Algebra II
Course code
MLM6532.DT
old course code
Course title in Estonian
Algebra II
Course title in English
Algebra II
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 get acquainted with the terms connected with linear spaces and linear transformations of linear spaces.
Brief description of the course
The main topics of the course are: Derivative of a polynomial, multiple factors and irreducible factors. Rational fractions. Decomposition of the polynomial into irreducible factors. Irreducibility criteria for polynomials with integral and rational coefficients. Viète’s formulas. Real and complex roots of polynomials. Fundamental theorem of algebra. Polynomials in several variables, symmetric polynomials and the fundamental theorem of symmetric polynomials. Power sums. Resultant and discriminant of polynomials. Elimination problem. Linear transformations and isomorphisms of linear spaces. Matrix similarity. Characteristic polynomial of a matrix. Eigenvectors, eigenvalues and the canonical basis of a linear transformation of linear spaces. Jordan matrix. Matrix of a linear transformation and its Jordan canonical form. Euclidean (linear) space. Orthogonal and symmetric matrices. Orthogonal and symmetric transformations. Linear, bilinear and quadratic functionals. Linear, bilinear and quadratic forms. Canonical form of a quadratic form. Reduction of a quadratic form to its canonical form.
Learning outcomes in the course
Upon completing the course the student:
- is able to decompose polynomials into irreducible factors;
- is familiar with the Basic notions connected with polynomials in several variables;
- is able to solve exercises related to polynomials in several variables;
- is familiar with the basic notions related to linear spaces and their linear transformations;
- is capable to solve exercises related to linear spaces.
- is able to decompose polynomials into irreducible factors;
- is familiar with the Basic notions connected with polynomials in several variables;
- is able to solve exercises related to polynomials in several variables;
- is familiar with the basic notions related to linear spaces and their linear transformations;
- is capable to solve exercises related to linear spaces.
Teacher
Mart Abel
Prerequisite course 1
Study programmes containing that course