Introduction to Algebra
Course code
MLM7094.DT
old course code
Course title in Estonian
Algebra algkursus
Course title in English
Introduction to Algebra
ECTS credits
5.0
Assessment form
assessment
lecturer of 2025/2026 Autumn semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
lecturer of 2025/2026 Spring semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
Course aims
The aim of the course is to broaden the horizons of future school teachers and provide fundamental knowledge of linear algebra and polynomial algebra, along with their applications.
Brief description of the course
Algebraic operation. Ring. Field. Complex numbers and operations with them. Matrices and operations with them. Determinants, their properties, and calculation. Inverse matrix, methods for finding it, and its properties. Vector space. Linear dependence of a set of vectors. Basis of a vector space. Rank. Systems of linear equations. Concept of a polynomial. Roots and factors of a polynomial. Bezout's theorem and Horner's scheme. Greatest common divisors of polynomials and Euclidean algorithm. Interpolation problem. Factorization into irreducible factors. Rational fractions. Vieta's formulas. Fundamental theorem of algebra. Multivariable polynomials, symmetric polynomials
Learning outcomes in the course
Upon completing the course the student:
- will understand algebraic structures, matrices, vector spaces, systems of linear equations, and complex numbers;
- will solve typical problems related to matrices, systems of linear equations, and complex numbers;
- will be familiar with concepts related to polynomials;
- will solve problems related to polynomials.
- will understand algebraic structures, matrices, vector spaces, systems of linear equations, and complex numbers;
- will solve typical problems related to matrices, systems of linear equations, and complex numbers;
- will be familiar with concepts related to polynomials;
- will solve problems related to polynomials.
Teacher
Tatjana Tamberg
Study programmes containing that course