Join Peggy Fisher for an in-depth discussion in this video Abstract discrete math, part of Programming Foundations: Discrete Mathematics.
- [Voiceover] Abstract Math Problems.…Abstract math provides the conceptual background…and theory that justifies…the way math is used in applications.…Abstract math requires conceptual reasoning…about abstract ideas, as well as manipulating symbols,…particularly, understanding and constructing proofs.…In doing abstract math, you state theorems and prove them…mostly in the context of mathematical ideas.…The level of abstraction allows for solving complex problems…by breaking them down into smaller problems.…
When completing proofs, we often start…with a statement similar to this one.…One supposes that a particular but arbitrarily chosen…element x in D, where D is the domain,…for which P(x), the proposition, is true,…and proves that Q(x) must also be true.…As you can see, this is an abstract version…of the proof which allows us to determine…the validity of the proof, and therefore…we can use this to generalize to more specific solutions.…
In discrete mathematics,…there are relatively few formulas to memorize.…Instead, there are a number of fundamental concepts…
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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