Mathematical induction is a specialized technique for writing mathematical proofs that's specially suited to situations that involve proving a statement is true for all integers above a minimum value. In this series, we're going to first talk about the steps in writing these kinds of proofs that look at some example from a variety of fields.
Video Lectures
Strong induction takes the idea of mathematical induction a setp further. The basis step stays the same but the induction step is expanded to include every value less than n + 1 rather than just the next value less.
In this lecture, we're going to finish what we started earlier in our number theory discussion: showing the existinece of the prime factorization of an integer using strong induction. (lecture slides)
Strong induction isn't just for algebra and number theory. It can also be used to prove geometric statements like the one we discuss here about triangulations of polygons. (lecture slides)
In our earlier discussion of number theory, we talked about the importance to computer science of being able to represent a decimal number in a binary form. In this lecture, we're going to fill in an assumption we made in that discussion by showing that the every positive integer does in fact have a binary representation and that that representation is unique. (lecture slides)
In this last lecture in our series on strong induction, we're going to look at the relationship between mathematical (weak) induction, strong induction and the well ordering principle. (lecture slides)
