Unit 1: Logic
In this unit, you will begin by considering various puzzles, including Ken-Ken and Sudoku. You will learn the importance of tenacity in approaching mathematical problems including puzzles and brain teasers. You will also learn why giving names to mathematical ideas will enable you to think more effectively about concepts that are built upon several ideas. Then, you will learn that propositions are (English) sentences whose truth value can be established. You will see examples of self-referencing sentences which are not propositions. You will learn how to combine propositions to build compound ones and then how to determine the truth value of a compound proposition in terms of its component propositions. Then, you will learn about predicates, which are functions from a collection of objects to a collection of propositions, and how to quantify predicates. Finally, you will study several methods of proof including proof by contradiction, proof by complete enumeration, etc.
Completing this unit should take you approximately 31 hours.