Join Peggy Fisher for an in-depth discussion in this video Evaluate conditional proofs, part of Programming Foundations: Discrete Mathematics.
- [Voiceover] When evaluating conditional proofs…it's important to first review the definitions…in previously proven theorems related to number theory.…An integer n is even if, and only if…n equals twice some integer…written as n equals two k.…An integer n is odd if, and only if,…n equals twice some integer plus one,…written as n equals two k plus one.…An integer n is prime if, and only if,…n is greater than one…and for all positive integers r and s,…if n is equal to r times s,…then either r equals one or s equals one.…
In other words, n is prime as long as…n is only divisible by one and itself.…An integer n is called a perfect square…if, and only if, n equals k squared…for some integer k.…A real number r is considered rational…if, and only if, it can be expressed…as a quotient of two integers…with a nonzero denominator.…A previously proven theorem…says that the sum of any two rational numbers is rational.…
And finally, it's important to know…that integers are closed under addition,…subtraction and multiplication.…
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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