Course title in Estonian
Course title in English
approximate amount of contact lessons
lecturer of 2019/2020 Spring semester
Alar Leibak (eesti keel) tavaline kursus
lecturer of 2020/2021 Autumn 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: Concept of an algebraic operation. Algebraic structures with one binary algebraic operation (groupoid, semigroup, monoid, group, Abelian group). Algebraic structures with two binary algebraic operations (ring, field, algebra). Substructures (at least subspace of the linear space). Finding roots of complex numbers. Roots of unity. Solving the cubic and quartic equations. Concept of a polynomial. Roots and factors of polynomials. Bézout’s theorem. Greatest common divisors of polynomials and the Euclidean algorithm. Interpolation problem (interpolation polynomials of Newton and Lagrange). 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.
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
Kangro, G. Kõrgem algebra. Tallinn: 1962;
Kilp, M. 2005 Algebra I. Tartu: TÜ.