Daily Prep 7A -- MTH 350-01

--- tags: mth350, dailyprep --- # Daily Prep 7A -- MTH 350-01 ## Overview We saw in Module 5/6 over the last two weeks that we can do arithmetic and algebra in a "number system" that is not the integers --- in fact in a system that is very unlike the integers im many ways. We can take a set of objects, define operations on them, and then look at what "arithmetic" and "algebra" works and what doesn't. In this Module, we are going to expand this notion considerably by asking the same kinds of questions on number systems that range widely, from the real numbers and rational numbers to matrices, complex numbers, and even sets. This module lays the ground work for the main concept of this course, coming in Module 8. ## 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. - (Review) Multiply and add two $2 \times 2$ matrices. - (Review) Multiply and add two complex numbers. - State the definitions of the following sets: $\mathbb{Q}$, $\mathbb{R}$, $\mathbb{C}$, and $\cal{M}_{2 \times 2}(\mathbb{R})$.  **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. - Determine which properties of number systems listed in the rows of Table 6.2 are satisfied by $\mathbb{Q}$, $\mathbb{R}$, $\mathbb{C}$, and $\cal{M}_{2 \times 2}(\mathbb{R})$. ## Resources for learning **Reading:** We are in Investigation 6 this time, but you'll need to be selective about what you read. You can **skip** everything up until the section "Subsets of the Real Numbers". (Go ahead and look at this material if you want but it's considerably more abstract than we are going this week). Then read that section up through, but *not* including, the section "Collections of Sets" (that's for Thursday). This is about 3-4 pages in all. **Video:** There's no required video this time but I *highly suggest* watching some of the tutorial videos for the "Matrices and Complex Numbers" review assignment on Blackboard. **You will need to be fluent with adding and subtracting $2 \times 2$ matrices as well as complex numbers for Tuesday's class.** In fact, completing that review assignment all the way would not only get the assignment done, you'd be very well prepared to focus on the main concepts on Tuesday. ## Exercises The exercises for this Daily Prep are found on the Google Form: https://docs.google.com/forms/d/e/1FAIpQLSdix09BoXL6uLlpRkv48Zs8wLZiUezkBxYfsyrsxNI45PsosQ/viewform ## Submission and grading To submit your work, simply submit the Google Form. You will receive a receipt via email to confirm your submission. (Look in your spam folders if you do not see the receipt.) A **Pass** mark is given if the Daily Prep is turned in before its deadline and if each item on the Daily Prep has a response that represents a good faith effort to be right. **Mistakes are not penalized**. A **No Pass** is given if an item is left blank (even accidentally), has an answer but it shows insufficient effort (including responses like "I don't know"), or if the Daily Prep is late.