AIT 2026 — AI Intensive Summer School
UUUCourse structure
Chapter 3. Elements of combinatorics and probability theory
- §16. Set and its elements
- §16. Set and its elements (Part 1)
- §16. Set and its elements (Part 2)
- Check your competence
- §17. Elements of combinatorics. Arrangements, permutations, combinations
- §17. Elements of combinatorics. Arrangements, permutations, combinations (Part 1)
- §17. Elements of combinatorics. Arrangements, permutations, combinations (Part 2)
- Check your competence
- §18. Random experiment and random event. Probability of an event
- §18. Random experiment and random event. Probability of an event (Part 1)
- §18. Random experiment and random event. Probability of an event (Part 2)
- §18. Random experiment and random event. Probability of an event (Part 3)
- Check your competence
- Home independent work No. 6
- Tasks for knowledge verification for §§16-18
- §19. Operations on events. Axioms of probability theory and their main consequences
- §19. Operations on events. Axioms of probability theory and their main consequences (Part 1)
- §19. Operations on events. Axioms of probability theory and their main consequences (Part 2)
- §19. Operations on events. Axioms of probability theory and their main consequences (Part 3)
- Check your competence
- §20. Independent events. Conditional probability
- §20. Independent events. Conditional probability (Part 1)
- §20. Independent events. Conditional probability (Part 2)
- Check your competence
- §21. Random variable and its mathematical expectation
- §21. Random variable and its mathematical expectation (Part 1)
- Check your competence
- Home independent work No. 7
- Tasks for knowledge assessment for §§ 19-21
- Exercises for reviewing section 3 (§16-§17)
- Exercises for reviewing section 3 (up to §18-§19)
- Exercises for reviewing section 3 (up to §20-§21)
- Ukrainians in the world
Basic information about the course
Expected results upon completion of the course include the formation of the following skills in students:
- understandswhat permutations, arrangements, combinations (without repetitions) are, the classical definition of the concept of probability, what a population and a sample are, the definition of the mean, mode, and median of a sample;
- calculatesthe relative frequency of an event; the number of permutations, arrangements, combinations; the probability of an event, using its definition and combinatorial schemes;
- explainsthe content of average indicators and characteristics of a sample;
- findsnumerical characteristics of the data sample;
- appliesprobabilistic characteristics of surrounding phenomena for decision making.
Necessary skills for course completion
Proficiency in computer and its devices at a basic level, ability to read and write. Knowledge of mathematics at the level of the 11th year of study.