Introduction to Discrete Mathematics and Number Theory
Course code
MLM7093.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
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 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:
- knows the of propositional and predicate calculus; is able to write substantive statements in formal formulas and deny them;
- knows operations on sets, their basic properties and relations, including the ability to define and apply them;
- knows the basic concepts related to divisibility (divisibility, GCD, LCM, prime number), knows their properties and can prove them; can use Euclidean algorithm and sieve of Eratosthenes;
- knows the basic numbertheoretical functions, is able to prove and apply their properties and is able to calculate values;
- can represent natural numbers in a positional number system on any basis, perform operations.
- knows the of propositional and predicate calculus; is able to write substantive statements in formal formulas and deny them;
- knows operations on sets, their basic properties and relations, including the ability to define and apply them;
- knows the basic concepts related to divisibility (divisibility, GCD, LCM, prime number), knows their properties and can prove them; can use Euclidean algorithm and sieve of Eratosthenes;
- knows the basic numbertheoretical functions, is able to prove and apply their properties and is able to calculate values;
- can represent natural numbers in a positional number system on any basis, perform operations.
Teacher
Tatjana Tamberg
Study programmes containing that course