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
Mathematical induction is a proof technique that's useful for proving statements where some property can take on integer values, e.g. formulas about sequences and series or geometric objects that have to have an integer number of sides. In this lecture, we're going to talk about the steps you have to follow to use this technique. (lecture slides)
The Well Ordering Principle is a statement about the existence of a minimum value in subsets of the natural numbers. We're going to talk about this just briefly here so that we have it available when we start trying to write proofs using mathematical induction. (lecture slides)
Now that we've seen the basic behind mathematical induction, we're going to see some examples of how it can be used to prove algebraic statements or formulas. (lecture slides)
In this second lecture in our series of examples of mathematical induction, we're going to see how it can be used to verify algebraic inequalities. (lecture slides)
The examples that we've seen so far for using mathematical induction have all been very algebraic. In this lecture, we're going to go in a slightly different direction and look at how this technique can be used to prove a result from number theory. (lecture slides)
All of the things that we've discussed so far have been very algebraic, including or number theory divisibility example. In this lecture, we're going to see a little more of how versatile number theory is with a proof of a theorem from geometry (lecture slides)
