IMPORTANT TO DO: Watch this YouTube video I made: Modular Arithmetic User’s Manual (9:23). This is part of the course lecture material, in flipped form.

To Do: Here’s a follow-up worksheet to do and hand in on canvas’s daily dropbox.

To Do (time permitting): Think about how to finish off the proof from Friday’s class; I’ll finish it up on Monday.

To Know: There’s a proof quiz due Monday on canvas.

To Know: I’ve posted more badges for Friday. I’ve opened the Relations I & II badges. Make arrangements for any oral exams you may need. Please please review the videos/material for functions and figure out what you got wrong before attempting them again (there are standard errors you can overcome with a little attention to your first few attempts). The fastest way to reach me is via discord, and I’m always happy to help.

To Know: It’s getting close to end of semester. The last two badges may end up compressed (either more frequent deadlines or fewer attempts). That’s basically just Modular Arithmetic and Proofs III.

To Do: Look over your Proof Quiz 7 and 8 and compare to Proof Quiz 7 Solutions and Proof Quiz 8 Solutions. I’ve also posted a video solution for Proof Quiz 8 because I had some things to say about it. Please watch the video (available on canvas).

To Do: Read Section 14.4 of your text. This has the detailed proof that I only sketched in class today. Do exercises 1 and 2 to hand in.

To Know: I extended all the badges due dates to Monday, to give everyone more breathing room.

To Know: A proof quiz has been posted, due Monday.

To Know: There was some problem with the playlists on canvas; the other tab (instead of the default Playlists view) is a full directory of videos. They are all there. I’ve tried to fix the playlists by breaking them up by month. If a video is missing try the other tab.

To Do: In class on Wednesday we gave three “properties” of the definition of “same cardinality” that I labelled “Reflexivity”, “Symmetry” and “Transitivity”. Review the video/notes and then attempt a proof of Symmetry and a proof of Transitivity (I did Reflexivity in class). Hand in on canvas.

To know: I’ll be putting up the other functions badges tonight, as well as some repeats on older ones (notably the two proofs badges); make sure you take a crack at all of them. I’ll also open up some oral exams, so please schedule those with me if you’d like.

To Do: I ended Wednesday’s class with some sets you are familiar with, and I’d like you to try to come up with bijections between some of them, to show they are the same cardinality. Bring your bright ideas to class. To hand in on canvas: whatever thoughts you have on this, e.g. some bijections or some ideas that didn’t work, etc. (It’s a gently-graded daily post, since I want to give a bit of a break this week, but do hand in something thoughtful.)

To Know: I have posted another proof quiz due Monday. It’ll be about the definitions of injective/surjective. The text has examples, and we did examples in class, but here’s two more from YouTube: surjective and injective.

To Know: I’ll soon (over the weekend) be posting a video solution to Quiz 6, whose scores were released.

To Do: Optionally: Watch the YouTube videos above giving an injective and surjective proof example, in preparation for the quiz.

To Do: Read Chapter 12.4 (Composition) and do Exercises 1-8 to hand in.

To Know: I have posted new badges, including Proofs I and II on contrapositive and contradiction proofs, and Functions II (on injective, surjective, bijective). Schedule oral exams as needed (check canvas; these open after three written attempts expire).

To Know: My classes lately have been improvisations based around the worksheets I would normally assign for groupwork on this topic. I’ll be posting them on the “History” pages along with solutions, and they are excellent study aids.

To Do: Check out your badges status on canvas. Schedule oral exams and plan to do new badges as needed!

To Do: Return to Chapter 12.2 and do more exercises. Do 5-10 and hand in on canvas. There are similar examples in the chapter.

To Know: Please keep an eye on oral exams if you are eligible. In particular, Counting II is this week if you’d like to schedule it. Reminder that you need to have at least attempted two of the written attempts to be eligible for the oral exam.

To Know: The book introduces functions in Section 12.1, but does them in terms of relations, which I don’t like. So you might want to skip that chapter.

To Know: I’ve made videos with solutions to Quizzes 4 and 5 (available on canvas). Here are PDFs of Soln Quiz 4 and Soln Quiz 5.

To Do: Open up your proof quiz 4 and 5 in canvas where you can see my comments and view the solution video (available on canvas). Contact me with any lingering questions.

To Do: Read Section 12.2 (actively as always!). Do Exercises 1-4 and hand in on canvas.

To Know: Canvas is not doing a great job at estimating grades, because of our unusual grading system. Please keep in mind the grade it shows you is not very accurate. You can always refer to the formulas/info on the website and compute where you actually stand.

To Do: Finish the second proof (continuity) example we did in class today. We did all the warm-up and discussion and scratch work in class, but didn’t write the proof (class ended). The theorem is: The function f(x) = x^2 is continuous at x=0. Hand this in on the daily canvas dropbox.

Read (actively) Section 13.7 on Convergence of Sequences. This may help with the proof quiz due Monday also. Note: the textbook treats continuity a little differently than I did in class today; just a different perspective.