Introduction to Discrete Mathematics and Number Theory
Course code
MLM7073.DT
old course code
Course title in Estonian
Diskreetse matemaatika ja arvuteooria algkursus
Course title in English
Introduction to Discrete Mathematics and Number Theory
ECTS credits
6.0
Assessment form
assessment
lecturer of 2026/2027 Autumn semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
lecturer of 2026/2027 Spring semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
Course aims
The aim of the subject is to provide basic knowledge of logic and bulk theory, classical elementary number theory and some of the most important areas of discrete mathematics and number theory for applications. This is a very necessary part of mathematics teacher education.
Brief description of the course
Elements of logic, laws of logic. Predicates and quantifiers. Proof methods, mathematical induction. Sets, operations with sets. Images, relations and their properties. Cardinality of set, countable and non-countable sets. Division, its main properties. The prime numbers and the basic theorem of arithmetic. GCD and Euclidean algorithm, LCM. Numbertheoretical functions: number and sum of divisors of a natural number, function of a integer part. Positional number systems.
Learning outcomes in the course
Upon completing the course the student:
- formally represents and applies the basic laws of logic, predicates, quantifiers, and negation in propositional and predicate logic;
- applies formal proof methods, including mathematical induction;
- performs operations on sets, explaining and applying basic properties, relations, and types of sets;
- explains fundamental concepts related to divisibility (divisibility, greatest common divisor, least common multiple, prime numbers), proves their properties, and solves related problems, including using the Euclidean algorithm and the Sieve of Eratosthenes;
- proves and applies properties of key number-theoretic functions (including the number and sum of divisors of a natural number) when computing function values;
- represents natural numbers in positional numeral systems with arbitrary bases and performs related operations.
- formally represents and applies the basic laws of logic, predicates, quantifiers, and negation in propositional and predicate logic;
- applies formal proof methods, including mathematical induction;
- performs operations on sets, explaining and applying basic properties, relations, and types of sets;
- explains fundamental concepts related to divisibility (divisibility, greatest common divisor, least common multiple, prime numbers), proves their properties, and solves related problems, including using the Euclidean algorithm and the Sieve of Eratosthenes;
- proves and applies properties of key number-theoretic functions (including the number and sum of divisors of a natural number) when computing function values;
- represents natural numbers in positional numeral systems with arbitrary bases and performs related operations.
Teacher
Tatjana Tamberg
Study programmes containing that course