This is your last daily post!

1. No proof for feedback because we have the functions quiz in class.  The practice problems are available under the Materials Archive tab.  That’s your work for today.
2. By midnight Wednesday night, please hand in your completed final self-eval sheet.  There’s a separate submission box on canvas for this.
3. The final exam is on Monday.  It will have proofs, yes.  It will be as if I stapled together a bunch of proof quizzes and content quizzes.
4. The deadlines have passed for grade improvements, but if you have MISSED a content quiz and not made it up, please contact me ASAP.
5. There is an opportunity for a proof improvement activity due at the final exam.  This is optional, and may improve your proof grade.
6. By midnight Tuesday night, please do your FCQs.  I read them with care, and they inform my future teaching, and they factor into department teaching evaluation.  They really do matter.
7. For office hours from now until the final, there’s a link to reserve a slot on the canvas main page (a google calendar reservation system), in case you want individualized reserved times (Math 308 in math building).  You can also email/discord me.
8. Class was recorded and will be on canvas.

For Monday:

Proof for feedback:

give a bijection

Tasks:

1. Please make sure you have kept your self-eval sheet updated.  There are some optional opportunities to improve your grades.  Please fill out FCQs.  See older post for some details.
2. Finish reading and doing exercises as needed from chapter 12 (all sections).
3. With remaining time, see how many bijections you can come up with between the sets on the last page of the class notes.
4. I have posted a functions practice sheet on the Materials Archive tab.

Proof for feedback:

pigeonhole proof

Tasks:

1. Please make sure you have kept your self-eval sheet updated.  There are some optional opportunities to improve your grades.  Please fill out FCQs.  See older post for some details.
2. Read Hammack, Section 12.3 and 12.4, and do exercises as needed.

Proof for feedback:

function on sets proof

Tasks:

1. Read through the administrative announcements from the last daily post.  Topics include FCQs (please fill them out!), opportunities for grade improvement, etc.
2. Class was recorded on Mon Apr 24 and is on canvas.
3. The proof quiz will be a quiz about showing something is or is not injective/surjective/bijective.  Review using Hammack, section 12.2.
4. In class, I left one half of one proof unfinished.  Please complete it.  (See class notes.)
5. Here are Pigeonhole Principle puzzle problems.  Please work on them.  The challenge is to find out what are the pigeons, what are the holes, which will lead you to a proof.

Proof for feedback:

bijective function

Tasks:

1. For office hours for the rest of term, there’s a link to reserve a slot on the canvas main page (a google calendar reservation system), in case you want individualized reserved times (Math 308 in math building).  You can also just email me.
2. There is an opportunity for a proof improvement activity due at the final exam.  This is optional, and may improve your proof grade.
3. Relations quiz solutions and past proof quiz solutions are on the Materials Archive tab.  Check them out.
4. You can also do a grade improvement for your relations quiz, as with previous quizzes.  Time is short, though; please get me a study sheet by early next week.
5. Next week’s proof quiz will be a proof about functions (injectivity, surjectivity, bijectivity).  We’ve been practicing these in class.
6. I will ask you to turn in your final self-eval form on the last day of class on canvas.  Make sure you are keeping it up to date.
7. FCQ administration starts next week.  I really appreciate you filling them out.
8. Class was recorded Fri Apr 21 and is on canvas.
9. Please complete and compare functions 2 worksheet and solutions.
10. Read Hammack, Section 12.2 and do exercises from that section (injective, surjective, bijective).

Proof for Feedback:

equivalence-relation-proof

Tasks:

1. Consider the following relation on the rational numbers:  rational numbers a and b are “integrally related” if their difference is an integer.  Prove that this is an equivalence relation.
2. Read Chapter 12 up to the end of Section 12.1 and do the exercises from 12.1.
3. Keep going on the second functions worksheet we began on Monday.  We will take this up in class.

Proof for feedback:

none (test on Relations wednesday)

Tasks:

• You have a test on Relations Wednesday.  There are practice problems on the Materials Archive tab.  You can also re-read Hammack, Chapter 11 and do exercises there.
• Late addition/notice/clarification:  I will also test modular arithmetic (I forgot to include some practice problems in the practice problems sheet, but see Hammack, 11.5 and its exercises.  Know how to do modular arithmetic.

Proof for Feedback:

function proof

Tasks:

1. Check out solutions to the last proof for feedback (in Materials Archive).
2. Read Hammack, Section 12, up to the end of 12.2.  This is what we covered in class on Friday (if you missed, see the video on canvas and course notes in the Materials Archive).
3. Do exercises from 12.2 and the proof for feedback.

Proof for feedback:

equiv-relation

Tasks:

1. This is a slightly longer daily post, because on Wednesday class was shortened to just the quiz because I was ill.  You should give yourself at least 1.5 hrs.
2. Read Hammack, Sections 11.3 and 11.4.
3. Do exercises from these sections.
4. In particular, in 11.4, Hammack is showing that an equivalence relation really captures a notion of “sameness” because it just “partitions” the set into “equivalence classes” (groups of things that are the same, like when you sorted your toys by colour as a kid).  Make sure the words “partition” and “equivalence class” are clear to you.
5. To aid in your reading, I’ve posted a lecture I gave and recorded in 2020 on the canvas Media Gallery.  This covers the reading material, in particular the formal proofs aspect.  Watching it is not required, but it may help you with the reading.

Proof for Feedback:

Induction again!  Hamkins, exercise 4.1:  Show that for all integers .

Tasks:

1. Compare your recent proofs for feedback to solutions (all listed on “Materials Archive” above).
2. Compare your last proof quiz (6, induction) to the solutions.  If you missed Monday’s class and don’t have your quiz back, contact me and I can send a picture.  Also, class was recorded so you can view it on canvas.
3. Be prepared for the induction proof quiz on Wednesday.
4. Read Hammack, Chapter 11 up to the end of 11.2.  Do exercises from 11.1 and 11.2.