Monthly Archives: August 2015

Homework Hints: Set-theoretic notation

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Hi everyone,

I wanted to give an example of writing a given set in set-theoretic notation – this should help out with some of the problems on your first homework assignment (Section 1.1).

Example: Write in set-theoretic notation:  \{5,10,15,20,\ldots \}

In this case, you can see that the given set consists of all multiples of 5.  A good way to approach problems like this is to start with one of the basic sets, for example

  •  the natural numbers \mathbb{N} = \{1,2,3,4, \ldots \}
  • the integers \mathbb{Z} = \{\ldots,-3,-2,-1,0,1,2,3,\ldots\}

In this example, I can see that multiplying every natural number by 5 should give me the set that I want.  Therefore, I will use the formula 5n , and the condition n\in \mathbb{N}.  Combining these in set-theoretic notation gives the solution:

Solution \{ 5n : n\in \mathbb{N} \}

Here are two ways to read this solution aloud:

  • “the set of all 5n such that n is a natural number”, or
  • “for each n in the natural numbers, multiply n by 5 and include the result in the set”

I hope this helps – feel free to respond here if you any questions.

Best,
Prof. Reitz

 

Week 1 Assignments

Assignments

Hi everyone,

Your first homework assignment will be exclusively in the book (you do NOT have a WeBWorK assignment this week), and is due on Tuesday.  Your first OpenLab Assignment is due on Thursday.

Welcome back,
Prof. Reitz

Week 1 Assignments
Written work  due Tuesday Sept 1st –  Sec 1.1 p.7: 1, 12, 19, 26, 29, 35
NOTE: On this assignment, odd problems are worth 2 points and even problems worth 4 points.
WeBWorK – none
OpenLab – Register for the OpenLab and join this course (instructions provided in a separate post).  “OpenLab #1: Advice from the Past” due Thurs Sept 3.

OpenLab #1: Advice from the Past

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Two years ago I taught this same course for the first time.   At the end of the semester, I gave my students the following assignment:

Imagine that you are invited to speak on the first day of MAT 2071, to give advice to entering students.  Write at least three sentences … describing what you would tell them.

To see the assignment and the students’ responses, follow this link.

Your assignment, due next Thursday, September 3th, is to:

  1. Read through ALL the responses (there are 22 of them).
  2. Write a reply to this post (1 paragraph) responding to all of the following:
    1. What advice seemed most relevant to you personally? Why? (you can copy/paste a short statement, or put it in your own words)
    2. Based on this advice, what changes can you make right now to help you with this course?

Extra Credit. For extra credit, write a response to one of your classmates’ comments.  Do you have any advice?  Be kind.