Join Peggy Fisher for an in-depth discussion in this video Visualize data with graph theory, part of Programming Foundations: Discrete Mathematics.
- [Voiceover] Graph theory can help…visualize, analyze and optimize networks.…In graph theory, mathematical structures…are used to model pairwise relations between objects.…A graph in this context is made up of vetices or nodes…and edges that connect them.…A graph may be undirected,…meaning that there is no distinction…between the two vertices associated with each edge,…or its edge may be directed from one vertex to another.…
Graphs are one of the prime objects of study…in discrete mathematics.…Here's an example of two graphs,…referred to as trees.…On the left is a free tree.…On the right, this is called a rooted tree.…A tree is an example of an undirected graph…that connects nodes and edges…but has no cycles.…When using trees in graph theory,…the root is the base of the tree.…
Trees can have parents, children,…ancestors, siblings and descendants.…Leaves of the trees are vertices that have no children.…A tree can also contain a subtree.…Trees can be used to model social interaction.…For example, if the vertices represent people at a party…
This course relies on an open-source SML (standard machine language) library to demo the concepts behind discrete math. Peggy Fisher shows you how to manipulate sets of data, write proofs and truth tables, analyze data sequences, and visualize data using graph theory. Challenges at the end of every chapter allow you to test your knowledge. By the end of the course, you should be able to make the leap from theory to using discrete math in practice: saving time and resulting in code that's cleaner and easier to maintain in the long run.
- Real-world discrete math
- Objects as sets
- Set notation and operations
- Standard machine language (SML) setup
- Working with data types, strings, and functions in SML
- Analyzing data sequences
- Writing truth tables
- Identifying and evaluating predicates
- Validating arguments
- Writing proofs: subset, conditional, and biconditional proofs
- Visualizing data with graphs
- Advanced discrete math techniques
Skill Level Intermediate
1. Discrete Math Uses
3. Setting Up SML
4. Analyzing Data Sequences
5. Effective Arguments and Defensible Decisions
6. Proofs Made Easy
7. Advanced Discrete Math Topics
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