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.

To Do:

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.

Note: This may take more than an hour. Find time to do the rest when you can; if you need to hand in the daily before you are done, just hand in at least a dozen exercises total.

Final Note: There’s a Math Club at CU that hosts talks. Here’s the website (I’m speaking Tue morning) http://math.colorado.edu/mathclub/.

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: There’s a proof by contrapositive due Monday. You can now schedule an oral exam for Sets IV if you need/want. Logic badges will be gradually appearing, beginning with truth tables (this week), then logical equivalences (for next week), then the others.

To do: Read (actively, as always!) Section 2.7 (Quantifiers), and do all the exercises for 2.7 to hand in on canvas.

Don’t forget: New badges quizzes for this Friday, and a new proof quiz will be up soon.

In class, we studied proof by contrapositive. Read Section 5.1 of your text. Do at least 4 exercises from Chapter 5 Part A to turn into the dropbox; more if time permits.

To Know: Soon more badges and a proof quiz will appear. Don’t forget about doing your Sets III oral exam if you didn’t already earn 2/2 on one of the written versions! It’s not required (I’m not going to chase you) but your grade is based on the number of badges you earn.

Do as much of the LaTeX’ing as you find useful from the worksheet from class today. Ask me if you have any questions. I’m not going to grade you on LaTeX but I strongly encourage you to try it for your proof quizzes! Next time I’ll include the LaTeX source from the proof quiz so you can use that as a template to start with.

Read Section 2.4 and 2.6 from the text, and do at least six of the 2.6 Exercises Part A.

To Know: Some of you have been slacking a bit on the daily tasks, and the grader asked me about it; I’m going to tell him to be a little more rigorous in his expectations.

To Know: There is a proof quiz due Monday. The Sets III badge is open for the “Oral Exam” — arrange with me or show up at office hour with your study sheet according to the instructions in the Grading page.

To Do: Actively read Sections 2.2 and 2.3 of your text. Then actively read Section 2.5 and do Exercises from 2.5 (you can skip 2 because it includes a symbol we haven’t done, or you can read up on it and then do it). Hand in at least a handful of these truth tables. Do enough so you “get it” and feel confident you could do more.