TLÜ ÕIS

Algebra I

Course code

MLM6522.DT

old course code

Course title in Estonian

Algebra I

Course title in English

Algebra I

ECTS credits

4.0

Assessment form

Examination

lecturer of 2023/2024 Spring semester

Alar Leibak (language of instruction:Estonian)

lecturer of 2024/2025 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 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.

Learning outcomes in the course

Upon completing the course the student:
- is familiar with the basic algebraic structures;
- knows the notions connected with polynomials;
- is capable to solve problems connected with polynomials.

Teacher

Alar Leibak

Prerequisite course 1

Linear Algebra (MLM6521.DT)

The course is a prerequisite

Algebra II (MLM6523.DT)

Study programmes containing that course