Discrete Math and Analyzing Social Graphs

The main goal of this online course is to introduce topics in Discrete Mathematics relevant to Data Analysis

  • The course is related to the online specialization ''Mathematics for Data Science"
  • Flexible Terms
  • 6 weeks (2 credits)
  • Time to completion: 20 hours
  • Online
  • Certificate
Apply for the specialization

About the Course

We will start with a brief introduction to combinatorics, the branch of mathematics that studies how to count. Basics of this topic are critical for anyone working in Data Analysis or Computer Science. We will illustrate new knowledge, for example, by counting the number of features in data or by estimating the time required for a Python program to run.

Next, we will apply our knowledge in combinatorics to study basic Probability Theory. Probability is everywhere in Data Analysis and we will study it in much more details later. Our goals for probability section in this course will be to give initial flavor of this field.

Finally, we will study the combinatorial structure that is the most relevant for Data Analysis, namely graphs. Graphs can be found everywhere around us and we will provide you with numerous examples. We will mainly concentrate in this course on the graphs of social networks. We will provide you with relevant notions from the graph theory, illustrate them on the graphs of social networks and will study their basic properties. In the end of the course we will have a project related to social network graphs

Course Objectives


Categorize basic combinatorial problems into standard settings


Use methods of combinatorics to count objects


Calculate probabilities of events using definition and properties of probabilities

Learning Outcomes

1. Use standard algorithms for traversing graphs

2. Analyze the structure of graphs using parameters: clustering coefficients, diameter etc.

3. Compare social network graphs (from datasets) with random graphs, and see how the parameters change

4. Practice in using NetworkX for social network analysis

Course Syllabus

Week 1. Basic Combinatorics

Week 2. Advanced Combinatorics

Week 3. Discrete Probability

Week 4. Introduction to Graphs

Week 5. Basic Graph Parameters

Week 6. Graphs of Social Networks

Подольский Владимир Владимирович

Департамент больших данных и информационного поиска: Доцент

Кузнецов Степан Львович

Департамент анализа данных и искусственного интеллекта: Доцент

Ilya V. Schurov

Associate Professor


As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in Python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in Data Analysis, starting from motivated high school students

Graduation Document

Earn a Certificate upon completion



Learning Activities



Low-Stakes Assignments


High-Stakes Assignments

Final project

Cost and Conditions

17 000 ₽

Full access to the learning materials + Graduation document

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