To Know: Don’t forget that the first Proof Quiz is available and due on Wednesday. Don’t worry too much if you feel a little lost on how to write a proof so early in semester — we all have to start from somewhere. There’s a lot to learn from the attempt. And I will drop half your proof grades, so this is just a practice run.

To Know: I will soon be opening up Sets III (Set-Builder Notation) there’ll be a third written attempt at Sets I. Remember these are due Fridays.

To Do: Please read Section 4.2 in the book. Remember to read actively. This section is about things you know — like what it means to be even, odd, or for one integer to divide another. But it’s an exercise in formalizing these things, and choosing language for them.

To Do: Please read Section 1.3 in the book (read actively as always!). This is about subsets, which we’ve already studied, but it will give you an opportunity to practice some more. It also introduces the idea of systematically listing all the possible subsets of something. Do the exercises.

As far as the canvas dropbox, you can hand in the exercises from Section 1.3.

Be aware that there’s another attempt at the Sets 1 badges available (written attempt #2), due Friday. This cannot lower your grade, so please attempt it if you feel you’d like a chance to raise your grade, or just extra practice.

Be aware that later today (Wednesday) I will post a first Proof Quiz, due Monday. Remember, I use the best half of your grades throughout semester, so just give it a try as your first chance to get some concrete feedback from me on a written proof.

In class, we introduced set-builder notation. Do Exercises for Section 1.1, A and B.

Solve the Sandbox problem (as we discussed in class) for 8 and 10 gallon scoops. Write up a proof that you like, drawing from the best aspects of the proofs I gave in class (click History above for resources, and see videos on Canvas).

Hand in a picture of your daily work on canvas for a completion check (exercises and sandbox problem).

Please note: I grade the daily tasks on participation. If you have spent your hour working hard, and you’re not totally done the tasks, then hand in what you have and make a note to that effect. That’s fine! Sometimes things may take longer than I expect; you can come back to them when you have other study time. (From now on, late receives 0 on daily posts, however.)

View the Sandbox problem notes (these include some conclusions from class, and some further discussion to get you started). In class, in groups, we tried to write proofs of this theorem. Starting from that experience/discussion, please try to write up a proof of your own.

Please read this interesting opinion piece about teaching mathematics. I’m curious of your reactions.

Please watch this very cool Numberphile video about square root of 2. Pause, rewind, decipher his crazy accent, and figure out the proof he gives that square root of 2 isn’t rational (isn’t a ratio of integers). Then write it up in your own words. Your proof should contain complete sentences. It should not be a transcript of the video. It should be your own explanation of why it works. You may find you want to use the same equations he’s used; that’s fine. But make it your best written english essay as to why sqrt(2) is irrational.

Hand in both these proofs (the Sandbox and Sqrt(2)) on the canvas dropbox.

Revisit the reading of Section 1.1. Read from the page 5 sentence “A special notation called set-builder notation…” until the end of Section 1.1. Read with careful attention to your mental process, and take note of 3 specific mental activities you did. Choose mental activities that occurred at or after the sentence “In general, a set X written with set-builder…” (i.e. not the same sentences we read in class). Be as specific as possible, i.e. give the sentence you are working on, and describe explicitly what you did as an active reading mental activity at that point. Jot these down and submit them to the canvas dropbox Due Aug 31.

Revisit the worksheet from class and make sure you are comfortable with all the answers, and have completed it if you didn’t in class.

Read Chapter 4 from the beginning to the end of Section 4.1. Don’t forget to read actively!

Read the text Hammack, Section 1.1, from the beginning until we get to set builder notation. This is material we covered in class. Read actively! (The text is available as PDF; link at the upper left of your screen.)

What we have covered in class today pretty much covers the topics for the badge “Sets I”. Recall that you have several attempts to earn “badges” (=”certificates of mastery”) (see The System and Grading). You might as well give it a go and try the first one after you finish your daily task today! It cannot count against you. Your grade is made out of your best scores on each badge. You have four attempts total.

The first attempt is open on canvas “Sets I Written #1” meaning attempt #1 in written form to earn the badge “Sets I”. The honor code rules are given in the assignment, which you can download and read carefully. It is a written assessment on your own time, due Friday at 11:59 pm. You can print and fill it or use a separate sheet of paper. You will have 3 other chances (two written, one an oral exam) for this badge. So doing this isn’t part of your daily task, but I suggest you do it before the first due date Friday at 11:59 pm.

Now, keep reading to the end of Section 1.1. This will be new material we didn’t get to during class today. All the more important: read actively!

Do a handful (say 4-5) of Exercises for Section 1.1 from each of the three sections A, B and C. Note that this book has answers to odd numbers at the back. These exercises deal with material you’ve only learned in the reading. We will also cover it in class, so this is just a first attempt or first pass. Math takes many passes. Hand in a photo of your work to the canvas dropbox for a completion check.

If you have not already, then view the welcome video for the course, and the discord intro video (both available on the main landing page in canvas), and get set up on discord.

Read through Classroom Expectations in detail. Make sure you are set up technologically and contact me with any concerns. In particular, I’m hoping everyone will find discord useful.

On the discord text channel #polyhedron-exploration (in Category DISCUSSION TOPICS), post a sentence or two describing what insight you gained from Monday’s class.

Write me a note! I have set up an assignment in canvas where you can share a quick description of where you are coming from mathematically (what’s your relationship to math?) and your hopes and fears for the course (do you expect any particular challenges?). This is your opportunity to let me know anything you think will be important for me to know during semester. It will help me prepare a better course!