Course title in Estonian
Course title in English
approximate amount of contact lessons
lecturer of 2020/2021 Autumn semester
õppejõud on määramata
lecturer of 2020/2021 Spring semester
lecturer not assigned
To get acquainted with the basic terms in algebra, which are necessary part of the higher education in mathematics.
Brief description of the course
The topics of this course are: Basic algebraic structures. Complex numbers, operations with them in algebraic and trigonometric form. Roots of unity. The concept of polynomials. Polynomial roots and linear factors. Theorem of Bezout. Great common divisors of polynomials and Euclidean algorithm. Interpolation problem. Derivatives of polynomials, multiple roots and irreducible factors. Rational functions, decomposition into partial fractions. Criteria for irreducibility of a polynomial over Z or Q. Viete formulas. Roots of polynomials over R and C. Fundamental theorem of algebra. Polynomials in several variables, symmetrical polynomials with fundamental theorem. Power series. Resultant and discriminant of two polynomials, elimination problem.
Work with the lecture materials and individual work solving exercises.
Learning outcomes in the course
After passing the course, the student is familiar with the basic algebraic structures, knows the notions connected with polynomials and is capable to solve problems connected with polynomials.
The examination grade (maximum 100 points) is based on the total number of points gained from assignments completed during the semester (maximum 50 points), including 2 in-class tests, 2 individual home tests and the examination (maximum 50 points).
The course is a prerequisite
Vinberg, E. I. Algebra mnogotschlenov. Moskva. 1978