Join Peggy Fisher for an in-depth discussion in this video Valid reasoning and inference, part of Programming Foundations: Discrete Mathematics.
- In the study of valid reasoning,…statements, also called propositions,…are sentences that are either true, or false.…This provides a perfect correlation with computing,…as true or false answers are represented…as a one or a zero, on or off.…For the study of discreet math,…it is important to understand…that not all sentences are propositions.…In other words, not all sentences,…can be evaluated to true or false.…
Here are some sentences that are propositions.…All apples are red.…Today is Monday.…Two plus two equals five.…You might be wondering…what statements are not propositions.…How about, what day is it?…How are you?…Have a nice day.…Exclamatory and questioning sentences…are not usually propositions.…A sentence containing a single proposition…is not hard to evaluate to true or false.…
But when it's combined with logical operators,…it can be quite a different story.…Logical operators are used…to make compound statements or…compound propositions.…To help with evaluating these more complex statements,…we can dissect the sentence into predicates…
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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