Multidimensional Geometry
Course code
MLM6314.DT
old course code
MLM6314
Course title in Estonian
Mitmemõõtmeline geomeetria
Course title in English
Multidimensional Geometry
ECTS credits
6.0
Assessment form
Examination
lecturer of 2024/2025 Autumn semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
lecturer of 2024/2025 Spring semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
Course aims
To introduce main terms and theorems of geometry and their applications. To enlarge the knowledge about the geometry. To demonstrante the connections between geometry and ohter branches of Mathematics.
Brief description of the course
n-dimensional (affine) vector spaces, main problems in these spaces. Equations of affine subspaces, their positions with respect to each ohter. Euclidean vector space. Metric matrix. Main problems in Euclidean spaces. Calculation of areas and volumes. Quadrics in affine and Euclidean space. Affine properties of quadrics. Transformations of affine and rectangular coordinate systems. Canonical equations of quadrics. Classification of quadrics in affine and Euclidean spaces. Simplifying the equation of a quadric using eigenvalues. Pseudo-Euclidean plane. Pseudo-Eulidean spaces of dimension 3 or 4. Their interpretation in physics.
Learning outcomes in the course
Upon completing the course the student:
After passing this course the student:
1. knows the notions of affine space, affine subspace, affine transformation and is able to solve exercises on these topics;
2. knows the notions of Eucidean space, the transformation of an Euclidean space, area and volume in Euclidean space andis able to solve exercises on these topics;
3. knows the notions of quadratic form and quadric, is able to simplify their equations and to classify them in affine and Euclidean spaces.
After passing this course the student:
1. knows the notions of affine space, affine subspace, affine transformation and is able to solve exercises on these topics;
2. knows the notions of Eucidean space, the transformation of an Euclidean space, area and volume in Euclidean space andis able to solve exercises on these topics;
3. knows the notions of quadratic form and quadric, is able to simplify their equations and to classify them in affine and Euclidean spaces.
Teacher
prof Mart Abel
Prerequisite course 1
Study programmes containing that course