Foundations of Discrete Mathematics

Course code

MLM6196.DT

old course code

Course title in Estonian

Diskreetse matemaatika elemendid

Course title in English

Foundations of Discrete Mathematics

ECTS credits

6.0

Assessment form

assessment

lecturer of 2023/2024 Spring semester

Tatjana Tamberg (language of instruction:Estonian)

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 provide the fundamentals of set theory, logic and elementary Number Theory. To introduce the methods used in those topics with their applications.

Brief description of the course

Sentential logic. Truth tables. Normal forms of sentences. Predicate calculus and its main formulas. Types of theorems. Necessary and sufficient conditions. Methods of proof. Mathematical induction. Sets, set operations, their properties. Cartesian product of sets. Relations on sets and their properties. Maps. Cardinality of a set. Basic properties of divisibility. Prime numbers and fundamental theorem of arithmetic. GCD and LCM. Number theoretic functions: number-of-divisors function, sum-of-divisors function, integer part (floor) function. Positional numeral systems.

Learning outcomes in the course

Upon completing the course the student:

- knows the operations with sets, their main properties and relations, being able to determine the type of a relation and applying relations;

- knows the main laws of sentential logic and predicate calculus;

- is able to write down the contextual claims using formal symbols and negate the sentences;

- knows main facts about divisibility (divisibility, GCD, LCM, prime number), is able to prove them and apply them for problem solving;

- knows the main number theoretical functions, is able to apply them for problem solving;

- is familiar with positional numeral systems; is able to convert an integer, represented in one base, to another base and to add and multiply numbers in any base.

- knows the operations with sets, their main properties and relations, being able to determine the type of a relation and applying relations;

- knows the main laws of sentential logic and predicate calculus;

- is able to write down the contextual claims using formal symbols and negate the sentences;

- knows main facts about divisibility (divisibility, GCD, LCM, prime number), is able to prove them and apply them for problem solving;

- knows the main number theoretical functions, is able to apply them for problem solving;

- is familiar with positional numeral systems; is able to convert an integer, represented in one base, to another base and to add and multiply numbers in any base.

Teacher

lekt T.Tamberg

Study programmes containing that course