For Wednesday, April 1st, 2020

For Wednesday:

  • Please try to prove the three properties of the definition of cardinality given in Monday’s video (you can watch the video on canvas), namely reflexivity, symmetry and transitivity of the notion of “same cardinality.”
  • Reminder that due April 3rd are the next proof quiz (see Assignments on Canvas) and any badges quizzes you want to attempt this week (see Quizzes on Canvas).  Read “Remote Structure” in the menu above for details on how these work.
  • On Wednesday, I’m going to give a LaTeX workshop.  LaTeX is a typesetting system for mathematics and its an invaluable tool to learn as a math major; and it only takes one class period to really get going.  It’s a total break from the work we’ve been doing.  Join zoom as usual and I’ll have instructions.

For Monday, March 30th (with Spring Break Update)

The Spring Break Post

  • I hope you’re all hanging in there!
  • Read my post on remote learning.
  • Read the page “Remote Structure” in the menu above for my planned structure for the rest of the course.  Read in detail!
  • Over the course of spring break, please study and attempt Badges Quizzes as they appear in Canvas (they will gradually begin to appear over break).  Each quiz is one badge, so study that badge, and then set aside 10 minutes for the quiz when you feel ready.
  • Read Hammack, 12.5 and 12.6 and do exercises.
  • Catch up anything that needs catching up (“Remote Structure” above lists resources for everything you may have missed).
  • If you’d like to form a Zoom study group (which I encourage, see my email for info on that).

For Friday, March 20th, 2020

For Friday:

  • If you are moving home etc., be aware that I’m recording lectures, which you can find on Canvas under “Media Gallery” and you can view the blackboard screenshots and other materials under “Lectures” above.  There will be no due dates until after spring break.  Please catch up as time allows!
  • Right now my plan is to make the course as adaptable to your varying circumstances as I can.  That means I will set up a synchronous, regular work schedule for those that can, with options to be asynchronous and/or uneven in worktime for those who need it.  I’ll be taking spring break to set things up for the rest of semester in this regard.
  • Read Hammack 12.4, Composition, and do exercises.
  • Do the first problem on the worksheet (visit Wednesday’s links in “Lectures” above), which I will take up on Friday.
  • When time permits, read Hammack 12.3 for a revisit of the pigeonhole principle (as I discussed in Wed’s zoom lecture).
  • In today’s Zoom meeting I didn’t quite get to the definition of “inverse”.  I’ll get to that at the beginning of Friday, but it’s ok to work ahead!  It’s Hammack 12.5.

For Wednesday, March 18th, 2020

For Wednesday:

  • I hope you are all well.  Some of you have been missing since the move online, and I’m concerned; please email me to let me know your situation.  Also please email if you are unable to join Zoom for any reason and let me know how I can help… please just email me in general!  I’m trying to keep track of and help every one of you individually if needed.  Please rest assured that I’m dedicated to helping you succeed in this course, and we can catch up anything that is missed during the first week or two of online instruction.  Just reach out to me.
  • We continue via Zoom!  Thanks for giving feedback on the canvas survey of your preferences for how to continue.  Please log in and do that if you haven’t yet.
  • Please go over the two functions worksheets and solutions (click Lectures), comparing to your own work.
  • Read Hammack, Chapter 12.2 on proofs of injectivity and surjectivity.  The exercises from this chapter are excellent; do them.
  • Reminder:  no due dates until after spring break.  If anyone wants a zoom office hour, email me, but for now I won’t schedule them until after spring break, either, once we get a schedule in place.

For Monday, March 16th

For Monday:

  • Please fill out the survey you’ll find on Canvas, so I can get some feedback on how the shift to online is going, what I can do to help, if you would like to get paired up into zoom study groups, etc.
  • Please continue to work through the Second Functions Worksheet; here’s a google docs version.  Friday’s lecture (and all Zoom lectures) will be posted on Canvas under “Media Gallery”, and screenshots will continue to go up in the Google Pics folder, so you can review them; you’ll find this helpful for basics about functions, domain, codomain, injectivity, surjectivity and bijectivity.  On the second functions worksheet, you will also encounter new definitions (see PDF version for those), which you should try to decipher yourself.  Another resource is Hammack, Chapter 12 (although note: he does relations first, and I do relations second, which causes a little mismatch).
  • Please put your answers into the google docs version and we will try sharing these answers together in Zoom on Monday.
  • This is all a giant unexpected experiment; thank you again for your patience and willingness.

Taking care of ourselves and our community

Dear students,
Events are evolving very quickly, and for each of us, the particular pressures and anxieties are very personal and very different.  I just want to write to remind everyone that taking care of ourselves and our loved ones takes priority over grades and studies, even as classes continue.
As we move to online learning, I will try to make the rest of this class as modular and adaptable as I can.  I will record all the videos from Zoom sessions, and I will not require attendance at Zoom sessions (although I encourage and appreciate your participation if it works for you).  All future assessments will be available on Canvas and be flexible in timing (meaning, you can choose when to take the assessment from a relatively large date/time range).  I won’t set any due dates until after spring break.
I hope that your studies in this class can be a haven from the pressures you may be under right now — I certainly think of doing math as an escape.  But in any case, what I don’t want is for the pressures of this class to be adding to a difficult situation.  Please be in touch with me to discuss your personal situation with regards to the course, especially if you foresee personal circumstances interfering with your ability to continue in the course.  We still have material to cover and grades to assign, but I will be as flexible as I possibly can in getting us all to the finish line.
And finally, let’s all come together to support one another.  Let’s use Canvas to make contact with others to study with, and let’s have lots of patience and grace as we adjust to new modes.
Dr. Stange

For Friday, March 13th, 2020

For Friday:

  • Class is now fully online.  There are no quizzes this week, while we make the adjustment.  Thank you for your understanding as the transition is inevitably a little bumpy.  And please feel free to give me feedback on your experience and how we can make this better.
  • Please complete the first functions worksheet for Friday.  On a separate paper is fine, of course, no need to print.  I will be posting the pictures from today’s brief lecture in the Blackboard Pics Gallery.  I will start recording lectures as much as possible.
  • On Friday, I will mainly lecture with Zoom, to give people a bit more time to get up to speed with the technology.  However, please investigate ways you can make your Zoom experience as interactive as possible, so we can continue active learning:
    • Try to find a quiet place to Zoom, or a short-range microphone or headset, so you can talk without background noise.  The ECCR classroom is still available, if that’s helpful for a few days.
    • Investigate options for sharing math writing.  The best option for this is a zoom login from a tablet with writing capability (zoom has a “whiteboard” feature that everyone can share if they can write; you can log in to zoom twice at a time if needed).  But it could also include a workflow for uploading pictures from your phone, or a repositionable webcam, or even use of for those who know some LaTeX.  But we will need this if we plan to do math communication online, so please look into these options and find something that works for YOU to share math writing on Zoom.  Just do the best you can, and share your ideas and solutions with me so I can share them with everyone.
    • LATE ADDITION:  Check out how you can write equations in a shared Google document!  Here’s an example that is collaboratively editable by anyone at CU who clicks that link.  In a new Google doc, you can click “Insert” and choose “Equation” and an equation editor will pop up.


Dear all,

I’ve developed a cough this morning.  (No fever or anything else, but this follows on my young son developing a cough a few days ago.)

As a result, I’m moving up the timeline to switch to online learning, and I’ll be teaching from my home office this afternoon.  Here’s what you need to know:

1) Don’t go to class.  If you do go to class, and only realize what’s going on when you get there, please write a message on the blackboard:  “Math 2001 is online today:  go to”

2) Download Zoom ahead of time (

3) Then during the ten minutes before our regular lecture hour, go to and click on the new “Zoom” menu item in the top line menu.  You’ll find instructions there.

Please view today as a day to work the kinks out.  I will have a worksheet for the day, and if I do any lecturing, I will record it as a video you can watch later.  So if you have a technology issue, just take your time and arrive late, don’t give up.  You can call OIT for help with tech (303-735-4357), and you can email me ( to keep me updated on your efforts (although I can’t help with the tech, probably).  For those who hit the ground running with the tech, we’ll do breakouts in zoom for groupwork and try out the blackboard feature (where I write on the screen); for those who are just getting the tech up and running, use the hour to get yourself sorted out.

And please have patience, as I may myself be working the kinks out on my end too.  I’ll make sure to put resources up on the web for anyone who needs to catch up.

Dr. Stange

For Wednesday, March 11th, 2020

For Wednesday:

  • Please read my most recent coronavirus update concerning the course and moving to online learning.  In particular, no quiz tomorrow.
  • Please install and test Zoom to make sure it is working for you.  Please also click on the “Zoom” tab above.  You’ll find a link to a google calendar, available to CU Boulder logins, which has the zoom join links.
  • Please consider trying out the office hour zoom tomorrow just as a test, which would be a help to me and you.  You can just log in and say hi if you don’t have any questions.
  • Please work further through the worksheet from today, for which I also provided solutions.  Try the problems, and if/when you get stuck, check the solutions for ideas and keep going. Here are solutions to the first two problems, and then a longer solutions/study-sheet/hints-sheet to accompany it so you can work at home.

Coronavirus Updates

Dear class,

We all have loved ones who are in higher risk groups for coronavirus; I’ve spoken to some of you about your close contacts with those for whom this disease is potentially quite dangerous.  I also believe the move to online is inevitable, sooner or later.  For these reasons, I have decided to move as quickly as I can toward online-only teaching.

Please be aware of several changes in light of coronavirus:

  1. Office hours will be online only, effective immediately.   I will use Zoom for office hours.  This will give me an opportunity to test it out.  Check out the “Zoom” tab to the website where you can go for instructions.  Please also note the timing will be unpredictable for a while; please consult the calendar you’ll find under the Zoom tab.
  2. Please do not attend class if you are ill, even with a mild cold. You do not need a doctor’s note, although I appreciate an email, just so I’m in the loop.
  3. Effective immediately, there will be no more in-class quizzes or in-class homework checks.  I will roll out alternatives shortly.
  4. Please install and test Zoom at the first available opportunity, and contact OIT if you need help getting this capability up and running.  This is where we will eventually meet virtually.
  5. If we begin meeting virtually, it will be during the same hours as regular class.
  6. If I switch to online meeting, I will email you all individually and update this website to let you know.  Please check this website for up-to-date information.

Please stay healthy and safe.

Dr. Stange