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 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
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