1MA025
- Code
- 1MA025
- Education cycle
- First cycle
- Main field(s) of study and in-depth level
- Mathematics G1F
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 19 March 2007
- Responsible department
- Department of Mathematics
Entry requirements
Basic Course in Mathematics
Learning outcomes
In order to pass the course (grade 3) the student should be able to
Higher grades, 4 or 5, require a higher level of proficiency. The student should be able to solve problems of greater complexity, i.e. problems requiring a combination of ideas and methods for their solution, and be able to give a more detailed account of the proofs of important theorems and by examples and counter-examples be able to motivate the scope of various results. Requirements concerning the student's ability to present mathematical arguments and reasoning are greater.
Content
Linear systems of equations: Gaussian elimination, rank, solvability. Matrices: matrix algebra and matrix inverse. Determinants of order two and three. Vector algebra, linear dependence and independence, bases, coordinates, scalar product and vector product, equations for lines and planes, distance, area and volume. Description of rotations, reflections and orthogonal projections in R2 and R3. The linear space Rn and m×n matrices as linear transformations from Rn to Rm. The standard scalar product on Rn and the Cauchy-Schwarz inequality.
Instruction
Lectures and problem solving sessions.
Assessment
Written examination at the end of the course. Moreover, compulsory assignments may be given during the course.
Reading list
- Reading list valid from Autumn 2022
- Reading list valid from Spring 2022
- Reading list valid from Autumn 2021
- Reading list valid from Spring 2020
- Reading list valid from Autumn 2019
- Reading list valid from Spring 2013
- Reading list valid from Autumn 2012, version 2
- Reading list valid from Autumn 2012, version 1
- Reading list valid from Spring 2012
- Reading list valid from Autumn 2007