Course 5 · Module 1
Logic and Set Theory
This module covers the branches of mathematics that study proof itself. You'll see how logic turned valid reasoning into rules you can check, how Cantor showed that some infinities are larger than others, and how Gödel proved that no system of rules can capture every mathematical truth. The same logic runs every digital circuit and database you use.
Module objectives
- Evaluate a short argument for validity, and explain why some infinite sets are larger than others.
- Explain what Gödel's incompleteness theorems show, and describe how logic is used in computing.
Lessons
- Lesson 1 Logic and Set Theory: From Aristotle's syllogisms to Cantor's infinities: the logic of proof You'll see how logic sorts good arguments from bad ones by their form alone, and how set theory compares the sizes of infinite collections. You'll check arguments with truth… 61111h 3m
- Lesson 2 Logic and Set Theory: Gödel's incompleteness, the continuum hypothesis, and logic in circuits and databases You'll see how Boole's algebra of logic became the circuitry of every computer and how set theory became the language of databases. You'll also meet Gödel's proof that any… 611111h 33m