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.
Welcome to Math 2001, Section 5, Spring 2020.
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 5 pm.