Join Peggy Fisher for an in-depth discussion in this video Write subset proofs, part of Programming Foundations: Discrete Mathematics.
- [Voiceover] To help get a better understanding of proofs…let's take a look at a subset proof.…For subset proof's, we start with two sets A and B.…They are both subsets of the universal set U.…If possible it helps to use a Venn diagram…to visualize the proof.…This can help determine a course of action…for the more formal proof.…Let's start there.…I'm gonna label the rectangle U…to indicate my universal set.…Now, I'm going to draw two circles.…One representing set A,…and I'm going to show an intersecting set for set B.…
To help us visualize this a little bit more…here is the intersection of the two.…How about if I say that set A…contains the numbers…one, two, three and four…and that set B contains the numbers…two, four, six and eight.…Let's place them into our Venn diagram.…Okay, A has one, but A and B have two,…so I have to put two in there.…
A has the number 3,…and A and B have four.…And then B also has six and eight.…By doing that, we can see that the intersection…A intersects B is equal to the set…with the numbers two and four.…
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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