TLÜ ÕIS

Algebra I

Course code

MLM6203.DT

old course code

MLM6203

Course title in Estonian

Algebra I

Course title in English

Algebra I

ECTS credits

5.0

Assessment form

Examination

lecturer of 2023/2024 Spring semester

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

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: 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.

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

prof Mart Abel

Prerequisite course 1

Algebra and Geometry (MLM6402.DT)

The course is a prerequisite

Algebra II (MLM6233.DT)
Algebra II (MLM6205.DT)
Seminar in Algebra/ Geometry and its Applications (MLM6249.DT)
Seminar in Algebra/ Geometry and its Applications I (MLM6251.DT)
Work Placement in Mathematics I (MLM6404.DT)

Study programmes containing that course