Math105BKK
Combinatorics & Graphs
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 Graphs (C&G) is both deeply practical and non-trivially theoretical subject of a big demand nowadays because of huge development of programming (both algorithmical and data-analyzing directions). Combinatorics develops a math foundation for dealing with a huge variety of data structures, establishing computational methods in their study. Graph theory helps in organizing the data and suggests some unique adjustable techniques.
Learning highlights
- The main goal of the course is to establish a solid understanding of the basic principles of Combinatorics and Graphs 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 structures of graph theory, powerful methods of optimization and structure design as processes and flows on graphs.
Course outline
15 classes
Session 1
Context. Modeling the situation, object-oriented approach in mathematics.
Session 2
Context. Modeling the situation, object-oriented approach in mathematics.
Session 3
Enumeration. Axiomatic approach.
Session 4
Axiomatic systems in math. Inference rule.
Session 5
Double counting.
Session 6
Addition principle, recurrent sequences.
Session 7
Processes, half invariant.
Session 8
Midterm.
Session 9
Basic structures on graphs: paths, cycles, traversals, trees, cliques, flows.
Session 10
Spanning trees and colorings.
Session 11
Double counting and tournaments.
Session 12
Processes on graphs and flows.
Session 13
Computational techniques. Problem solving.
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 for solving in class, discussions and further completion as a home task. Each topic will be accompanied with theoretical blocks, discussions and personal or group in-class solution presentation sessions. The remaining unpresented part of a day’s task becomes a task for self-preparation. One home test is planned for completing at home by the start of the second week. Most of the classes will start with a ‘Quiz of the day’ with an easy question on the previous material of the course.
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 & Graphs
by Andrey Gavrilyuk
Total hours
45 Hours
Dates
Nov 11 - Nov 29, 2024
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.