Thank you all for a great semester! I can have office hours if you like over the next few days. I’ll be on discord at the usual Tuesday 12 pm slot tomorrow.
Final proof quiz solutions
The last daily post is below — this is just a spot to post the most recent proof quiz solutions.
 Proof Quiz 11
 Proof Quiz 12
 Proof Quiz 13 will be coming after it is graded
Due Monday December 7th
For Mon:
 Don’t forget there’s one more proofs quiz due Monday (one more chance to replace one of your lower grades with a higher one!). It is induction.
 This is our last daily post! It is full of announcements, so please please read through them all.
 UPDATE: Online FCQs are open until Monday. FCQs are used to evaluate your instructors for reappointment, promotion and tenure, and to inform the department about their teaching effectiveness. I, personally, greatly appreciate feedback and work to improve my teaching using your feedback. Also, if you haven’t answered my own additional feedback form, please please do!
 The FINAL EXAM will be available for the entire exam period. It will be takehome style, on canvas, due at 11:59 pm on the 13th. This is a HARD DEADLINE. Plan ahead! Plan to complete it the day before the deadline if possible. Upload a draft of whatever you have earlier in the day so that if you have internet troubles, you don’t lose the entire exam. Email me before the deadline if you are having problems.
 The final day will be a review exercise of some sort (in the past I’ve done clickerstyle team competition in class like trivia night… I’ll have to see how to adapt it online, I just heard of something called kahoot… We’ll see, but hopefully fun!)
 And finally, a big THANK YOU to everyone for attending the course and for keeping a positive attitude through our online learning experience, for making me smile and putting forth your best efforts. It’s you, the students, who make all the work worth it. Thank you.
 To Do: For your final daily post, you can use the text entry box to write one thing you learned from this course that you think will be useful or that you are glad you learned. I’m curious what students take away. That’s it!
Due Friday December 4th
 Please know that online FCQs are open until Friday. FCQs are used to evaluate your instructors for reappointment, promotion and tenure, and to inform the department about their teaching effectiveness. I, personally, greatly appreciate feedback and work to improve my teaching using your feedback. Also, if you haven’t answered my own additional feedback form, please do!
 The FINAL EXAM will be available for the entire exam period. It will be takehome style, on canvas, due at 11:59 pm on the 13th. This is a HARD DEADLINE. Plan ahead! Plan to complete it the day before the deadline if possible. Upload a draft of whatever you have earlier in the day so that if you have internet troubles, you don’t lose the entire exam. Email me before the deadline if you are having problems.
 To Know: On Friday, we will have some other professors from the mathematics department join the class to ask for some feedback on my teaching. They will run a “classroom interview.” I greatly appreciate your feedback, both positive and negative. It goes into my file for future evaluation for promotion.
 To Still Know: Because of the Thanksgiving break, badges and proofs due dates are pushed back. Here’s the remaining due dates:

 Badges will be due Friday, December 4th.
 Proof Quizzes will be due Wednesday, December 2nd and Monday, December 7th. They will both be on induction.

 Last chance at ORAL EXAMS should be scheduled THIS WEEK (Thursday). There’s no oral exam for Modular Arithmetic or Proofs III (no time left). But you can do Functions and Relations badges this week.
 For Fun: 20 proofs of Euler’s Formula! (The thing we proved in class: VE+F=2)
 To Do: Read section 10.2 of Hammack, and do Exercises Chapter 10, #10 to hand in.
Due Wednesday, December 2nd
For Wed:
 To Still Know: Because of the Thanksgiving break, badges and proofs due dates are pushed back. Here’s the remaining due dates:

 Badges will be due Monday, November 30th and Friday, December 4th.
 Proof Quizzes will be due Wednesday, December 2nd and Monday, December 7th. They will both be on induction.

 Last chance at ORAL EXAMS should be scheduled THIS WEEK (Tuesday and Thursday). There’s no oral exam for Modular Arithmetic or Proofs III (no time left). But you can do Functions and Relations badges this week.
 The final exam will be take home and will be similar to badges quizzes and proof quizzes. Some short answer questions will involve more than one badge at once.
 Please know that online FCQs are open. FCQs are used to evaluate your instructors for reappointment, promotion and tenure, and to inform the department about their teaching effectiveness. I, personally, greatly appreciate feedback and work to improve my teaching using your feedback.
 To Do:
 Please take some time to fill in this feedback form on aspects of the course. I list some of the design aspects of our course and ask whether they were helpful or problematic. It’s a big help to me for designing for future students. It’s anonymous.
 Read Chapter 10, up to the end of 10.2 (end of page 186). There are a bunch of proof examples, and please spend some careful time with each one to isolate the inductive structure for yourself. Notice the differences in his style (from mine) and convince yourself they are only stylistic differences.
 Hand in Exercise 2 from Chapter 10.
Due Monday November 30th
For Mon:
 I hope everyone has/had a wonderful thanksgiving, whether remote, takeout, whatever it is/was. 🙂
 To Know: Because of the Thanksgiving break, badges and proofs due dates are pushed back. Here’s the remaining due dates:

 Badges will be due Monday, November 30th and Friday, December 4th.
 Proof Quizzes will be due Wednesday, December 2nd and Monday, December 7th. They will both be on induction.

 Practice setting up induction using this induction worksheet. This is your first practice for the Proofs III badge, and we’ll take it up in class, so you may wish to leave this badge for last and do it after class (it’s due Monday at midnight).
 Hand in your worksheet answers on canvas.
Due Wednesday November 25th
For Wed:
 Please know that online FCQs are open. FCQs are used to evaluate your instructors for promotion and tenure, and to inform the department about their teaching effectiveness. I, personally, greatly appreciate feedback and work to improve my teaching using your feedback.
 To hand in as the daily exercise, try your hand at a few proofs (whatever the 1 hour allows):

 Complete the proof I ended class with on Monday. I’ll complete it in class Wednesday.
 Prove that if G is a tree, then every edge of G is a cut edge. An edge is a “cut edge” if removing that edge produces a disconnected graph.
 Prove that if every edge of a connected graph G is a cut edge, then G is a tree.

Due Monday November 23rd
For Mon:
 To Know: There is a pigeonhole proof quiz on canvas. Check canvas for available oral exams to schedule.
 To Know: On Monday we’ll start talking about graph theory. We’ll use it to practice methods of proof, including induction, and return to the problem we started Day 1 of class with.
 To Do:

 Read Section 3.9 of Hammack, where he discusses the pigeonhole principle and its related “division principle” and does a couple of nice problems with it.
 Hand in Exercises Section 3.9, #1,2,3

Due Friday November 20th
For Fri:
 To Know: I have opened up the modular arithmetic badge and continued the open badges (due Friday). The only badge missing is Induction, which is our next big topic.
 To Know: Here’s a solution to the previous day’s daily post.
 To Do: Find 3/7 mod 13.
 To Do: Here’s a list of pigeonhole problems that I am drawing from for the problems in class. Try your hand at the ones we haven’t yet done in class.
 To hand in: 3/7 mod 13 and any guesses/ideas/solutions for the pigeonhole problems from that sheet that we haven’t done in class.
Due Wednesday November 18th
For Wed:
 To Do: Read the Solutions to Proof Quiz #9. Read them actively, as always. There are three proofs presented, and you only submitted one, so there’s something to learn there. And please read the second page with common errors, where I explain the most common error with surjectivity! (I decided to do solutions just text, not video this time.)
 To Do: Take a look at the multiplication tables here, and collect as many patterns as you can. Just try to describe them.
 To Do (IMPORTANT; NEW CONTENT): Watch my followup YouTube video on defining the integers modulo n (17:26). This is more practice with the formalism, and the work one needs to do to make sure integers mod n are welldefined.
 To Do: Complete the exercise mentioned at 12:48 in the video. Hand in on canvas.