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.
To Know: More badges will be posted soon, and a new proof. Badges due Friday, proof due Monday. Check canvas for dates on oral exams as needed.
To Know: I got slightly behind on grading proofs; apologies and I’ll be back at it shortly.
To Do: Check over your logic badges and contact me on discord to double check your errors and correct responses.
Revisit the proof we did in class about an irrational between two rationals. Use the recipe of the proof itself to find an irrational between 110 and 113. Write up a proof that the number you get is in the range given (it will look a lot like the general proof, but with these two numbers).
Prove that there exists a real number x such that x^6 = e^x. (Hint: Monday’s lecture).
Spend more time on Chapter 6, doing at least 2 new exercises.
To Know: More badges and proof quizzes will be up soon (badges are due Fridays and proofs Mondays). In the meanwhile, you can schedule an oral exam if needed for Sets II or Counting I by this Thursday, or Counting II for next Thursday.
I finished class with a theorem we didn’t get to prove; spend a few minutes pondering it; we’ll start next class there.
Read Chapter 6 up to at least the end of Section 6.2. Then do exercises from Chapter 6 Part A. Hand in at least 4 exercises. When time permits, read the rest of Chapter 6 and do some more exercises.
Reminders: The logic badges are open now, and from now on, in order to qualify to take the oral exam, you must make a good faith effort on at least two of the written attempts. If you earn 2/2 on any attempt (written or oral) you’ve earned the badge and you need do nothing more. If not, keep trying!
Reminder: There’s a proof due on Monday as usual. This one is a proof by contradiction.
To Do: In class we started on a contradiction worksheet. Please go through this worksheet and make sure you “set up” for a proof for contradiction for each puzzle. That means, explain what you will “assume for a contradiction”. Hand this in on canvas.
As time permits, continue to think about these puzzles and how to reach a contradiction once you have “set up” the beginning of the proof. I will give solutions in class, and you’ll get the most out of it (and enjoy it all the more) if you’ve struggled with them and tried to find answers, even if you haven’t actually succeeded on all of them.
To Know: Friday there are lots of new badges, the logic ones are open. Schedule an oral exam for sets badges or counting I if needed by the end of this week. The proof for Monday will be a proof by contradiction.
IMPORTANT: I’m instituting a policy that you must attempt at least 2 of the 3 written attempts for a badge to be eligible for an oral exam for that badge. The oral exams are not meant to be a substitute for the written work, they are meant to help work out the bugs after you’ve put in the hard work. Note: if you want a one-time exemption for this because this is a new policy and you didn’t anticipate it, drop me an email. But you must do the written badges from now on to have an attempt at an oral exam.
To know: Oral exams for Sets II and IV are open, and for Counting I.
To know: The rest of the logic badges will open up this week.
To Do: Read Section 2.9 and do about 6 of the exercises.
To Do: Read Section 2.10 and do all the exercises.