Join Peggy Fisher for an in-depth discussion in this video Objects as sets, part of Programming Foundations: Discrete Mathematics.
- [Voiceover] Let's start with the building…blocks for discrete mathematics, set theory.…A set is a way to express a collection of objects.…Sets can represent objects in the physical world…such as a set of books, a set containing…all the colors of the rainbow or even a set of numbers.…All sets have a value for the number of items in the set.…How many books?…And, how many colors are in the rainbow?…How many positive odd numbers?…This is called the cardinality of a set.…
The books in this example would have a cardinality of 17.…There are seven colors in the rainbow…and there's an infinite number of positive odd numbers.…Other examples occur all the time around us.…How about a set containing the…names of your favorite fruits?…Or a set that contains a list of…the names of all students in a class?…Your favorite players on a basketball team?…Or even the employees in a company?…Let's take a quick review of some of the set properties.…
It's important to note that the order of elements…in a set is not important.…When a set has no elements, it's called an empty set.…
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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