An Overview of Algebra and Number Theory

Course code

MLM7414.DT

old course code

Course title in Estonian

Ülevaade algebrast ja arvuteooriast

Course title in English

An Overview of Algebra and Number Theory

ECTS credits

5.0

Assessment form

assessment

lecturer of 2024/2025 Autumn semester

Alar Leibak (language of instruction:Estonian)

lecturer of 2024/2025 Spring semester

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

Course aims

The idea of this course is to give students an overview of the basics of modern (discrete) mathematics and to demonstrate how to apply them in practice.

Brief description of the course

Fundamentals of propositional logic: truth table, logical operations, logical equivalence, tautology, contradiction, contingent propositions. Definitions in

mathematics. Fundamentals of set theory: axioms, operations with sets, mappings, binary relations (incl. partially ordered sets), cardinality. Basics in number

theory: divisibility, modular arithmetics, fundamental theorem of arithmetics, primes, arithmetical functions. Basics in algebra: algebraic operation and its Cayley table, algebraic systems with one binary operation (quasigroup, semigroup, monoid, group) and two binary operations (ring and field).

mathematics. Fundamentals of set theory: axioms, operations with sets, mappings, binary relations (incl. partially ordered sets), cardinality. Basics in number

theory: divisibility, modular arithmetics, fundamental theorem of arithmetics, primes, arithmetical functions. Basics in algebra: algebraic operation and its Cayley table, algebraic systems with one binary operation (quasigroup, semigroup, monoid, group) and two binary operations (ring and field).

Learning outcomes in the course

Upon completing the course the student:

- is able to define mathematical notions;

- is able to check the logical equivalence of given propositions;

- applies Euclidean algorithm to calculating the greatest common divisor of given two integers;

- is able to construct simple mathematical proofs.

- is able to define mathematical notions;

- is able to check the logical equivalence of given propositions;

- applies Euclidean algorithm to calculating the greatest common divisor of given two integers;

- is able to construct simple mathematical proofs.

Teacher

Alar Leibak

Study programmes containing that course