For Monday:

- Quizzes: I somehow completely forgot to give the badges quiz on Friday, for which I apologize (I really try to avoid surprises). We will take it on Monday instead. That will also push the proof quiz back to Wednesday next week.
- Today we did a warmup direct proof and I left you with two proofs to write at home:
- Let a,b,c be integers. Then .
- If a,b,c are integers such that a|b and a|c then a|(b+c) and a|(b-c).

- In class we used the fact that the equation xy=1 has only two solutions in the integers, namely x=y=1 and x=y=-1. Can you prove this? Try contradiction!
- Review the proofs by contradiction from class and also the first Proposition in Chapter 6 of Hammack (first page of the chapter), which is an example. Pay careful attention to the negation of the theorem, i.e. the supposition you make for contradiction.
- With your remaining time, try a few at home: Chapter 6 exercises 1,2,6,7,8,9 as time allows.

For Friday, January 29, 2020:

- Complete the worksheet we did today if you didn’t finish it in class. The circled letters spell a message (read from bottom to top) as a way to check your work. If you don’t have a copy, you can always find handouts under “Lectures”.
- Grades: Quiz grades should stay basically up-to-date in canvas, so please log in regularly to check that there are no administrative errors! Please keep your quizzes until the end of semester, for reference.
- Friday we will have a badges quiz! It will cover Sets I, III and IV. A little advice: choose one to focus on in your studying, and earn that one for sure, then move on to the next. Don’t spread yourself too thin and only do a halfway job on all of them. Better to do fewer problems well.
- Reading: Hammack 1.4 on powersets, and exercises as needed.
- Study for the badges quiz.

For Wednesday’s class:

- Look over your returned quizzes so far (proof and badges) and make sure you understand the scoring and can complete the problems correctly. If you have any questions, email me or see me during office hour! I’m happy to help.
- Active reading (it’s always active!): Hammack, Section 1.2 on Cartesian products.
- Finish the Worksheet on Cartesian products we did in class (you can always find worksheets on the Lectures page), at least to the end of the first page. Consider the open-ended problems on the second page, as far as your brain takes them, but I won’t check those for completeness. We’ll take up the worksheet in class on Wednesday.
- Do exercises from Hammack, Section 1.2 for what time remains.
- Note: There’s a math club talk on Wednesday! (
**Speaker:** Elizabeth (Boo) Grulke (CU Boulder); **Title:** A MIXED-METHOD STUDY OF ONLINE DISCUSSIONS IN MATHEMATICS; **Time:** Wednesday, January 29 at 5-6pm; **Place:** Math 350)

For Monday’s class:

- Please read Section 1.3 and do as many Exercises as there’s time for (all are good ones). If anything refers to a Cartesian product (e.g. Exercises Part C), feel free to read ahead Section 1.2 for explanation, or wait until we cover that later.
- Monday there ought to be a proofs quiz (according to the schedule) but with the holiday we have had very little time for more work on proofs, so we will skip the proofs quiz for the week of Jan 27th.

For Friday’s class:

- Read Hammack, Chapter 1, to the end of Section 1.1. This is sets and set builder notation. In class Friday we will talk about set builder notation and get some practice.
**In class Friday, we’ll have our first badges quiz!** Remember, each quiz is just one opportunity to demonstrate knowledge of a badge. But there will be later chances for the same grade. So there’s no harm in trying early and often. This will have an opportunity to test Sets I and III badges (see “Grading” in the menu above for a list of badges). This will give you an opportunity to see what badges quizzes are all about.
- As preparation for Friday, I suggest all the exercises from Hammack, Section 1.1, including especially sections A and B, but why not also do C? (You’ll find the definition of “cardinality” in the reading.) Do as many from each section as you need, meaning: as long as you are learning something from doing them. Section D is great too, if not now, then later.
- I have set office hours (now listed in “About” above), but I’d like you to know that if you can’t make those hours, you should email me and I’ll make a “floating office hour.” This happens whenever someone wants more time than the scheduled hours, and I announce the agreed-upon time to the whole class (unless it is for a personal matter such as grades), so that everyone can benefit from the extra hour. (So I have 2 fixed hours + 1 or more floating.)

For Wednesday’s class:

- I hope you all have a great long weekend!
**We will have a proof quiz in class. ** I will allocate 15 minutes at the end of class, and the proof will be of the style of the following exercises from the book: Chapter 4, Exercises 1-11. Here is my grading rubric.
- Office hours have now been set, and they are:
**Tuesday 1-2 pm and Wednesday 11am-noon**. If these don’t work for you, just drop me an email and we’ll find a time.
- Reading: Finish reading Section 4.3.
- Please take note of 3-6 places during your reading where you read actively, and explain what you did (a sentence suffices).
- Please use the rest of your hour to prepare for the quiz and work on problems.

To do for Friday’s class:

- Catch up on the last daily post if you missed the first day.
- Read the book’s section on Direct Proof (Section 4.3), up to the end of where they explain the proof that “if x is odd then x^2 is odd”. That is, pages 118-120 in the newest edition.
- Following the guidelines and examples from the last lecture (the handout can be found, as always, under Lectures), and from your reading, write a proof of the statement “The sum of two even integers is even.”
- Read the book’s Section 4.2 on Definitions.
- As time permits, do exercises from Chapter 4. I suggest exercises 2-5.
- Note: Proof Quizzes will occur on Mondays and Badges Quizzes on Fridays, starting the second week. That means Monday you’ll have a quiz writing this type of proof.

For our Wednesday class, please do the following (the list looks long but many tasks are quick):

- Read all of the pages listed in the
**top bar of this website**: about, goals, lectures, resources, syllabus, 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: after each lecture, any handouts will appear under “Lectures”.
- 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 5 pm after each lecture and I expect that you are aware of these. Set aside **one hour** between every lecture for this; if the tasks are running longer than that, finish them at a convenient time for you.
- 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**. I will take attendance for the first several weeks.
- Please read Chapter 4, intro and Section 4.1, two pages of the textbook, Hammack. Read also the first half-page of section 2.3, which describes conditional statements.
- In that first example of section 2.3, the theorem is “If a is a multiple of 6, then a is divisible by 2.” Do the following (write your work down, as always):
- What is the
**hypothesis**? (the *if* part, i.e. the P of “if P then Q”)
- What is the
**conclusion**? (the *then* part, i.e. the Q of “if P then Q”)
- Give an example satisfying the hypothesis and satisfying the conclusion, if possible (hint: in this case, that means giving a number
*a *satisfying certain properties). If not possible, explain why.
- Give an example which fails the hypothesis and fails the conclusion, if possible. If not possible, explain why.
- Give an example which fails the hypothesis but satisfies the conclusion, if possible. If not possible, explain why.
- Give an example which satisfies the hypothesis but fails the conclusion, if possible. If not possible, explain why.

- As a way of engaging with this reading material, please find an “if P then Q” type theorem of your choosing. Tip: try www.theoremoftheday.org. Choose one that you find interesting and understand the statement of. Do not choose from your textbook, and don’t choose something high falutin’ with words you don’t understand. The goal is to be able to understand exactly what the theorem is claiming.
- Using the theorem you found, repeat the steps of part 7 above.
- 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.
- I have an intermittent blog aimed at math majors. (It is now linked under Resources tab also). If time remains, please read the first post. You may also optionally be interested in a lecture about the Importance of Mathematics by Timothy Gowers. You can put these tasks off to later if you’re out of time before Wednesday, but come back to the blog post eventually.
- Relax and get settled into your semester.

## Professor Katherine Stange, Spring 2018