Join Peggy Fisher for an in-depth discussion in this video Real-world discrete math, part of Programming Foundations: Discrete Mathematics.
- [Voiceover] Discrete math can be helpful…in solving real world problems.…Logic, is the study of formal reasoning.…Discrete math involves many forms…of evaluating logical statements.…A statement in logic always has…a specific and well defined meaning.…Let's consider an example involving a jury trial.…The defense attorney uses the facts presented…to show a time-line that proves…his or her client is innocent.…It might go something like this:…"The prosecution claims that my client"…"ran a stop sign outside the Casa Blanca club."…"Let's assume that they are correct."…"You've heard eyewitness testimonies that the incident"…"took place at 1:15 AM."…"We also know that the defendant was seen"…"on a security camera feed provided to us"…"by the apartment superintendent,"…"arriving at his residence that night at 1:30 AM."…"Based on this evidence, my client had 15 minutes"…"to get from the club to his residence, in order"…"to have been at the scene at the time of the incident."…"But we know that it takes at least 30 minutes"…
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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