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"…
Author
Peggy Fisher
Released
3/9/2016This 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
Duration
Views
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Introduction
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Welcome1m 11s
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1. Discrete Math Uses
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Real-world discrete math3m 8s
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Abstract discrete math1m 57s
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2. Sets
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Objects as sets2m 56s
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Set notation3m 56s
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Set operations5m 1s
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Power sets4m 29s
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Sequences and sums7m 22s
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Recursion3m 5s
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Solution: Practice with sets6m 53s
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3. Setting Up SML
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Functional programming2m 31s
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Datatypes4m 45s
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Characters and strings5m 19s
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Recursive functions4m 45s
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Challenge: Learn SML1m 40s
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4. Analyzing Data Sequences
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Use SML to create lists4m 39s
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Perform functions on lists4m 31s
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5. Effective Arguments and Defensible Decisions
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Truth tables4m 58s
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Conditional propositions5m 48s
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Valid arguments4m 40s
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Rules of inference4m 45s
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Prove logical equivalence6m 11s
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Solution: Write truth tables4m 55s
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6. Proofs Made Easy
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Write subset proofs3m 12s
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Evaluate conditional proofs8m 54s
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Solution: Write a proof4m 23s
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7. Advanced Discrete Math Topics
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Event probability3m 31s
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Cryptography2m 22s
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Conclusion
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Next steps35s
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Video: Real-world discrete math