Join Peggy Fisher for an in-depth discussion in this video Network optimization with trees, part of Programming Foundations: Discrete Mathematics.
- [Voiceover] Using trees and graph theory,…we can help with network optimization.…Optimization is the process of looking…for the best solution, whether this is…the shortest path, a minimum spanning tree,…or a minimum circuit.…One important example of optimization…is evaluating the amount of space…used to store information.…Remember, text files are stored on computers…as binary strings, a series of ones and zeroes,…in which each character is assigned…a binary code representing that character.…
ASCII and Unicode character sets…are examples of fixed length encodings.…Variable length codes are much more efficient.…Prefix codes are an example of variable length encoding.…A prefix code has the property that the code…for one character cannot be a prefix…of the code for another character.…They all must be unique.…The fact that the codes are organized as a tree…in which characters are only stored at the leaves,…ensures the prefix property.…
An example would be a textbook…that has 9,000 instances of the letter a,…because the letter a is common in the English alphabet.…
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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