Math108
Combinatorics & Probability
Faculty
Andrey Gavrilyuk
Team Leader of the HSE Team
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
Combinatorics and Probability (C&P) have a reputation of being the most practical and grounded subjects of mathematics, and indeed, they are! Combinatorics develops a math foundation for dealing with almost any sort of a situation where a decision might be made. Probability absorbs these methods for dealing with uncertainty and making effective forecasts.
Along with that, the disciplines of Combinatorics and Probability are considered to be the toughest to study because of their fuzziness. That is why this course is focused on the most basic concepts of C&P in relation to mathematical logic and practices of problem solving.
Learning highlights
- The main goal of the course is to establish a solid understanding of the basic principles of Combinatorics and Probability valid for further broadening and specialization for applications.
- The objectives are to get familiar with areas of model formalization, enumerative combinatorics, basic combinatorial methods and structures, basic notions of probability, conditional probabilities, probability distribution, standard probabilistic characteristics, and probabilistic estimations.
Course outline
15 classes
Session 1
Modeling the situation, object-oriented approach in mathematics.
Session 2
Configuration space.
Session 3
Enumeration. Set theory axioms. Mathematical induction.
Session 4
Addition principle, recurrent sequences.
Session 5
Double counting.
Session 6
Graph theory.
Session 7
Processes, half invariant.
Session 8
Midterm.
Session 9
Discrete and geometrical probability. Probability distribution.
Session 10
Conditional probabilities, Bayes’ formula.
Session 11
Random values, independency.
Session 12
Mathematical expectation and other characteristics.
Session 13
Conditional math expectation, limit theorems
Session 14
Recap, Q&A, problem solving.
Session 15
Final test.
Prerequisites
Precalculus, integration from Calculus 1 and Calculus 2.
Methodology
The course is practice oriented, each class will be supplied with a list of relevant problems to solve in class, discussions and further completion as homework. Each topic will be accompanied with theoretical blocks, discussions and personal or group in-class solution presentation sessions. The remaining part of a day’s task becomes a task for self-preparation. Mini-group assignments will be implemented.
Grading
Awards
- Winner of the 46th International Mathematical Olympiad (IMO),Merida, Mexico
Teacher, trainer, scholar and entrepreneur in education with almost 20 years of experience in 'big math'.
Taught the full range of students from 10 to 65 years old, from having zero background in math to the winners of respectful international competitions. Made his PhD thesis in collaboration in Russia, Canada and Switzerland and came back to Russia to launch his courses on mathematics for adults (after grad people).
See full profileApply for this course
Combinatorics & Probability
by Andrey Gavrilyuk
Total hours
45 Hours
Dates
Mar 13 - Mar 31, 2023
Fee for single course
€1500
Fee for degree students
€750
How to secure your spot
Complete the form below to kickstart your application
Schedule your Harbour.Space interview
If successful, get ready to join us on campus
FAQ
Will I receive a certificate after completion?
Yes. Upon completion of the course, you will receive a certificate signed by the director of the program your course belonged to.
Do I need a visa?
This depends on your case. Please check with the Spanish or Thai consulate in your country of residence about visa requirements. We will do our part to provide you with the necessary documents, such as the Certificate of Enrollment.
Can I get a discount?
Yes. The easiest way to enroll in a course at a discounted price is to register for multiple courses. Registering for multiple courses will reduce the cost per individual course. Please ask the Admissions Office for more information about the other kinds of discounts we offer and what you can do to receive one.