COMBINATORICS AND GRAPHS
SERGEY
NIKOLENKOWe offer innovative university degrees taught in English by industry leaders from around the world, aimed at giving our students meaningful and creatively satisfying top-level professional futures. We think the future is bright if you make it so.
Combinatorics and graph theory lay at the heart of discrete mathematics and computer science. In the course, we begin with a brief review of the fundamentals of combinatorics---counting, permutations, binomial coefficients, and the pigeonhole principle---and then devote most of the course to the fundamentals of graph theory. We cover the most common definitions and ideas of graph theory, proving important theorems and introducing important algorithms, but mostly aiming to simply establish the common language of discrete mathematics and computer science.
Sergey Nikolenko is a computer scientist with wide experience in machine learning and data analysis, algorithms design and analysis, theoretical computer science, and algebra. He graduated from the St. Petersburg State University in 2005, majoring in algebra (Chevalley groups), and earned his Ph.D. at the Steklov Mathematical Institute at St. Petersburg in 2009 in theoretical computer science (circuit complexity and theoretical cryptography). Since then, Dr. Nikolenko has been interested in machine learning and probabilistic modeling, producing theoretical results and working on practical projects for the industry. He is currently employed at the Steklov Mathematical Institute at St. Petersburg and Higher School of Economics at St. Petersburg. Dr. Nikolenko has more than 100 publications, including top computer science journals and conferences and several books.
• Machine learning: probabilistic graphical models, recommender systems, topic modeling
• Algorithms for networking: competitive analysis, FIB optimization
• Bioinformatics: processing mass-spectrometry data, genome assembly
• Proof theory, automated reasoning, computational complexity, circuit complexity
• Algebra (Chevalley groups), algebraic geometry (motives)
• Understand the basic tools of combinatorics for counting
• Know and understand the basic notions of graph theory
• Be able to prove the basic theorems of graph theory taught in the course
• Know and be able to apply basic algorithms of graph theory taught in the course
SKILLS:
- Machine learning
- Algorithms for networking
- Bioinformatics
- Mathematical Modeling
- Python
ABOUT SERGEY
HARBOUR.SPACE WHAT YOU WILL LEARN
DATE: 8 - 26 Jan, 2018
DURATION: 3 Weeks
LECTURES: 3 Hours per day
LANGUAGE: English
LOCATION: Barcelona, Harbour.Space Campus
COURSE TYPE: Offline
HARBOUR.SPACE UNIVERSITY
RESERVE MY SPOT
@snikolenko
DATE: 8 - 26 Jan, 2018
DURATION: 3 Weeks
LECTURES: 3 Hours per day
LANGUAGE: English
LOCATION: Barcelona, Harbour.Space Campus
COURSE TYPE: Offline
All rights reserved. 2018
COURSE OUTLINESession 1
Counting
The four principles of counting: addition, multiplication, subtraction, and division. Examples.
Session 4
Graphs: the basics
Definitions: graph, vertex, edge, loop, degree, path, cycle, directed and undirected graphs, connected and disconnected graphs, adjacency matrices.
Session 3
The pigeonhole principle
The pigeonhole principle. Sample applications. The Chinese remainder theorem.
Session 2
Permutations and combinations
Permutations, number of different permutations. Subsets, number of different subsets. Binomial coefficients. Sum of binomial coefficients.
COMBINATORICS AND GRAPHS
BIBLIOGRAPHY
Combinatorics and graph theory lay at the heart of discrete mathematics and computer science. In the course, we begin with a brief review of the fundamentals of combinatorics---counting, permutations, binomial coefficients, and the pigeonhole principle---and then devote most of the course to the fundamentals of graph theory. We cover the most common definitions and ideas of graph theory, proving important theorems and introducing important algorithms, but mostly aiming to simply establish the common language of discrete mathematics and computer science.
Combinatorics and graph theory lay at the heart of discrete mathematics and computer science. In the course, we begin with a brief
review of the fundamentals
of combinatorics---counting, permutations, binomial coefficients, and the pigeonhole principle---and then devote most of the course to the fundamentals of graph theory. We cover the most common definitions and ideas of graph theory, proving important theorems and introducing important algorithms, but mostly aiming to simply establish the common language of discrete mathematics and computer science.