Overview of Algebra and Geometry

Course code

MLM7408.DT

old course code

Course title in Estonian

Ülevaade algebrast ja geomeetriast

Course title in English

Overview of Algebra and Geometry

ECTS credits

5.0

Assessment form

Examination

lecturer of 2021/2022 Spring semester

lecturer not assigned

lecturer of 2022/2023 Autumn semester

lecturer not assigned

Course aims

The goal of the subject is:

To offer to the students an overview of terms and notions of algebra and geometry, which are useful for those who choose to teach mathematics at the secondary school level.

To offer to the students an overview of terms and notions of algebra and geometry, which are useful for those who choose to teach mathematics at the secondary school level.

Brief description of the course

Determinants, matrices and systems of linear equations. Complex numbers and polynomials. Algebraic structures. Equivalence relation, ideals, substructures, quotient structures. Linear space and its basis. Coordinates of an element in a linear space and coordinate transformations in the case of the change of basis. Linear transformations of linear spaces.

Vectors and operations with vectors. Linear space of free vectors, coordinates of a point and coordinate transformations. Equations of lines and planes, their different forms. Quadric curves and surfaces. Implicit and parametric equations of curves. Length and curvature of a curve. Measure and area. Axiomatic approach to geometry. Examples of different geometries.

Participation in the auditorial lectures is a prerequisite of the learning process.

Vectors and operations with vectors. Linear space of free vectors, coordinates of a point and coordinate transformations. Equations of lines and planes, their different forms. Quadric curves and surfaces. Implicit and parametric equations of curves. Length and curvature of a curve. Measure and area. Axiomatic approach to geometry. Examples of different geometries.

Participation in the auditorial lectures is a prerequisite of the learning process.

Learning outcomes in the course

Upon completing the course the student:

- knows main notions of algebra and geometry;

- is familiar with the main poperties, relations and theorems of this course;

- is able to solve the standard exercises of algebra and geometry.

- knows main notions of algebra and geometry;

- is familiar with the main poperties, relations and theorems of this course;

- is able to solve the standard exercises of algebra and geometry.

Teacher

Alar Leibak