---
tags: mth225, dailyprep
---
# Daily Prep 3.2 -- MTH 225
## Overview
In this lesson, we'll build on our new concept of sets to determine when one set is a **subset** of another or **equal to** another, and learn the **set operations** of **union**, **intersection**, **complement**, **difference**, **symmetric difference**, and **Cartesian product**. We'll also learn the concept of **cardinality** of a set and how to form the **power set** of a set.
## 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.
* State the definition of "subset" and given two sets, determine if one is a subset of the other.
* State the definition of "equality" of sets, and given two sets, determine if they are equal.
* Given a finite set, write its power set.
* Given a finite set, state its cardinality.
* Given two sets, find their intersection, union, difference, symmetric difference, and Cartesian product.
* Given a set and its universal set, find its complement.
**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.
* Use Venn diagrams to make conjectures about combinations of set operations and then give explanations for why the conjecture is true.
## Resources for learning
**Video:** Watch these from [the MTH 225 playlist](https://vimeo.com/showcase/8667148) (total running time 25:29):
<iframe src="https://player.vimeo.com/video/606554057?h=367ebde300" width="640" height="360" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen></iframe>
<iframe src="https://player.vimeo.com/video/606573917?h=e0ea25ff64" width="640" height="360" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen></iframe>
<iframe src="https://player.vimeo.com/video/606600971?h=e256db4c8a" width="640" height="360" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen></iframe>
<p><a href="https://vimeo.com/606600971">Screencast 3.6: Set operations</a> from <a href="https://vimeo.com/user132700952">Robert Talbert</a> on <a href="https://vimeo.com">Vimeo</a>.</p>
<iframe src="https://player.vimeo.com/video/606627934?h=0a0e06f5a8" width="640" height="360" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen></iframe>
**Text:**
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
Once you have watched the videos above, go to this form and complete all the non-optional items on it:
https://docs.google.com/forms/d/e/1FAIpQLScv7SMR9SEdrkjq-eYvrI2H97DWLDMVgh-1A9cYF02-T95wXg/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.

:::info Welcome to MTH 201! I'm Dr. Robert Talbert, Professor of Mathematics, and I am grateful that you are signed up for the course and am looking forward to working with you this semester. ::: What's MTH 201 all about? MTH 201 is a first course in Calculus, which is all about modeling and understanding change. Change is maybe the most important facet of the world around us, and we care about it more than we realize. For example, we care a lot about the number of Covid-19 cases in our community, but we might care even more about how fast the number of cases is changing (either up or down). In MTH 201, you'll learn the mathematical language of change and apply it to models that you build to draw conclusions, make predictions, and give meaningful answers to real problems. MTH 201 goes beyond just computation. In MTH 201, you'll build skills with understanding complex concepts, communicating those concepts and the meaning of your results to appropriate audiences, using professional tools to help you in your work, and practice working with others to improve your learning (and theirs). These are valuable skills no matter where you go next. Success in this course doesn't come easy, and you can expect to be pushed and stretched intellectually. But the struggle you experience is normal and healthy, a sign of growth and that you are doing things the right way. And you will receive tireless support from me and your classmates in the process. Above all, my top priority is to support you in your work and help you succeed.

11/11/2023Initial due date: Sunday, April 9 at 11:59pm ET Overview Our final miniproject reaches back into linear algebra to look at diagonalizable matrices and their uses in solving systems of differential equations. Prerequisites: You'll need to be able to solve basic systems of differential equations and find the eigenvalues and eigenvectors for a small matrix. You'll also need a basic comfort level with concepts of linear independence and matrix arithmetic from earlier in the course. Background This entire problem comes from Section 3.9.1 in your textbook. Here is a rephrased version of the introduction to that section.

3/29/2023Initial due date: Sunday, April 9 at 11:59pm ET Overview This miniproject will teach you about the Runge-Kutta method, a standard numerical solution technique for differential equations. Prerequisites: A strong grasp of Euler's Method for single DE's is needed. You will also need to be comfortable using a spreadsheet. Miniproject 6 (Euler's Method for systems) is also recommended. Background A description of the Runge-Kutta method along with an example is given in this tutorial. Read it carefully and make sure you can work along with the example before proceeding.

3/29/2023Initial due date: Sunday, April 9 at 11:59pm ET Overview This miniproject introduces a version of Euler's Method as a numerical solution technique for systems. Prerequisites: You will need to be comfortable with using Euler's method for single differential equations. You'll also benefit from some familiarity with spreadsheets or Python in order to automate the calculations. Background This tutorial gives you the background you need for this assignment. Please read it and make sure you understand the concepts and the example: https://github.com/RobertTalbert/linalg-diffeq/blob/main/assignments/Euler's_Method_for_Systems.ipynb

3/22/2023
Published on ** HackMD**

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