SUBMIT
COMBINATORICS 
AND GRAPHS
SERGEY
NIKOLENKO

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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
RESERVE MY SPOT

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

Harbour.Space University
Tech Heart
COURSE OUTLINE
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Session 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.

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