Unit 4: Mathematical Induction and Proofs
So far, we have learned about symbology, truth tables, writing equations, and determining how many units could be in a set under specific circumstances. We have done all of this has under the assumption that we can easily see the results of our efforts. However, in practical situations that you will encounter in real life with serious applications, we cannot always see our results quickly, or necessarily even traverse the situation easily. For that, we must turn to the methods behind mathematical systems and proofs. These allow us to "get the big picture" without having to visualize it all at once. Proofs also give us a way to consider all of the available information in a given arrangement of facts, even when some of the "facts" might not actually be true. They also have the added advantage of letting us ignore whole portions of a situation when we know they do not hold the answer we seek.
Completing this unit should take you approximately 5 hours.
4.1: Mathematical Systems
4.2: Direct Proof
4.3: Indirect Proof
4.4: Propositions over a Universe
4.5: Mathematical Induction
4.6: Strong Induction
Unit 4 Assessment
- Receive a grade