## Exercises on Mathematical Induction (10 Must See)

What are the four types of induction problems that are must-see for any student just starting out learning mathematical induction? In this video, I work through 10 exercises using mathematical induction. For each of these exercises, I demonstrate how to brainstorm the problem and then how to write up a rigorous solution. Some of these exercises involve the factorial function, and others involve the well-ordering of the natural numbers.

## The Mathematical Induction Equivalence

Why is mathematical induction an axiom to some and to others its a theorem? Should the well-ordering of the natural numbers be an axiom or theorem? Why does any of this matter?

## Introduction to Proofs (Learn to Write Mathematical Proofs)

Making the transition from calculus to analysis (or from elementary algebra to abstract algebra) can be one of the most challenging transitions for students. In this article, I guide you through this process and explain how to become confident and skilled. You’ll see many articles and videos that will explain and provide insights to help keep you on track and inspired.

## Learn Precalculus (Online Precalculus Tutorials)

In this article, I take the student on a journey where we’ll learn precalculus. I’ll describe each step for you and provide tutorials and videos where you get the necessary understanding. You will understand the process and goals for each chapter, and you’ll gain valuable insights from a seasoned math educator. Precalculus is a gateway to many other subjects. Let’s get started.

## The Strong Form of Induction (with Examples)

You’re trying to prove a statement is true using mathematical induction, but then you realize that the induction hypothesis doesn’t seem strong enough. What do you do? It turns out that there is more than one way to do induction. Let’s learn what strong induction is.

## Arithmetic and Geometric Progressions

In this video, I am going to explain what arithmetic and geometric progressions are. I’ll also give several basics examples. Then I will prove the summations formulas for both the arithmetic and geometric progressions. In the end, I’ll discuss how these progressions arise in nature.

## Induction Principles (Basis Step Required)

In this video, I discuss various forms of mathematical induction, including strong induction. I establish that the base case of an induction argument is required. Also, I explain the differences between the second-order logic induction principle and the first-order statement.

## Examples Using Mathematical Induction

In this video, I’m going to work through five examples using mathematical induction. The first two examples involve summations, and the last three examples have an inequality. In each of these examples, I work through specials cases before wiring a proof so that you can get a feel for the result before actually proving the result holds using mathematical induction.

## Well Ordering Axiom (Principle or Theorem?)

In this video, I’m going to talk about the Well-Ordering Axiom. First, I’ll discuss the ordering and why it’s reflexive, antisymmetric, and transitive. Then I explain the Well-Ordering Axiom followed by some basic examples. After that, I’ll discuss whether it should be an axiom or a theorem.

## First Examples Using Mathematical Induction

In this video, I’m going to cover three first examples using mathematical induction. So I’m going to assume that you have never seen mathematical induction before. So this is the first step, in a series of steps, to learn how to use and what mathematical induction is. Of course, to do that, we need to start with what the natural numbers are.

## Learning to Learn (What It Is and How to Do It)

In this article, I go over what Learning to Learn is and why it matters. I also discuss for you tackling procrastination and how to unlock your potential. After that, I discuss books and courses on Learning How to Learn, and in the end, I discuss how Dave4Math can help you with your educational goals.

## Math Help (Who Should You Ask for Help and When)

In this article, I take on the questions of why you might use your math instructor for help or why you might use a math tutor? I also discuss getting math help online for you.