Daily Prep 3.1 – MTH 225

Overview

Welcome to Module 3! In this module we'll be learning all about another fundamental concept in mathematics and in computer science: the set, which is the foundation for all data structures and a basic tool for expressing collections of objects. In this lesson we'll learn what a set is, the differences between a finite and an infinite set, what it means to be an element of a set, and some famous sets we'll use repeatedly. The main focus of our class work will be on mastering the two different ways of expressing a set: roster notation and set-builder notation.

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.

• Determine whether a set is finite or infinite.
• Given a set in roster notation and given an object, determine whether the object is an element of the set and express the outcome using the
  $\in$ or
  $\notin$ symbol.
• Identify "famous" sets corresponding to their notation: The empty set, the natural numbers, and the real numbers.

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.

• Given a set in roster form, rephrase the set in set-builder notation; and vice versa.
• Given a set in either roster or set-builder form and an object, determine whether the object is a member of the set.

Resources for learning

Video: Watch these from the MTH 225 playlist (total running time 19:50):

Screencast 3.1: Sets from Robert Talbert on Vimeo.

Screencast 3.2: Roster and set-builder notation from Robert Talbert on Vimeo.

Screencast 3.3: When is an object an element of a set? from Robert Talbert on Vimeo.

Text: Read in the textbook, Section 0.3 through Example 0.3.2.

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/1FAIpQLSdShs66LpjTaMkyfSoXu9fxn38Zn5ZQRQ-ifdW80WrMRLrjfQ/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 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.