Foundations of Programming: Discrete Mathematics

What is discrete math, and how does it apply to programming? Math is an important part of all programming. Discrete mathematics is the study of mathematical structures that are unique (aka discrete). Think integers, graphs, and logical statements—things we use a lot in programming. Discrete math can be used for software design specifications, analysis of algorithms, and other practical applications, but it’s really a great tool to develop as a programmer. Put simply, it’s a building block for logical thinking.

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.

Topics include:
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