Sometime this week you’ll be meeting with your group. Looking ahead, your group should produce a PDF to submit on Canvas by 8 am Friday, and also a groupwork report (handwritten is fine) to hand in in class Friday. (Meet for approximately one hour and get as far as you can in the work, hopefully that will be enough to write the three main proofs as a team.)

No quizzes this week, since we’re just getting started.

Last Friday you were asked as a group to write a proof of the fact that the sum of two even numbers is even. Take the time now, before Wednesday, to write for yourself a nice version of this. We will do another proof in class, so this will be good preparation for seeing that.

Please read Section 1.2 of Hammack. Read actively. Make yourself a brief outline of the topics. Do as many of the exercises as are needed for you to feel comfortable.

If you are just joining the class, please look at the handouts on the Resources page for an update on what we’ve done, and also read the previous daily posts (left navigation bar) and go through the daily checklists there. The first day we did a general warmup activity about polyhedra. On the second day we did a first proof (see the associated handout).

Both days we worked in (the same) groups and shared contact info. Make sure you are part of a study group and have arranged one hour to meet your group outside class before Friday. The groupwork assignment can be found on the Resources page. If you are having insurmountable troubles meeting, consider skyping in. If that really won’t work, or if you don’t have a group, please email me (kstange@math.colorado.edu). Group homework is due Friday at 8 am.

Reminder: please contact me ASAP if you have an ADA accommodation, or if you’d like to discuss how I address you, concerns about religious accommodations, etc.

Please read Chapter 1 of Hammack, up to the end of Section 1.1 (i.e. pages 3-7). This introduces the notion of a set. Please read actively. One thing this means is that whenever you come across an assertion, you try to create your own novel examples and non-examples. Every example you should work through yourself (e.g. for Example 1.1, cover the right side of the equation and guess what is there, then compare). Three pages of active reading can take a long time!

Make a summary sheet giving the “cliff notes” version of the reading. This doesn’t need to be detailed; an outline of the big points is the goal.

Do as many exercises for Section 1.1 as you feel is appropriate. If you are finding the reading difficult, then focus on reading for now, or just one topic for now. If you felt you understand the reading, then do all the odd numbered problems (answers in the back), to make sure. Some of them may trip you up!

Note: this assignment, done right, is a challenge to everyone, but for everyone it is a challenge in different ways. There’s always more to understand. (If you really feel everything is easy, and you got all the exercises in an instant, then challenge yourself by inventing interesting questions, corner cases, and trickier problems, or read section 1.10, or ponder how sets could be used to define the integers, or define the real numbers.) Put in an hour of solid effort and get where you get.

For our Friday class, please do the following (mostly easy tasks this time!):

Read all of the pages listed in the top bar of this website: about, goals, syllabus, resources, grading, fun. This is all the info about how the course will run. I expect you to know it without covering it all explicitly in class. Pro tip: all my handouts will all be found on the Resources page.

Understand that this course is unusual in that:

It is run very interactively, with lots of active learning. I expect you to create a supportive environment in all your interactions.

I expect you to check this website and do work for the course between every lecture. I will post announcements and tasks etc. by 1 pm after each lecture and I expect that you are aware of these.

I expect you to meet with a study group once per week outside class and present your solutions on Fridays

We will use a non-standard grading system.

If you have any ADA Accommodations, or other concerns about the above, please talk to me as soon as possible.

Please make sure you have a copy of the text. It is available for free in PDF form (linked also on the left nav bar) or cheaply in paper form at the bookstore.

Please plan to attend class faithfully unless you are contagious or ill etc (see my note about flu on the About page). If you are waitlisted, a spotless attendance record will give you priority as room opens up (and those who do not attend will be administratively dropped). About waitlists: I am not allowed to enroll over the fire limit of the room. Although in past everyone who faithfully attended was able to take the class, I cannot promise.

Please read Chapter 4, intro and Section 4.1, i.e. pages 87-88 of the textbook, Hammack. Read also the bottom half of page 41 (start of section 2.3).

As a way of engaging with this reading material, please find an “if P then Q” type theorem of your choosing. Tip: try googling “awesome theorems” or surfing wikipedia. Choose one that you find interesting and understand the statement of (not from your textbook, and don’t choose something high falutin’ with words you don’t understand). The P is called the hypothesis, and the Q is called the conclusion.

Using the theorem you found, (a) identify the hypothesis and the conclusion; (b) give an example which satisfies the hypothesis and conclusion if possible; (c) give an example which fails the hypothesis and conclusion if possible; (d) give an example which fails the hypothesis and satisfies the conclusion if possible; (e) give an example which satisfies the hypothesis and fails the conclusion, if possible. (Hint: in the example “R” of page 41, the integer 12 is an example which satisfies both hypothesis and conclusion, while 3 fails both the hypothesis and conclusion. The integer 2 fails the hypothesis but satisfies the conclusion.) Bring your work to class. A reminder: I will spot check these tasks for completeness and/or use them in class, but will not generally collect and grade. Make your best effort, but if you can’t complete a task, show me your attempts.

Relax and get settled into your semester. On Friday we will do a first proof.

I am teaching two sections, and your online environment will be combined. I look forward to meeting you all in person, and having a productive and fun semester exploring mathematics. Meanwhile, please look around the website.

Between each lecture this website will have a post describing your tasks before the next lecture. I will post this after class MWF by 1 pm.