IMPORTANT: You task for today is to do some independent reading. This is important — I’m asking you to cover this new material using the textbook independently (I won’t also lecture it from scratch in class). So view it as building skills in reading mathematics actively and study skills. That being said, I’m going to be available on discord etc. and will happily read with you if you want to bring questions and discuss. My goal is to teach you math study skills (teach a man to fish, you know?). So talk with me individually to get advice and help as you do this. Everything I assign during daily posts is considered part of the class and I will expect you to know this material.
The relevant section to read is Section 1.5 and 1.6 (they are each just over a page). Please read actively, learn the material, and do exercises for at least the hour.
To hand in: some of the exercises and/or any study notes you created for yourself.
To know: There are sets badges Sets III and Sets IV open and due on Friday.
To know: There’s a proof quiz due on Monday.
To know: Sets I has run through its three written evaluations. If you didn’t earn 2/2 on at least one of these, then you have not yet earned the badge. You have one more opportunity, which is an oral exam with me. I’ve just added detailed instructions for preparing for this (you must come with a prepared study sheet), under “Grading” above. Arrange with me individually, or just show up at office hours to do it. But show up prepared — if I don’t like your study sheet, you won’t earn the badge. I’ve opened an “oral exam” assignment on canvas, which gives me a place to put the grade, but doesn’t have a submission (I just enter the grade). But the deadline listed on canvas is a real deadline (you can’t leave this to the end of semester). For Sets I the due date is the end of office hours on Thursday Sept 24th. But don’t all crowd into those office hours, or I won’t be able to do them all. Find a time between now and then.
To Know: Please use PDF, PNG or JPG formats to upload files to canvas dropboxes. Don’t ZIP or compress files. Multiple files are fine. Please make sure they are readable. There are apps like CamScanner that turn photos into nice high-contrast PDFs.
To Know: I will post more badges and a proof quiz in the next day or so.
To Do: Log in to canvas and check on all the feedback/comments on all of your assignments so far. If you don’t understand anything on them, please ask me on discord (or email), and I’m always happy to meet with students online.
To Do: If you got less than 7/8 on the first proof quiz, please take a look at my video format solution to the quiz, available under “Media Gallery” on canvas.
To Do: Read Section 1.4 and do as many exercises as are appropriate for you from that section (i.e. keep doing them until you find them boring). Hand in a page’s worth of these exercises.
To Do: Read Section 3.2 in the book, up to the end of Example 3.2, about the Multiplication Principle. This is described in terms of lists in this book instead of in terms of tasks, but you should be able to see the connection.
To Know: No proof quiz due Monday. We are still ramping up to full speed with regard to proofs.
To Know: Thanks for your feedback on the feedback survey. I read these carefully and consider all your suggestions and really try to see if I can implement changes. I can’t always, but I try!
To Do: Practice proofs from the book: Chapter 4 Exercises 1-5 are similar to the proofs we’ve discussed in some detail so far. (If needed, read again Section 4.2 the first few pages. Also, recall there are odd-numbered answers in the back.)
To Do: Read Section 1.2 and do its exercises; this is practice on Cartesian products.
Hand in exercises to the daily dropbox on canvas.
If time remains, read a little further in Chapter 4 (it begins to discuss some examples with the notion of “divides”).
To Know: I have lowered the threshold to 36 daily tasks out of 45 to count as 100%. See the Grading page. This is because I know life happens, so if you have to quarantine, are ill, have religious observances, etc., this should cover it.
To Know: Until Friday night, you can attempt this week’s iteration of Sets I and Sets III written assessments. If you haven’t yet earned one or both badges, please give them a try. Sets I is on its third iteration, so pull out all the stops before you try it, to make sure you earn it: study up on that topic (review zoom videos, study textbook 1.1 and 1.3 with exercises, and contact me for clarifications on anything you got wrong on the earlier assessments. I’d rather talk to you personally about your errors than hand out solutions, so we can catch any misconceptions; try me on discord).
To Know: I will soon post the next proof quiz (this one is due Sept 9). There will be one due each Monday, ideally.
Without having the video evenness proof visible, write your own proof of the oddness theorem (If n is an odd integer, then n-squared is odd.) You’re aiming for the ability to transfer what you learned without having the structure of the proof available as a crutch. If you can’t, then watch the video again, then put it totally away again, and then try the proof again.
Hand our proof into the canvas dropbox.
With what time remains, or when you have time in the near future, you should read textbook Section 4.2 and the first three pages of 4.3 (at least). Don’t do this until after you’ve done the proof above (as it discusses the proof!). Then try exercises from Section 1.1 C and D on set builder notation.
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 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!