Join Peggy Fisher for an in-depth discussion in this video Basics of discrete mathematics, part of Programming Foundations: Discrete Mathematics.
- [Voiceover] You may be wondering…what is discrete mathematics?…A short definition would be…the study of mathematics that falls…outside the realm of calculus.…Calculus is the study of continuous math concepts,…whereas, this topic is discrete -…the study of separable, countable,…or quantified objects.…If you're familiar with electronics,…it can be thought of as the difference…between analog and digital.…One of my favorite analogies…refers to a list of baking items needed to make cookies.…
Most of those supplies are continuous,…such as milk, flour, sugar, etc.…They can be measured in various increments…such as cup, teaspoon, or even ounce.…But if you need eggs, they are more discrete.…You either need a whole egg,…just the yolk, or just the egg white.…But either way, they must be in whole egg units.…So the baking supplies are continuous…and the eggs are discrete.…
Another example is the remote control…used to control your television.…The power button puts the TV…into a discrete state.…It is either on or off.…Think about how that differs from the volume buttons…
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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