To Do: Here are solutions to Proof Quiz #2. Please (1) open up your quiz comments on canvas and view the annotations I’ve added to your proofs, and (2) watch the video guide to the solutions I gave (it is on canvas under “Media Gallery > Other…” playlist).
To Do: Watch this YouTube Video showing how graph theory can be used to solve Instant Insanity. It’s pretty involved, and I’m not going to quiz you on the details, but it will give you an idea of its uses.
To Know: More badges quizzes are always appearing. Reminder that Thursday is the last day for the oral exam for Sets I.
To hand in on canvas:
Explain how many ways you can order 12 different dogs in a row, and why (in terms of multiplication principle).
Explain how many ways you can choose a subset of exactly 4 dogs from the 12 different dogs, in terms of multiplication principle and overcounting. Explain every part of the formula from first principles (don’t just say “it’s a binomial coefficient” or “use the formula for subsets” — I want the _why_. Review the class video if needed.)
With what time remains, do Exercises for Section 3.2, starting at the beginning, working until your hour is up. You may find you wish to read some of the text Section 3.2 to support your work, although we have covered the basic strategies you need for these problems. Check your answers in the back (for odds) as you go and self-correct.
You have until Thursday the 24th office hour to do the Sets I oral exam if needed.
If groupwork continues to the end of class, I’ll make a “broadcast” announcement at the end of class, because sometimes I’m still helping students. I won’t always pull the groups back to the main room. Feel free to politely log out at the appointed hour.
I’ve noticed a few students “running away” when we transition to groupwork. The material covered in groupwork is important, so I urge you not to, but it is your choice. I am aware of who it is, so no need to do it covertly. Instead, I appreciate if you do it immediately, before I set up the breakout rooms, because if you wait to do it, then the breakout rooms end up populated unevenly and it’s a pain to fix.
To Do: Write up solutions to the Counting Worksheet, problems 1-6. For each problem, give the solution in the following format:
Explain the “process” of creating a burrito, picking a team, committee, or whatever is appropriate. What are the sub-tasks?
Give the solution by reference to this “process” description. If you use multiplication principle, label each number you are multiplying by the corresponding sub-task.
Hint: for problem 5, choose the chair before the remainder of the committee.
Hand these in on canvas.
When time permits: Read Section 1.7 and do some exercises. This concludes the Sets II material and that badge will open shortly.
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.