Join Peggy Fisher for an in-depth discussion in this video Set notation, part of Programming Foundations: Discrete Mathematics.
- [Voiceover] Now that we have a better…understanding of what sets can include,…let's look at some set notation.…Sets are written as a series of elements…separated by commas…and enclosed in curly brackets.…Here are some sample sets.…In this set,…we have the elements a, b, c, d, and e.…It is important to note…that sets can actually be empty.…Sets can also have just one element,…they might have a limited number of elements,…or even an unlimited,…or they have an infinite number of elements.…
The cardinality of a set…refers to the number of items in a set…and it's denoted using the symbol…that you normally see with absolute value.…In this example,…the cardinality is written as…the cardinality of set A.…An empty set can be written in two different ways,…with curly brackets that have nothing in between…or a zero with a line through it.…To indicate that an object is…an element of a set,…we use this symbol,…which looks a little bit like E.…
In this case we say…x is an element of set A.…Let's talk next about a subset.…If every element in set A…
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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