For Monday, March 9th, 2020

For Monday:

  • In class we considered the following problem:  How many ways can pairs be formed from 2n total people?  We obtained an answer:  (2n)!/ (n!2^n).  Give an argument that the result should also be {2n}\choose{2}   {2n-2}\choose{2} \cdots {4}\choose{2} {2}\choose{2}   / n! .  Are these really the same?  Can you give an algebraic proof that they are?
  • Read Hammack, Sections 3.3 and 3.4 and do Exercises (this will take more than an hour, so continue when you have time).  Hammack goes into more detail that we did in class, but all the extra detail is really just more practice of the same ideas, and more ways to talk about the same ideas.  In some cases, he just gives names to the different types of things we encountered already:  permutations, k-permutations.  In other cases, you’ll see him discuss the same principles I talked about in class, but written out formally with set notation (Subtraction Principle, Addition Principle etc).  This is great practice in set notation!  Try to line up what he writes with what you learned in class.  So although he goes into more detail, I think it’s great practice to read these chapters actively.  But it will also take a while, so budget some time when you have it to finish this task.
  • For pedagogical reasons, I plan to put Monday’s proof quiz off until Wednesday.  I’m hoping to do more examples of proofs that argue about counting.

For Friday, March 6th, 2020

For Friday:

  • Read Hammack, Section 3.4.
  • Do Exercises from Hammack, Sections 3.2 and 3.4.
  • On Friday’s badges quiz we will have two new badges, Counting I and Counting II.  These will be problems similar to the worksheets, asking you to count something.
  • I will keep the Proofs I and II badges on this week and next by request, but do try to make sure you earn them this week.
  • I’ve started a google album of blackboard photos from class.

Special Post: Update on Coronavirus Adjustments

Dear class,

I am making an attempt to adapt the course so as to decrease the opportunity for the spread of viruses.  We must do everything we can to protect the community at large, and vulnerable populations.

There will be several adjustments:

1) I want to make explicit that students can (and are strongly encouraged to) stay away from class if they have viral symptoms, including those that may indicate a common cold, such as a simple cough.  (The coronavirus can present as a simple cold for one person and be deadly for another.)  Please email me if this happens and I will do everything I can to make sure you are caught up.  The course structure allows for many dropped quizzes, and for following along via online handouts etc.  I am looking into recording lectures for those who cannot attend.

2) Earning Badges after they expire from the quiz will now take place via an online interaction in Canvas.  (Historically, doing them in office hour has resulted in crowded office hours.)  I will not do these in office hour.  See Canvas for info (you can earn a Sets badge this week if you don’t have all of them).

3) Office hours have recently changed, but are still available; consider using email.  I am also available to Skype.

4) Please contact me with any concerns you may have.


Dr. Stange

For Wednesday, March 4th, 2020

For Wednesday:

  • Please finish the counting worksheet and come with your answers to class.
  • Please read Hammack, Chapter 3, up to the end of Section 3.2.  Compare his and my versions (from class today) of the “Multiplication Principle for Counting”
  • Do some exercises from Chapter 3.2 with what time remains.
  • OFFICE HOUR CHANGES:  please see “About” in the menu above.

Special Post about Illness

Dear class,

As I’m sure you are aware, this cold and flu season has the potential to be more serious than some, with the advent of COVID-19.  I’d like to take a moment to remind you to take symptoms such as fever seriously, and do not attend class while ill.  Some illnesses, including the seasonal flu, which is circulating on campus now, can be deadly to certain populations, and it is our responsibility as a community to limit spread.  I have designed the course to be adaptable to those times when life gets in the way, and I’m happy to correspond in email and help you get back on track.

Thank you, and please stay healthy and happy!


Dr. Stange