There will be a proof quiz, on a combinatorial proof. To prepare, study the ones we have touched on in class. I’ve prepared a sheet that has a list of these, together with hints. Use this to practice writing combinatorial proofs.

You may come to office hour this week for a badge. Office hours are set for Wed/Thur 1-2 pm. Please email if you’d like to set other hours.

The final exam is in our regular room. This information should show in your my.cu.edu and also via the registrar’s list of times. It is:

Study counting by doing Hammack’s exercises in Sections 3.1-3.3, completing any you haven’t yet done.

Campus FCQs had some error and questions changed on Tuesday. Please log in and make sure your FCQs are the way you want them: http://colorado.campuslabs.com/courseeval. I greatly appreciate your feedback.

Monday there will be a badges quiz (same badges as last time).

Wednesday there will be a final proof quiz on Combinatorial Proof.

Next week you can earn a badge in office hour. There will be office hours at least 1-2 pm on Wed and Thur. I can expand these as needed; please email.

I was missing a few presentations in canvas and these are being added in. There is still an opportunity to present if you wish. See Grading for info on how grading is computed. Currently canvas is not correctly computing grades.

The Association for Women in Mathematics, CU Boulder Chapter, is hosting a study session Thursday, May 3, 5-7pm in ECCR 135. This study session is primarily aimed at undergraduates, graduate students are welcome to come, enjoy some free pizza and snacks, and talk to/get help from other graduate students in preparing for your final exams.

Office hours this week are Thursday 12:30-2:30 and Friday 1-2. Remember you can earn a badge in office hour, by preparing as described in this old post.

The last badges quiz is Monday. Plan which ones you will study for. All information is updated in canvas.

You can present on Friday if you wish. I have posted my records of presentations/scribing/assignments for your participation grade on canvas. Out of concern for sufficient remaining time for presentations, I’m dropping one of the 6 requirements for the grade. See Grading.

See the last post for grading changes and quiz schedule changes, as well as exam times.

Please complete your online FCQs. I read these very carefully and reflect on all your feedback. The department and university also use these to evaluate faculty. They really do have an impact, so I very much appreciate your thoughtful responses.

My apologies, but I have to move today’s (Wednesday’s) 1-2 pm office hour to Friday 1-2 pm. I am also expanding Thursday’s office hour. Please email me if you need to set up a separate time. Just to confirm, this week I have office hour:

Thursday 12:30-2:30 pm
Friday 1-2 pm

My apologies about this.

For Wednesday:

I will administer online FCQs on Wednesday. I’ll set aside 10 minutes at the end of class for you to log in and fill out FCQs on your phone, tablet or computer (I will leave the room). FCQs are very important and I strongly encourage you to fill them out. I use them to improve my teaching, and my department and university use them to evaluate me as a faculty member. If you miss class, you can also fill them out anytime at http://colorado.campuslabs.com/courseeval

Note the grading changes below. I have been careful to make sure these do not penalize you for my miscalculation; please contact me if needed.

Revisit the homework from the last daily post if you have not finished it.

Read Hammack, Section 3.3. Try Exercises 1-5.

Recall the definition 3.2 on page 74 of Hammack, of “n choose k”. Try to write a combinatorial proof that (n choose k) is the same as (n choose (n-k)). Don’t write this as an algebraic proof (it is possible to prove it by writing out both formulas as in Fact 3.3). Instead, explain why both quantities count the same thing, and must therefore be equal.

There are a lot of useful things in the last daily post: review it (exam schedule, info on badges in office hour, consider presenting this week, etc.)

Important Grading Changes: I miscalculated and didn’t realize we are missing one last friday. Here are the adjustments:

There will be only one more proof quiz, on Wednesday May 2nd. Your grade will be best 7 of your 13 efforts, overall.

This week’s group assignment is the last assignment. For participation, your 5% presentation/participation/groupwork grade in the class will be based on 6 items instead of 7: if you present at least 2 times, and scribe at least 2 times for a group, and hand in at least 2 decent efforts at the individual works on canvas. (Your grade will otherwise be proportional to how many of the 6 tasks above you have done decently.)

These adjustments are now changed in the Grading page.

Return to the Counting Worksheet and work on 1-12 if you aren’t sure about your answers yet. We’ll finish taking this up (and badges quiz questions) in class Monday.

To help with Counting, check out Hammack, Examples 3.2 and 3.3. You can read Chapter 3 as needed to work up to these examples.

Try the following problems from Hammack: Section 3.1, 2,4,5,7; and Section 3.2, 3,7,8.

Be aware this coming week is the last groupwork week. It will be posted soon.

The Monday badges quiz will include everything except Sets, Logic and Proofs. In other words, it will be Counting, Relations, Functions, Modular Arithmetic and Synthesis.

Next week’s Friday Proof Quiz will be a Combinatorial Proof (count something two different ways to prove a formula).

We will focus on Counting and Combinatorial Proof all next week.

You may earn one badge in office hour next week (any badges except Synthesis). This is an excellent way to help your grade! Please prepare as described in the original post. Tip: choose a badge you are having trouble getting full credit on, or is no longer on the quiz. You can check which badges you have on canvas. You can schedule a time (email me) if the regular hours aren’t good for you.

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.)