- Individual Work is due on canvas.
- We will do some examples of proofs with sets and/or take up the individual work.
- The proof quiz will be something to do with sets. You can practice with the individual work due Friday, and with Chapter 8, Examples 8.8, 8.9, 8.11, 8.12, and Exercises 6, 7, 21, 22.

- Please attempt the counting worksheet, 1-12. (Problem 13 is a challenge problem, you can sleep on it if you want.) We’ll take this up in class.
- Reminders:
- You can earn any badge in office hour (preparation required: details here).
- Individual work due Friday (under Resources/Groupwork). Hand in on canvas.
- I believe I have a list of those interested in presenting one more time. If you’re willing to do this this coming Friday (this week), please let me know. I may take 1-2 presentations to make sure we aren’t too overloaded on the last day. Remember: you can present on anything mathematically relevant, including groupwork and individualwork you haven’t presented before.

- Please read Hammack, Section 11, up to the end of 11.3. This is review of all we have covered about relations.
- Please read Hammack, Section 11.4, The Integers Modulo n. Do Exercises 1–8.
**Badges quiz:**Last chance for Logic and Proofs badges. Any badges can be earned in office hour. I will also add Modular Arithmetic badge, and Counting Badges (these are the only ones remaining). The Counting Badges are certainly premature: we may or may not start that topic on Monday. But if you want to try them out, Chapter 3 of Hammack is the place to start.*There are only three more badges quizzes.*- Meanwhile, I suggest you use the weekend to review anything that needs reviewing to bring your badges score up. Hammack has exercises with solutions in the back which are very good preparation — just look up the relevant topic.
- Be aware there will be an individual work due Friday; it has been posted.
- The grading change to the 5% participation score (as described in this post) has been updated in the “Grading” tab above.

- Presentation day. You can present any proofs that you wish, including proofs from group work or individual work. The requirement is only that it be mathematically interesting and pertinent to the class. Even if you have presented twice, you can volunteer, but those needing presentation credit will be given priority. If you want to present something, it helps if you email me so I can get the computer set up ahead of time with the correct things (but it’s not strictly required).
- I will now open office hour badges to any badges you want to earn, whether they are active on the in-class quizzes or not. One per week.
- I will ask you to prove something with functions in the abstract. To study, I suggest you read the handouts about function having an inverse if and only if it is bijective (with slots, and filled). The type of problems I may ask are similar to that, so study those carefully.

- On Monday, we did this worksheet on relations. Finish it at home, and we will discuss it together in class.
- There’s a 5% presentation/participation/groupwork grade in the class. In light of the changes to our groupwork requirements in the second half of semester, I’m replacing the system with the following simpler, more generous system. This should not hurt your grade.
- You will get a full 5% if you present at least 2 times, and scribe at least 2 times for a group, and hand in at least 3 decent efforts at the individual works on canvas.
- Your grade will otherwise be proportional to how many of the 7 tasks above you have done decently.

- In light of the above, you may wish to volunteer to present on one of the two remaining presentation days, which are April 13th and 27th. You can present any proofs that you wish, including proofs from groupwork or individual work. The requirement is only that it be mathematically interesting and pertinent to the class. Even if you have presented twice, you can volunteer, but those needing presentation credit will be given priority.
- The remaining Logic and Proofs badges will only appear once more, next week. After that they can be earned in office hour. We will continue to have Functions, Relations and Synthesis on the badges quizzes. Soon we will add the remaining badges also.
- This coming Friday, I will ask you to prove something with functions in the abstract. To study, I suggest you read the handouts about function having an inverse if and only if it is bijective (with slots, and filled). The type of problems I may ask are similar to that, so study those carefully.

**Additional:**

- You may be interested in
**CSCI 3434 Theory of Computation**. Here’s the blurb:- The theory of computation is the mathematical foundation of computer science, developed by mathematicians when computers were a mere thought experiment. In fact, the theory of computation is not about computers at all, but about the nature of computation itself: what it means for a mathematical function to be amenable to calculation or computation. Perhaps surprisingly, some simple functions cannot be computed. Moreover, these incomputable functions are just the first floor of an infinite-story building; the second floor contains functions which cannot be computed even if one could compute the incomputable functions on the first floor, and so on. For functions on the ground level, which can be computed, we further ask, how efficiently can they be computed. CSCI 3434 is accessible to math majors, and the prerequisites will be waived for math majors having taken at least one proof-based course. (If interested, email the instructor at raf@colorado.edu.)

- We will start relations in honest on Monday.
- Badges quiz may include new relations Badges.
- To prepare, you can read Hammack, Chapter 11, especially Sections 11.0 and 11.1, and do some exercises. But don’t worry if anything is confusing — just bring your questions! We will work on it in class.

- homework is due (submission box on canvas is open)
- there will be another induction proof quiz
- you may want to view a completed version of the bijection-inverse proof we finished today.
- read Hammack, 12.4 – 12.6 to wrap up our study of functions.

- Please fill in a proof on this work-sheet. We’ll take it up in class.
- Reminder that Friday is a proofs quiz (induction) and an individual assignment (listed now under Resources).
- There’s a math club talk on Wednesday (Transforming shapes into algebra): math club.

**For Monday:**

- There will be a
**badges quiz**. It will cover Logic, Functions, Proofs, Synthesis. It will include Logic I,II,IV, Proofs I,II**for the last time.** - You can earn badges in office hour (W/Th 1 pm): you can earn any badge which has stopped appearing on the quiz, so Sets I-IV, Logic I,II,IV and Proofs I,II. See this old post for details how to do this (it requires preparation). Maximum one badge per week, so plan ahead. This is an excellent way to bring your grade up by making an extra effort during the last weeks.
**Look ahead:**the week following break will be another individual assignment due Friday. I’ll post it shortly. On that Friday we’ll have another induction proof quiz (because induction is so important).

**Proof Quiz**will be a proof that a function is/is not injective/surjective. Read Hammack Section 12.2. Examples 12.4 and 12.5 are ideal models, as are exercises 2-10 (where “verify” means “prove or disprove” (disprove means prove the negation).**Reminder that individual homework is due.**The assignment is under Resources (above) under Groupwork. (But you can do it individually.) Hand in on canvas.- You can still earn badges in office hour Wed/Thur, as explained previously.
- In class, we will continue talking about functions and cardinalities.