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In this course, you will learn :
This course's main goal is to introduce topics in Discrete Mathematics that are relevant to Data Analysis. We'll begin with a quick overview of combinatorics, the branch of mathematics that studies how to count. The fundamentals of this subject are essential for anyone working in data analysis or computer science. We will demonstrate new knowledge by counting the number of features in data or estimating the time required to run a Python programme.
Syllabus :
1. 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
2. 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
3. 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
4. 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
5. 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
6. Graphs of Social Networks
- Social Network Graphs
- NetworkX
- Visualization
- Computing Graph Parameters
