- [Instructor] Discrete math contains many topics … that can be demonstrated using SML. … Topics include: functions and recursion. … As part of the foundations of programming segment, … let's use SML to model some discrete math concepts. … If I enter five and a semicolon and hit enter, … SML tells me the value of the variable is five, … and it's an integer. … Notice, I didn't give the value a variable name. … SML automatically uses it, or I-T, as the variable name. … Let's try it again. … Let's put a number in that has a decimal point. … This time SML says the value is a real number. … How about if I enter a string? … Most programing languages use double quotes around a string, … so I'll enter my name, and SML works the same way. … An expression in SML is any construct … in the programming language that the program interpreter … can evaluate to a value. … So let's start with a simple expression. … Let's take away three from 15, so 15 minus three. … The SML interpreter computes the value of 15 minus three …
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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