---
tags: mth225, dailyprep
---

# Daily Prep 5.8 -- MTH 225

## Overview

This lesson is part 1 of a three-part series that will wrap up the entire course for us. You will be learning a structured technique for creating mathematical explanations, known as **mathematical induction**. It is an argumentation technique that is particularly well suited for situations involving recursion and induction and is used extensively in MTH 325, and throughout computer science.

## Learning objectives

**Basic Learning Objectives:** *Before* our class meeting, use the Resources listed below to learn all of the following. You should be reasonably fluent with all of these tasks prior to our meeting; we will field questions on these, but they will not be retaught.

- I can explain the overall process of mathematical induction and why a mathematical induction argument is a valid explanation.
- I can identify the base case in a mathematical induction proof.
- I can identify the induction hypothesis in a mathematical induction proof.
- I can state the proof step in a mathematical induction proof.

**Advanced Learning Objectives:** *During and after* our class meeting, we will work on learning the following. Fluency with these is not required prior to class.

- I can set up the framework for a mathematical induction proof without prompting for the individual parts.

## Resources for learning

**Print:** Rather than watch videos first, I've written this guide to mathematical induction for you. Please read the entire thing first: [Mathematical Induction](/QtgTZTnRQkeQYoe8BObF4A)

**Video:** Here are some videos to reinforce the reading you did. You can consider these optional if you fully understand the reading.

This video from Khan Academy does the problem from the second example in the reading:
<iframe width="560" height="315" src="https://www.youtube.com/embed/wblW_M_HVQ8" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>

And this video is rather long, but it has several fully worked out examples in it: <iframe width="560" height="315" src="https://www.youtube.com/embed/tHNVX3e9zd0" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>

**Text:** This material comes from [Section 2.5 in your textbook](http://discrete.openmathbooks.org/dmoi3/sec_seq-induction.html). There are some excellent extra examples there that you should study.

You are free to search for and use other resources in addition to, or instead of the above, as long as you can work the exercises below.

## Exercises

Go to this form and complete all the non-optional items on it:

https://docs.google.com/forms/d/e/1FAIpQLSf72Qw80ZlIGXLIVyqzVdmYXdOM0LtlRLiZYjGP_YBjeAUX-A/viewform

## Submission and grading

**Submitting your work:** Your work is submitted when you submit the Google Form. You should receive an email receipt indicating that the work was submitted successfully.

**How this is graded:** The pre-class portion of the Daily Prep is graded either 0 points or 1 point, on the basis of completeness and effort. Wrong answers are not penalized. Earning a "1" requires that you:

- Turn the work in before its deadline;
- Leave no item blank or skipped, even accidentally; and
- Give a good-faith effort at a correct answer on every non-optional item.

More information can be found in the [Specifications for Satisfactory Work in MTH 225](/Cy6P0rGZQzuOM3NwZ3ZuMw) document.

When you arrive for the class meeting, you'll be put into a group of 2-3 to complete a quiz over this material, which will be graded on a 0/1 scale on the basis of correctness.