Math114BKK
Combinatorics & Graphs
Faculty
Boris Demeshev
Senior Lecturer at Higher School of Economics
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
This course is an introduction to combinatorial techniques and graph theory concepts. Graph theory is widely used in many computer algorithms, and combinatorics is the art of counting applied across all areas of mathematics. We will also draw on probability theory as a source of inspiration for combinatorial problems.
Learning highlights
To grasp counting methods in combinatorics.
To get familiar with standard graph theory concepts.
To prepare for courses on data structures and algorithms.
Course outline
15 classes
Session 1
Binomial and multinomial coefficients.
Session 2
Double counting and inclusion-exclusion principle.
Session 3
Recurrence equations.
Session 4
Generating functions.
Session 5
Generating function tricks.
Session 6
How to avoid combinatorics?
Session 7
Review, Q&A and more problems!
Session 8
Midterm exam.
Session 9
Basic graph concepts.
Session 10
Trails and paths.
Session 11
Planarity.
Session 12
Graph colorings.
Session 13
Ramsey theory.
Session 14
Review, Q&A and guess what? Problem solving!
Session 15
Final exam.
Prerequisites
Basic calculus and acquaintance with discrete probability.
A little bit of linear algebra will help but is not required.
Methodology
We will focus on problem solving. Students will have a perfect opportunity to solve a lot of problems during classes and at home to experience a joy of a personal discovery. Each class will start with a quiz based on previously studied topics.
Grading
Apply for this course
Combinatorics & Graphs
by Boris Demeshev
Total hours
45 Hours
Dates
Jun 29 - Jul 17, 2026
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.