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Discrete Math and Analyzing Social Graphs

Approx. 20 hours to complete

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Course Summary

Learn how to apply discrete math concepts to analyze social graphs and networks in this course. Gain practical skills in data analysis and visualization using Python.

Key Learning Points

Learn how to analyze social graphs and networks using discrete math concepts
Gain practical skills in data analysis and visualization using Python
Explore unorthodox approaches to social network analysis

Learning Outcomes

Apply discrete math concepts to analyze social graphs and networks
Use Python to perform data analysis and visualization
Develop unorthodox approaches to social network analysis

Prerequisites or good to have knowledge before taking this course

Basic knowledge of Python programming
Familiarity with discrete math concepts

Course Difficulty Level

Intermediate

Course Format

Online
Self-paced

Similar Courses

Social Network Analysis
Data Analysis and Visualization

Related Education Paths

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Description

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

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. 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. This Course is part of HSE University Master of Data Science degree program. Learn more about the admission into the program and how your Coursera work can be leveraged if accepted into the program here https://inlnk.ru/rj64e.

Outline

Basic Combinatorics
Why Counting
Rule of Sum
Convenient Language: Sets
Generalizing Rule of Sum
Recursive Counting: Number of Paths
Rule of Product
Number of Tuples
Set Language for Tuples
Licence Plates
Tuples with Restrictions
Permutations
Unordered Pairs
Combinations
Slides
Slides
Slides
Rule of Sum in Programming
Numbers Divisible by 2 or 3
Sets and Operations with Them
Generalized Rule of Sum
Number of Paths
Rule of Product
Rule of Product in Programming
Tuples
Tuples with Restrictions
Number of Segments
Nested For Loops
Splitting Datasets

Advanced Combinatorics
Pascal’s Triangle
Binomial Theorem
Practice Counting
Review
Salad
Combinations with Repetitions
Distributing Assignments Among People
Distributing Candies Among Kids
Numbers with Fixed Sum of Digits
Numbers with Non-increasing Digits
Splitting into Working Groups
Slides
Generation of Combinatorial Objects
Number of Salads
Number of Large Salads
Slides
Slides
Comparing Binomial Coefficients
Sums of Binomial Coefficients
Applying Binomial Theorem
Practice Counting
Number of Salads
Combinations with Repetitions
Distributing Assignments Among People
Distributing Candies Among Kids
Numbers with Fixed Sum of Digits
Numbers with Non-increasing Digits
Splitting into Working Groups
Problems in Combinatorics

Discrete Probability
Random experiments, outcomes and events
Operations on events
Classical probability
Probabilities and combinatorics
Probabilities and operations on events
Analysis of bagging procedure
Outcomes with non-equal probabilities
Experiments, outcomes and events
Operations on events
Probabilities by definition
Probabilities and combinatorics
Finding probabilities using rules
Outcomes with non-equal probabilities

Introduction to Graphs
The Notion of Graph
Trees
Colorings. Bipartite Graphs
Konigsberg Bridges. Euler Cycles
Constructing a Euler Cycle
Hamiltonian Paths
Acyclic Directed Graphs. Topological Sorting
Traversing Trees
Traversing Graphs: DFS and BFS
Slides
Slides
Slides
Trees
Coloring
Euler Path
Hamiltonian Cycle
Topological Sorting
Traversing trees

Basic Graph Parameters
Graph Invariants and Graph Isomorphism
Handshaking Lemma
Clustering Coefficients
Distances. Diameter. Eccentricity
Cliques, Independent Sets
Vertex Covers
Approximating Optimal Vertex Cover
Connected Graphs and Connected Components
Inequations on the Number of Connected Components
Circuit Rank
Slides
Slides
Slides
Graph Isomorphism
Degrees
Clustering Coefficient
Distances
Cliques and Independent Sets
Vertex Covers
Connected Components and Circuit Rank

Graphs of Social Networks
Social Network Graphs
NetworkX
Visualization
Computing Graph Parameters
Slides

Summary of User Reviews

Discover the world of discrete mathematics and social graph analysis in this highly engaging online course on Coursera. Learn about fundamental concepts of graph theory and its practical applications in social network analysis. Students highly recommend this course for its comprehensive content and interactive approach to teaching.

Key Aspect Users Liked About This Course

The course is highly engaging and interactive.

Pros from User Reviews

Comprehensive content on discrete mathematics and social graph analysis
Interactive approach to teaching with quizzes and exercises
Engaging lectures with clear explanations and examples
Practical applications of graph theory in social network analysis
Great preparation for further study or work in data science

Cons from User Reviews

Some students found the course challenging and required additional resources
Lack of personalized feedback from instructors
Limited interaction with other students in the course
Occasional technical difficulties with the Coursera platform
Not suitable for those without a strong background in mathematics

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