Course code

MLM6531.DT

old course code

Course title in Estonian

Algebra I

Course title in English

Algebra I

ECTS credits

6.0

Assessment form

Examination

lecturer of 2024/2025 Spring semester

Not opened for teaching. Click the study programme link below to see the nominal division schedule.

lecturer of 2025/2026 Autumn semester

Not opened for teaching. Click the study programme link below to see the nominal division schedule.

Course aims

To provide an overview of matrices, linear spaces, systems of linear equations, complex numbers, cubic and quartic equations and polynomials: their roots, GCD, irreducible polynomials, interpolation.

Brief description of the course

Complex numbers and operations with complex numbers. Algebraic, polar and exponential forms of complex numbers. Solving the cubic and quartic equations. Matrices and operations with matrices. Basic algebraic structures: group, ring, field. Permutations and inversions. Determinants and their properties. Minors. Laplace expansion. Determinant of the product of matrices. Inverse of a matrix. Rank of a matrix. Linear space. Linear independence of the set of vectors. Basis of the linear space. Systems of linear equations: homogeneous system of linear equations and nonhomogeneous system of linear equations. Gaussian elimination method. Cramer’s rule. Polynomials: roots and factors of polynomials, Bézout’s theorem. GCD of polynomials and the Euclidean algorithm, Interpolation problem (interpolation polynomials of Newton and Lagrange).

Learning outcomes in the course

Upon completing the course the student:
- has basic knowledge of linear algebra: matrices, linear spaces, systems of linear equations, polynomials and complex numbers;
- is able to solve problems related to the mentioned topics.

Teacher

Tatjana Tamberg

The course is a prerequisite

Study programmes containing that course

Mathematics, Mathematical Economics and Data Analysis (MLMB/25.DT)
Integrated Natural Sciences (MLLB/25.LT)