Join Peggy Fisher for an in-depth discussion in this video Set operations, part of Programming Foundations: Discrete Mathematics.
- [Voiceover] Now that we've defined a set…and reviewed the set notation,…we can move on to Set Operations.…In the Exercises file, there is a folder…that contains several reference materials,…including a list of all the set operations…and laws used in this movie.…Use that as a reference…when you try the challenge for this section.…In set theory, we'll use the following operations:…Set Intersection.…It's written as A intersects B…and the formal notation says…that the result of the intersection of sets A and B…is the set of all values X such that…X is an element of A,…and X is an element of B.…
Set Union is A union B.…And this definition says…the set of all values X,…where X is an element of A,…or X is an element of B,…or both.…Next, we have Set Difference,…which takes the elements in set A…minus the elements in set B.…The formal definition says…the set of all values X…such that X is an element of A,…and X is not an element of B.…
Set Complement.…Set Complement is written as A with a line over it,…or A raised to the C power.…
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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